Conditional Random Field) DEM (Digital Elevation Models) DSM (Digital Surface Models) DTM (Digital Terrian Models) ERS (Entropy Rate Superpixel) GCP (Ground Control Point) GDAL (Geospatial Data Abstraction Library) GIS (Geographic Information System) IPM (Inverse procedural modeling) LiDAR (Light Detection and Ranging) LOD (Levels of Detail) LSD (Line Segment Detector) MRF (Markov Random Field) MVS (Multi-view Stereo) RPC (Rational Polynomial Coefficients) SEEDS (Superpixels Extracted via Energy-Driven Sampling) SGM (Semi-global Matching) SLIC (Simple Linear Iterative Clustering) VHR (Very High Resolution

Keywords:

eutomti ity modeling from stellite imgery is one of the iggest hllenges in urn reonstrutionF he ultimte gol is to produe ompt nd urte Qh ity models tht ene(t mny pplition (elds suh s urn plnningD teleomE munitions nd disster mngementF gompred to eril quisitionD stellite imgery provides ppeling dvntges suh s low quisition ostD worldwide ovE erge nd high olletion frequenyF roweverD stellite ontext lso imposes set of tehnil onstrints s lower pixel resolution nd wider tht hllenge Qh ity reonstrutionF sn this hh thesisD we present set of methodologil tools for generting omE ptD semntillyEwre nd geometrilly urte Qh ity models from stereo pirs of stellite imgesF he proposed pipeline relies on two key ingredientsF pirstD geometry nd semntis re retrieved simultneously providing roust hndling of olusion res nd low imge qulityF eondD it opertes t the sle of geometri tomi regions whih llows the shpe of urn ojets to e well preservedD with gin in slility nd e0ienyF smges re (rst deomposed into onvex polygons tht pture geometri detils vi oronoi digrmF emnti lssesD elevtionsD nd Qh geometri shpes re then retrieved in joint lssi(tion nd reonstrution proess operting on polyE gonsF ixperimentl results on vrious ities round the world show the roustnessD slility nd e0ieny of our proposed pprohF

Acknowledgments

s would like to express my sinere thnks to my reviewers X rofessor plorene upin nd rofessor rzemyslw wusilski for reding my thesis nd giving inE sightful ommentsF s thnk the ommittee memers X rofessor wthieu hesrunD rofessor prédo hurntD wrF vionel vurore nd wrF tustin rylnd for ttending s my exminersF s would like to sinerely thnk my dvisor plorent vfrge for his wrmEherted onerns of my dpttion to ompletely new environment in prneF s truly ppreited his ptiene nd onstrutive dvie for my reserh over these pst three yers of grdute studiesF his hh experiene t the sxse opened gret new world for meF s m grteful to ll the help nd trining s reeivedF s would like to thnk ll my ollegues in itne tem X ierre elliezD uliy rlkD nnik erdiéD uimo ruD hvid fommesD ent do egoD hvid linsD wnish wnddD imon qirudotD ven yesuD tenEhominique pvreuD tenEhilippe fuhetD immnuel wggioriD nd ro pngF s enjoyed very muh disussing nd solving prolems with youF wny thnks to plorene frrD she helped me to solve ll the dministrtive prolemsF hnks for ll the ollegues in ef nd htshpe temsD we shred nie period of time exploring di'erent interesting reserh works in our after tea eventsF remendously mny thnks hve to e devoted to vuxrt qroup for funding my hh nd giving me the opportunity to further explore suh n interesting topiF st is lwys gret honor to work for vuxrt in suh n impressive reserh tmosphereF s would like to thnk vionel vuroreD tustin rylndD éronique oujde nd prédéri rstour for ll your tehnil disussions nd support ll the timeF o ll the ollegues in vuxrtD s enjoyed lot working with you nd herish ll the time we shredF s thnk my fmily who loves me unonditionllyF wy deisions re lwys fully respeted nd understoodF s m luky to hve the gretest prents nd rotherF s would like to thnk ll my friendsF ou red for everything out me nd rought me so muh fun nd plesureF Résumé v modélistion utomtique de villes à prtir d9imges stellites est l9un des priniE pux dé(s en lien ve l reonstrution urineF on ojetif est de représenter des villes en Qh de mnière su0smment ompte et préiseF ille trouve son ppliE tion dns divers dominesD qui vont de l plni(tion urine ux téléommuniE tionsD en pssnt pr l gestion des tstrophesF v9imgerie stellite o're plusieurs vntges sur l9imgerie érienne lssiqueD tels qu9un file oût d9quisitionD une ouverture mondile et une onne fréquene de pssge uEdessus des sites visitésF ille impose toutefois un ertin nomre de ontrintes tehniquesF ves méthodes existntes ne permettent que l synthèse de hw @higitl urfe wodelsAD dont l préision est prfois inégleF gette disserttion dérit une méthode entièrement utomtique pour l produE tion de modèles Qh omptsD préis et répondnt à une sémntique prtiulièreD à prtir de deux imges stellites en stéréoF gette méthode repose sur deux onepts prinipuxF h9une prtD l desription géométrique des ojets et leur ssimiltion à des tégories génériques sont e'etuées simultnémentD onférnt insi une erE tine roustesse fe ux olusions prtielles insi qu9à l file qulité des imgesF h9utre prtD l méthode opère à une éhelle géométrique très sseD e qui permet l préservtion de l forme des ojetsD ve (nlementD une plus grnde e0ité et un meilleur pssge à l9éhelleF our générer des régions élémentiresD un lgorithme de prtitionnement de l9imge en polygones onvexes est présentéF fsé sur le digrmme de oronoïD et lgorithme exhie les régulrités géométriques u sein des imgesD en lignnt es polygones le long de segments préllement détetésF snspirés pr des trvux réents sur l reonstrution de sènes en Qh à l9ide de sémntiques prtiulières insi que sur l stéréosopieD l géométrie et l lsse sémntique des ojets sont simultnément extrites des imgesD dns un proessus ommun de reonstrution et de lssi(tionF ves lsses sémntiques rdiométriquesD les élévtions et l forme géométrique des ojets sont tritées simultnément u sein de hque pire d9imgesF sl en résulte une plus grnde roustesse fe à l dégrdtion de l qulité de l9imge iii insi qu9ux ires d9olusion prtielle dns les vues stellitesF xos résultts prouvent le pssge à l roustesseD l9éhelle et l rpidité de l9pprohe proposéeF Mots clés : reonstrution QhD modélistion de villesD imgerie stelliteD sène urineD stéréosopieD prtitionnement d9imgesD lssi(tion sémntiqueD optimiE stion de ontoursD minimistion d9énergiesD vision pr ordinteurD géométrie omE puttionnelle 1 Introduction 1 he min ontriutions re summrized s followsX @A @A @A @dA @eA pigure IFUX yverviewF snput stereo imges @A re (rst deomposed into tomi onE vex polygons @A using polygonl prtitioning lgorithm @ghpter PAF sn seond step detiled in ghpter QD the semnti lss nd the elevtion of eh polygon re simultneously retrieved in the two prtitions @AF he lst step @ghpter RA onsists in unifying the two prtitions enrihed y semnti lsses nd elevtion vlues into plnimetri elevtion representtion @dA tht llows the genertion of the output Qh model @eAF @iA e fully utomti pipeline is proposed for produing ompt nd semntillyE wre ity models from stellite imgesD whih is timeEe0ientD slleD nd le to reonstrut lrge ities in few minutesF @iiA e novel lgorithm is proposed to prtition imges into onvex polygonsD operE ting t the sle of the geometri shpeD nd not diretly t the pixel sleD whih Segmentation into superpixels. wethods prtitioning imges into superpixE els re usully evluted on (ve riteriX @iA dherene to oundriesD @iiA running timeD @iiiA omptness of regionsD @ivA memory e0ieny nd @vA simpliity of useF emong the numerous lgorithms proposed in the litertureD the most populr strtegy onsists in itertively re(ning superpixels from n initil rough prtition of pixelsF hese methodsD eFgFD e + IPD vu + HWD dff pigure PFV shows the results on the four qulity riteriF feuse our regions re onvex polygons of homogeneous sizeD our lgorithm outperforms the other methods in terms of omptness y signi(nt mrginF he lgorithm lso ompetes well in terms of undersegmenttion error nd running timeF gontrry to iih nd vsgD our running time inreses in funtion of the numer of regionsF xeverthelessD s our lgorithm mnipultes geometri ojetsD it is less impted when the imge size inresesF sn dditionD our memory onsumption is very lowD even on very ig imgesF yur result on the oundry rell sores low with respet to the three other methodsF he use of lineEsegments logilly penlizes the oundry uryD in prtiulr when the numer of regions is lowF his is the prie to py to gurntee highly ompt regionsD oundry rell nd omptness eing hrd to oniliteF xeverthelessD the oundry rell of our method improves when the evlution is restrited to suset of imges for whih mnEmde strutures re dominntD s shown in pigure PFVD ottom rowF sn prtiulrD the oundry rell eomes quite lose to vsgF por suh imgesD the oundry ury is less penlized y the use of lineEsegmentsF sn terms of model prmetersD our lgorithm does not hve weight lning etween imge fithfulness nd region regulrity s in vsg or iF yn the one hndD this hrteristi redues the )exiility of our lgorithmF yn the other hndD it llows us to gurntee some geometri properties @polygonl shpeD region onvexityD unique djeny grphA ontrry to the other methodsF esults from other qulity riteriD the hievle segmenttion ury @eeA dff + IP nd the preisionErellD re presented s well for generl omprisonF he ee results on the ferkeley dtset evolve in similr wy thn the oundry rell tests s presentedF he order of mgnitude in however less importnt s our

IFI Qh ity modelingX motivtions nd hllenges F F F F F F F F F F F F F P IFP ht quisition F F F F F F F F F F F F F F F F F F F F F F F F F F F F F T IFPFI vihe dt F F F F F F F F F F F F F F F F F F F F F F F F F F F F T IFPFP eeril imgery F F F F F F F F F F F F F F F F F F F F F F F F F F V IFPFQ tellite imgery F F F F F F F F F F F F F F F F F F F F F F F F F W IFPFR hw genertion F F F F F F F F F F F F F F F F F F F F F F F F F IQ IFQ elted work F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F IR IFQFI ene lssi(tion F F F F F F F F F F F F F F F F F F F F F F F F IS IFQFP rn ojet extrtion F F F F F F F F F F F F F F F F F F F F F IU IFQFQ Qh reonstrution F F F F F F F F F F F F F F F F F F F F F F F F F PH IFR tellite ontext F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PV IFS gontriutions F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F QP 2 Polygonal partitioning 35 PFI sntrodution F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F QS PFP eview of imge prtitioning F F F F F F F F F F F F F F F F F F F F F F QV PFQ wthemtil kground F F F F F F F F F F F F F F F F F F F F F F F F RH PFR hpe detetion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F RI PFS hpe onforming oronoi prtition F F F F F F F F F F F F F F F F F F RP PFT ptil homogeniztion F F F F F F F F F F F F F F F F F F F F F F F F F F RT PFU gomprison with superpixel methods F F F F F F F F F F F F F F F F F F RU PFV gonlusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F SI 3 Joint classication 55 QFI sntrodution F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F ST QFP eview of regionEsed stereo mthing F F F F F F F F F F F F F F F F ST QFQ ilevtion ssignment to polygonl prtitions F F F F F F F F F F F F F F SV QFR toint lssi(tion nd elevtion reovery F F F F F F F F F F F F F F F TH QFS gonlusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F TQ 4 Model fusion 67 RFI sntrodution F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F TU RFP eview of ojet ontouring F F F F F F F F F F F F F F F F F F F F F F F TW RFQ pusion of enrihed prtitions F F F F F F F F F F F F F F F F F F F F F F F UH RFR gonlusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F US viii Contents 5 Experiments 77 SFI smplementtion detils F F F F F F F F F F F F F F F F F F F F F F F F F F UU SFP ulittive evlution F F F F F F F F F F F F F F F F F F F F F F F F F F UV SFQ untittive evlution F F F F F F F F F F F F F F F F F F F F F F F F F VI SFR oustness F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F VQ SFS lility F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F VU SFT erformne F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F VU SFU vimittions F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F WH 6 Conclusion 93 TFI ummry F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F WQ TFP erspetives F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F WS TFQ gonlusion @version frnçiseA F F F F F F F F F F F F F F F F F F F F F F
C 1 C 2 seline e 1 e 2 x 1 x 2 v 1 l 1 l 2 X ∞ X ∞ X image1
X V (p i ) = {x ∈ K / x -p i ≤ x -p j , ∀p j ∈ P, i = j} @PFIA he oronoi digrm
U (l) = i∈P D data (l i ) + β 1 (i,j)∈Es V smoothness (l i , l j ) + β 2 (i,j)∈Ec V coupling (l i , l j ) @QFIA
where D data is the unry dt termD nd V smoothness nd V coupling re pirwise poE tentils fvoring respetively lel smoothness nd lel oherene etween left nd right prtitionsF E s nd E c orrespond to two sets of pirs of djent polygonsF β 1 nd β 2 re prmeters weighting the three terms of the energyF Polygon adjacency. he two djeny sets E s nd E c impose sptil depenE denies etween polygonsD either within the sme polygonl prtition for the former or in etween the polygonl prtitions for the lterD s illustrted on pigure QFSF E s ontins pirs of polygons who shre ommon edge whih is not supported y one of the lineEsegments emedded into the polygonl prtitionsF es illustrted in pigure QFS @rightAD this ondition on lineEsegments is prtiulrly e0ient for stopE ping lel propgtion when meeting uilding edgesF E c is de(ned s the set of imrite polygonsD iFeFD the pirs of polygons i ∈ P l nd j ∈ P r so tht τ ij > 0F

Data term.

st mesures the oherene etween the elevtion estimte of polygon nd its proposed lelF por polygons without n elevtion estimteD the ourrene of the lel other is fvored s polygon without depth estimte is most likely to pture n element visile only in one imge suh s fde ndD to lesser extentD groundF he dt term is expressed s

D data (l i ) =      1 -e -(l i -d i ) 2 2σ(l i ) 2 if i ∈ P α • 1 {l i =other} otherwise @QFPA
where d i is the depth estimte of polygon iD 1 {•} is the hrteristi funtionD nd α is the penlty weight for not hoosing otherF hen lel other is ttriuted to polygon i ∈ P D l i is set to 0F Smoothness. he smoothness term penlizes E s Edjent polygons with di'erE ent lels using generlized otts modelX

V smoothness (l i , l j ) = w ij • 1 {l i =l j } @QFQA w ij = 1.0 -d L 2 (F rgbhistogram (i), F rgbhistogram (j)) @QFRA
where the weight w ij redues the penlty of hving di'erent lels when the rdiomE etry of pixels inside the two polygons is not similrF sn prtieD w ij is hosen s one minus the normlized histogrm distne in norm L 2 F hi'erent si fetures inluding the vergeD medin of vef olorsD of qf olorsD nd the histogrm of qf olors n e used to mesure the similrity of the rdiometryF he histogrm of qf gives the most roust performne in most of our experiments in terms of the ury of disriminting rooftops from the othersD espeilly from fdes tht hve similr textures with roofsF

Coupling. imilrly to the smoothness potentilD the oupling term is de(ned y generlized otts modelD hereD etween imrite polygonsF

V coupling (l i , l j ) = τ ij • 1 {l i =l j } @QFSA
where τ ij llows polygons with di'erent lels to e penlized proportionlly to their overlpping rtioF Optimization. en pproximtion of the glol minimum of the energy is found he intuition ehind the dt term is tht @iA n empty ell is more likely to e ground with n elevtion vlue of 0D nd @iiA on)it ell is more likely to e roof with n elevtion vlue s lose s possile to its inherited elevtionsX

E(x) = k∈C A k • E d (x k ) + λ (k,k )∈N L kk • E r (x k , x k ) @RFIA where C = C conf lict ∪ C empty D the lel x k of ell k is n elevtion vlue in Z = {0, z 1 , ...z n }D nd N is
E d (x k ) =              0 if k ∈ C empty nd x k = 0 min{|x k -z| z∈Z k } else if k ∈ C conf lict nd x k = 0 γ otherwise @RFPA
where γ is penlty for not respeting this intuitionF he pirwise potentil is generlized otts model tht dereses the penlty etween two ells when their ommon edges projeted in Qh kEprojet well into the imgesF es the pirs of ells re onsidered with di'erent elevtions x k nd x k D eh pir hs extly two ommon edges in QhX one t elevtion x k D the other t elevtion x k F he pirwise term is expressed y pigure UFTX eonstrution of rgue downtownF elthough rgue exhiits urn hrteristis similr to wdrid @pigure UFSAD its reonstrution is more hllenging s @iA the rod network @nd y extension the uilding lok lyoutA is more omplexD nd @iiA dense vegettion is more frequent nd n esily e interpreted s uildings @see the middle left re on the output Qh modelAF

E r (x k , x k ) = min(G l (x k ) + G l (x k ), G r (x k ) + G r (x k )) • 1 {x k =x k } @RFQA where G l (x k ) @respetively G r (x k )A is

  photogrmmetry pplitions rirHVD yqfIID gIQD hpISD qrISF roweverD the physil sensor models n vry signi(ntly ross di'erent stellitesF sully di'erent models will e pplied for the lirtion of reltive stellites in indusE tril prodution hinsF hpIS proposes generlized sensor models to overome this limittion of spei(ity nd to hieve generliztion ross stellitesF por exE hustive disussion out lirtion nd selfElirtionD we refer the reders to rWUD rHRD wqHWF

  image2 pigure IFRX ipipolr geometry in nutshellX points x 1 nd x 2 re orresponding projetions of the Qd point XF sn image1 the point x 1 lies on the epipolr line l 1 F he epipoles e 1 nd e 2 indite the positions where C 1 nd C 2 projet respetivelyF he point v 1 in image1 is the vnishing point of the projeting ry of x 2 F smge in ourtesy of we + IQF the miguity of rdiometryD mke the omputtion of preise depth informtion di0ultF sn dditionD tmospheri nd loud intertions sometimes in)uene the qulity of stellite imgery s wellF 1.2.4 DSM generation por imgery dtD dense mthing is n importnt tehnique to generte hwsF Qh shpes re estimted through two or more perspetive views of the sme seneF hense mthing from two viewsD suh s stereo pir of stellite imgesD usully requires geometri reti(tion of the imges to (t the epipolr geometryF hen the remining prolem is to (nd the orresponding point in the other imgeF qlol pprohes like uHID fHI y grph utD nd HQ y elief propgtionD re quite memory intensive nd not e0ient enough for lrgeEsle ity modeling from stellite imgesF yn the other hndD lol methods re mostly sed on orreltion whih n e implemented e0ientlyF roweverD these methods ssume onstnt disprity inside orreltion windowD nd use lurred ojet oundriesF o overome these prolemsD rirshmuller proposes semiEglol wy to otin oth ury nd e0ieny nmed qw rirHVF he qw performs e0ient nd E urte stereo mthing nd is roust to reording or illumintion vritionsF he proess is sed on rdiometri roust mthing ost nd n optimiztion with glol smoothness onstrintF st pproximtes glol ost y pieeEwise mthE ing sed on the epipolr geometry nd glol smoothness onstrintF st n e performed in liner time to the numer of pixels nd disprities nd is lmost s urte s glol methodsF hue to the high ury nd e0ienyD the qw is vlule for reting models of lrgeEsle urn senesF por dense mthing from more thn two viewsD for instne eril photogrmE metryD golWT (rst proposed plane-sweeping proess to determine the Ph feture orrespondenes nd the Qh positions of feture points in the seneF st works for true multiEimge mthing with n ritrry numer of imges nD in liner lE gorithmi omplexity with nF por stereo mthing from pushroom imgesD he prnhis demonstrtes stereo pipeline to produe digitl elevtion mps utomtE illy from léides stellite imges provides y gxi @the prenh pe egenyA hpISF yn the other hndD to hndle the lrge mssive eril imgesD mny methE ods re proposed to improve the e0ienyD suh s pIHD ervISD qvIT sed on pthEsed multiEview stereo @wAD rirHVD prIPD rg + IT sed on the qwF purthermoreD g + IT proposes n lgorithm sed on optil )ow (eldD whih hieves good mthing e0ieny nd )exiility for omplex terrin surfe mthingF opulr dense mthing lgorithms suh s w pIHD wiw hHTD semiEglolElokEmthing @qfwA stsISD i prIP nd PC. De FranchisD re pulily ville for demi reserhesF 1.3 Related work he relted work of Qh ity modeling minly involve prolems in tegories ofX sene lssi(tionD urn ojet extrtionD nd Qh reonstrution pprohesF pigure IFSX hense mthing from stellite imgeryF prom the left to the right re respetively the twoEview imges of the stereo pir in epipolr geometry over rgueD nd the disprity mp omputed y the qw @thnks to hrF reiko rirshmüllerAF

  nd fes while keeping lose to the input meshF frief reviews of mesh genertion methods nd mesh simpli(tion pprohes re given s followsF •Generation of dense meshes he input mesh for mesh simpli(tions is usuE lly generted from set of points otined from w tehniques or vihe snE ningF w genertes dense point louds from eh pixel in imges @wFrFtF sprse point louds from mthing feture points in fwAF es typil tehnique in wD fw extrts slient fetures from eh registered imgesD nd pplies lustering within feture speF Ph trks re onstruted y mthing these feture points etween imgesD from whih the position of mers re utomtilly reovered y solving the fw model rHRF fw provides networks of registered imgesD their mer propertiesD nd sprse point loudF ine w is sensitive to reprojetion errorsD undle djustment is often requiredF por detiled overviewD we refer the reder to HPD gh + HT for twoEview stereo methods nd multiview stereo methE ods respetivelyF ith the developments of tehniques suh s mer lirtion nd dense mthingD w produes high qulity point loudsF gompred with viE heD it still often su'ers from severe noise nd null dt holes vufIHF sn terms of dt density nd uryD vihe is powerful dt soure for mesh simpli(tion methodsF •Simplication approaches. prom the input dtD polygonl models re (rst generted diretly y rsteriztion or heluny ringultionD then simpli(ed with generl mesh simpli(tion lgorithmsD usully involving edge ollpse nd vertex relotion y minimizing severl error metris qrWUD vWWF he ury meE surement is otined with two error metrisX the eurte wesure of udrti irror @ewiA nd the ymmetri wesure of udrti irror @wiAF he mesh simpli(tion step signi(ntly redues the numer of tringles while preserving low (tting error xIHD veISF en errorEdriven pproh is presented y gehHRD whih pplies vritionl geometri prtitioning to pproximte the mesh with set of shpe proxiesF xIH proposes PFSh dul ontouring methodD using n dpE tive grid dt struture to reonstrut the geometry in eh grid y minimizing udrti irror wesureF his method produes PFSh ity models with geometry nd topology reted respetively y disovering glol regulritiesF wesh deiE mtion is powerful solution for mesh simpli(tionF st provides n pproh to greedily luster geometri elementsD reting prtition of the originl input meshF veIS explores the deimtion of tringle surfe meshes y deteting set of plnr shpe proxies nd struturing them vi n djeny grphF he (delity is gurnteed y the plnr proxiesD suh tht the simpli(tion pproh is roust to defetElden meshesF sn vufIHD the proposed hierrhil method strts from n QhEsurfe mesh otined y wD nd then inserts set of deteted primitives into the surfeF st omines the meshEsed surfe @desries detilsA nd Qh primE itives @desries regulr shpesAD hene it hieves high ompression rtio while keeping detilsF hue to the sttistis nlysis in primitive extrtionD this strtegy llows the introdution of semnti knowledgeD the simpli(tion of the modelingD nd orretion of registrtion errorsF Volumetric Modeling olumetri modeling is dtEdriven pproh nd hs een proved to e roust wy of generting rkEfree models vgVUD gvWTD tvHPD pfqHSF olumetri pprohes prtition the sene into elements suh s ui voxels gHUD qhheIQD tetrhedrs tIID vuIP or polyhedrl ells gvIHF hese elements re lssi(ed s inside or outsideF olumetri methods re known to produe nonEsmooth surfes with wtertight hrteristis vuHUF roweverD due to the voxelEsed mehnismD these methods generlly su'er from poor slility tIID ut see few pplitions to lrgeEsle urn reonstrution from eril imges gvIHD qhheIQF gvWT employs wrhing gues method vgVUD nd integrtes lrge numer of rnge imges to produe semlessD highE detil tringle mesh modelsF eentlyD ru + IPD ruhfIQ propose wy to pply the insideGoutside resoning s new input from fw nd lolly updte the tetrE hedrliztionF en updted mesh is (nlly otined onEtheE)yF pfqHS develops modeling method omining eril nd groundEsed viheD sed on the dul ontouring method tvHP whih retes one mesh vertex in eh miniml grid node y optimizing qudrti error funtion nd polygons re onstruted y trversl over the dptive gridF yn vergeD volumetri representtions ontin oth inside nd outside informtionD whih is n dvntge ut lso limittion sine it is di0ult to modelD time onsuming nd ostly in terms of storge speD ompred to mesh surfesF Primitive based. rimitiveEsed modeling methods re mostly sed on the deE tetion of prede(ned roof shpesD eFgFD plnr shpes urHTD w + HVD HWD xHWD vg + IID given userEde(ned primitives rxpHQD vhhHVD fufHVD xHVF hese methods work well for the reonstrution of uildings omposed of preEde(ned shpesD while lose ury when deling with ritrry roof struturesF epprohes of utomti pipelines urHTD w + HVD xHVD HWD xHWD xIPD introdue segmenttion module seprting points into ground nd individul uilding pthesF egettion nd noise re removed in dvne through lssi(tion proessF hen mesh models re onstruted y modeling lgorithms over these pthesD nd (nl uildings re reonstruted through di'erent heuristis sed on the extrtion of plnr shpesF he topology etween plnr roof pthes n e extrted y grphEsed method urHTD nd roof ontours n e regulrized y estimting uilding orienttions w + HVF ith the segmented regions from lssi(tion proessD lightweight nd wtertight polygonl models re reted y simplifying oundries of (tted plnes HWF oof oundries re ligned y lerning set of prinipl diretions xHVD whih is further extended to ity sle dt in xHWF vhhHV serhes for the optiml omintion of prmetri models using twgwg smpler qreWSF purthermoreD vg + II pplies exeg to detet primitives nd uses glol mutul reltions etween these primitives to generte syntheti modelsF por intertive pplitionsD rxpHQ shows the reonstrution of omplex uilding roofs nd irregulr shpes y re(ning the primitives with user intertionF sn generlD primitiveEsed methods produe resonle strutures tht follow the userEde(ned primitive lirriesD ut re limited when hndling ritrry shpesF Superpixel based. ome Qh modeling pprohes re sed on tomi regions @superpixelsAF por exmple in xp + HVD it presents relEtime plneEsweep stereo on the qD using the orienttions nd plne priors deteted from fw point loudsF purtherD wuIH ggregtes the superpixels of surfe dt nd extends the plne sweeping to hndle textureless regionsF pgHW presents n e0ient modeling wy y simplifying the deteted plnes over wrkov ndom pieldD to generte pieewise plnr wnhttnEworld geometryF e semnti nlysis is performed in fqIR sed on superpixelsF his strtegy is further explored y omining with imge edges to perform perEview dense depth optimiztion fqISD nd produes meshes with ompetitive surfe qulity e0ientlyF sn summryD superpixelEsed modeling methods usully o'er high slilityD timeEe0ienyD nd pility to integrte semntis nd geometryF Joint reconstruction. eonstrution of urn ojets nd senes hs een deeply explored in visionD with request towrds full utomtionD qulity nd slE ilityD nd roustness to quisition onstrints we + IQF eentlyD mny joint methods re proposed to omine di'erent informtions nd tke n dvntge of their impliit reltionsF hus these di'erent lues mutully ene(t from eh other through n glol optimiztion shemeD improving the reonstrution qulityF wost of joint reonstrution methods either simultneously explore semntis nd geomE etryD or integrte multiple dt quisitions s input souresF •Semantically-aware approaches. sn the urn reonstrution dominD geomE etry nd semntis re losely reltedF he most trditionl strtegy onsists in reE trieving semntis efore geometryF sn mny ity modeling methods vwIID veISD the input dt is (rst segmented into di'erent lsses so tht the susequent Qh reonstrution n e dpted to the nture of urn ojetsF eent works rg + IQD vq + IQD gpIS demonstrte tht the simultneous extrtion of geE ometry nd semntisD lso known s semnti Qh reonstrutionD outlsses mulE tiple step strtegies in terms of output qulityF fsed on gonditionl ndom pield @gpA vwHI formultionD v + IP introdues lerning sed method to jointly optimize the semnti lssi(tion nd the disprity ssignmentF imilrlyD fu + II develops joint optimiztion for ojet lss segmenttion nd depth estimtion over gpD ut in n unsupervised wy with onstrints of Ph onsisE teny nd Qh geometry preservtionF roweverD these works typilly su'er from low slility nd often produe Qh models without struturl onsidertionF eE mnti Qh reonstrution remins hllenge t the sle of stellite imgesF sn dditionD to further integrte more semntisD fqIS reonstruts the surfe sed on imge edgesD superpixels nd seondEorder smoothness onstrintsF he geometry nd topology re preserved y ooperting imge disontinuities nd Ph shpe nlysisF he mesh is simpli(ed in strtegy of point lustering nd region segmenttionD whih is omprle to lssil w reonstrutionF •Multiple data sources. hi'erent dt quisitions present spei( ttriutes nd dvntgesF gity reonstrution methods integrte multiple dt souresD suh s eril dtD ground dtD nd depth mpsD to gin more perspetive informtion nd more lues from oth Ph nd Qh spesF e method presented in peHS retes uilding models with fde y integrting two quisitions of irorne vihe nd terrestril viheF rHT similrly omines eril imges nd ground imges to hieve more detiled reonstrutionF fufHV integrtes Qh line segments nd glol optimiztion of dense mthing tehnique to otin glolly optiml level of detils of depth informtion nd presents fully utomti reonstrution from eril imgeryF fsed on the footprints of uildings extrted from optil imgesD e informtion is integrted for the uilding presene vlidtion nd the height retrievl in hHWF wethods in this group employ more informtion nd lues to reonstrut Qh urn senes with higher ury nd level of detilsD while inresing the omplexity nd produing ost of the systemF Conclusion. sn summryD mny pprohes hve een explored for Qh modeling of ity senesF pew of themD howeverD re slle nd dptive to lrgeEsle urn sene reonstrution from stellite imgeryF row to hndle the omplex ontexts found in stellite imgery in order to e0iently nd urtely reonstrut semnti ojets is still hllenge in the Qh modeling (ledF 1.4 Satellite context tellite imgery imposes set of tehnil onstrints with respet to trditionleril imgeryD in prtiulr @iA lower sptil resolutionD typilly ≥ 0.5 meterD @iiA lower signlEtoEnoiseErtio @xA impting the imge qulityD nd @iiiA wider seline to gurntee resonle depth uryF elthough these onstrints hve low impt on some pplitions suh s hnge detetion qrIS or genertion of dense hws hpISD they hllenge the utomti extrtion of semntis nd the reonstrution of semntillyEwre ity modelsF Characteristics.tellite imges over urn senes pture the ity optil pperne from speF sullyD Qh informtion from stellite imgery is derived from overlpping stereo pirsF sn order to preserve resonle height preisionD the seline of the stereo pir is neessrily long so tht the rGf rtio @heightGselineA is reltively smll qpwHVF roweverD long seline rings huge di'erenes in terms of perspetivesD whih introdues ovious olusions from ojetsF ispeilly in modern downtown resD lower uildings lose to skysrpers my e severely oludedF pdes of the sme uildings my e visile in one imgeD ut ompletely missing in the other oneF por uildings with nonE)t roof strutures @eFgFD domeD gmrelD rhomiD onilD spire etFAD imges from two perspetives re insu0ient to reover omplete Qh informtion sine they re prtillyEselfEoludedF rn ontents suh s uildingsD rods nd vegettion re disseminted in the entire sene withGwithout orrespondene from eh otherF rtiulrlyD uildings re onstruted with diverse rhiteturl struturesD surrounded y vrious undeE sired ojetsF he pperne of roofs my di'er signi(ntly due to temporry ojets on topF egettion n e prolemti for uilding reonstrution sine it introdues miguities on disontinuities nd onfusion with uildingsF mll uildings my e oluded or even emedded inside dense vegettionF hue to the limited sptil resolution of stellite imgeryD it is di0ult to preisely reover smll uildings or smll detils of nonE)t roofs for lk of informtionD not to mention noise or interfering surroundingsF e typil stellite ontext is shown in pigure IFTF Challenges. tellite imgery is interesting for Qh ity modeling for its high quisition )exiilityD lrge re overgeD nd reltively low ostD while imposes severl tehnil hllenges with respet to trditionl eril quisitionsF • Image quality constraints. yptil stellite imges re tken from mer mounted on stelliteF etmospheri onditions nd loud over in)uene the visE iility of the irth9s surfeF pei( wether onditions suh s fog nd louds pper ommonlyD whih usully use wek ontrst in imgesF edditionllyD rE tifts used y perturtions of the signl from sensor sturtion or eGh @nE logGdigitlA onversionD ring spekleEstripes or rti(il struturesF hepending on the type of sensor usedD the sensor noise n e modeled s either dditiveD multiE plitive @spekleA or impulsive @slt ndEpepperA qHVF purthermoreD to reover the Qh informtion from Ph projetions more thn one imge is requiredF tereo imges re rrely ptured t the sme momentD whih rings miguities of the rdiometri informtion of the seneD prtiulrly from temporry ojetsF• Depth calculation challenges. emoteEsensing dt need n essentil preE proessing for geometri orretions due to vrying quisition nd trnsmission onditionsF fsed on the g modelsD imges re lirted to stisfy the epipoE pigure IFTX tellite ontextF op rowX wide seline is neessity to reh resonle depth uryD ut rings severe olusion prolemsF e fde side is typilly visile only in one imge @see loseEupsAF xote lso the high proportion of shdow nd the timeEvrying ojets s rsF fottom rowX dense residentil res ring hllenges to preisely reonstrut eh individul uilding from the nonE negligile lol vritions in elevtion @inset shows where houses in n prnisoD D re uilt on highErelief terrinAF lr geometry with ids from set of qround gontrol oints @qgsAF rowever the preision of lirtion signi(ntly impts the dense mthing lultionF he tolerne of geometri error is usully required to e less thn I pixelF yn the other hndD the long seline mkes it sometimes impossile to ompute the depth of eh pixel due to olusionsF por exmpleD the qw serhes for the mthing pixel long the reltive epipolr line in the other imgeD whih works well for ojet oundries nd disontinuities ut not for oluding prtsD repetitive ptterns nd textureless regionsF enother di0ulty is the mthing preision over slopes or domes whose depth mp hnges ontinuously nd rpidlyF es onsequeneD disprity mps quired from lrge seline stellite imges re usully sprse nd noisyF• Automatic 3D city reconstruction challenges. eeril quisitions with viE he snning or multiEview imgery onstitute the est wy so fr to utomtilly rete Qh models on lrgeEsle urn senes we + IQF feuse of high quisiE tion osts nd uthoriztion onstrintsD eril quisitions reD howeverD restrited to some spotlighted ities in the worldF sn prtiulrD qeogrphi snformtion ysE tem @qsA ompnies propose tlogs with typilly few hundred ities in the worldF tellite imgery exhiits higher potentil with lower ostsD worldwide ovE erge nd high quisition frequenyF tellitesD howeverD hve severl tehnil restritions tht prevent qs prtitioners from produing ompt ity models in n utomti wy gIQF vrgeEsle ity reonstrution from stellite imgery is prtiulrly hllenging due to lking imge qulity nd resolutionF he sptil resolution of high qulity stellite imgery is limited y the given sensorD whih vries from pproximtely HFQIm to IFSmF por instneD in stellite imge with HFSm resolutionD 10m × 10m roof re)ets 20 × 20 pixelsD whih is usully not su0ient for pplitions tht require high ury in detilF wost methodologil pprohes usully sepE rte the utomti ity reonstrution from stellite imgery into severl hierrhiE l tsksX imge lssi(tion gIID wgeITD wgeITD semnti extrtion gu + IRD wgeITD

  of regions re expeted to hve strong geometri onstrintsF sn stereo mthing for instneD gurnteeing onvexity of regions mke the mthing proedure more roust thn the susequent extrtion of their onvex hull fqIRF elsoD in presE ene of mnEmde ojets nd urn environments fpIPD ghrhIQD preferring regions with stright line oundries is nturl hoie whih n e preious soure of geometri knowledge for susequent proessing stepsF pew existing works hve ddressed the prolem of the geometri prtitioning of imgesF sntegrting suh geometri knowledge fter superpixel deomposition is omplex nd delite tskF snonsistenies within the grph of region djeny re frequent nd led to struturl inoherenes in susequent proessingF elsoD modifying the region shpes typilly destroys the e'ort done to mke superpixels dherent to the imgeF sdellyD oth geometry nd rdiometry must e jointly exploited to generte the regionsF sn this hpterD novel prtitioning method is proposed for deomposing imges into tomi regions with onvex polygonsD while imposing geometri gurntees on the shpe nd onnetion of these regionsF pigure PFI illustrtes our golF he proposed solution onsists of prtitioning imges into onneted onvex polygons using oronoi digrms for whih rief introdution is given in etion PFQF egion onvexity hs mny dvntgesD in prtiulr for @iA simplifying suE sequent geometri opertions s the omputtion of region distnesD @iiA fvoring the region omptnessD nd @iiiA insuring unique djeny grph etween reE gionsD without miguitiesF sn our pprohD geometri properties re gurnteed y onstrution of the oronoi digrm wheres rdiometry is exploited to @iA lign edges seprting two neighoring polygons with imge disontinuitiesD nd @iiA enE ter the polygons in homogeneous resF gontrry to interest point sedEstrtegies uyIHD gpvIQD imge disontinuities re pproximted through the detetion of geometri shpesD iFeFD lineEsegments similrly to gpIRD p + IPF he proposed lgorithm tkes n imge s input nd produesD s outputD prtition into polygons de(ned into the ontinuous ounded domin supporting the pigure PFIX qol of polygonl prtitioningF yur lgorithm prtitions imges into regulr onvex polygonsF hree di'erent polygon sizes re displyedF he use of )oting polygons llow for the preservtion of ojet oundries t supixeli sle @loseEupAF imgeF e model prmeter ε hs to e spei(ed to (x the prtition sleY onretely ε orresponds to the verge rdius of regionD ssuming the region pprohes rounded shpeF he min ontriutions re summrized s followsX ! Shape anchoring. e strtegy to preserve geometri shpes within the oronoi prtitions is proposedF he key ide relies on the insertion of pirs of oronoi seedsD lled anchorsD lose enough to eh other to onstrin the oronoi edges to e prt of geometri shpeF feyond preservtionD the onnexion of the geometri shpes re lso struturedD in prtiulr for enhning shpe juntionsF ! Geometric guarantees. he output provides some geometri gurntees relted to the shpe nd djeny of the tomi regionsF pirstD eh region is onvex polygon with low numer of edgesF gontrry to mny superpixel methodsD the djeny of regions is lso gurnteed to e unique y onstrutionD two polygons eing neighors if they shre ommon edgeF pinllyD region oundries re polygons with ext geometryD iFeFD under the pixel sleF ! Eciency. fy mnipulting geometri entitiesD the pixelEsed informtion is simpli(ed nd the lgorithmi omplexity of the prtitioning proess is strongly reduedF sf the e0ieny of superpixel methods n e strongly fE feted y ig size imgesD the proposed lgorithm is wekly impted oth in terms of time e0ieny nd memory onsumptionF he proposed strtegy is omposed of three steps illustrted in pigure PFPF pigure PFPX yverview of the polygonl prtitioningF veftX lineEsegments re (rst extrted from the input imgeD nd onsolidted to ring sptil oherene @etion PFRAF widdleX n initil oronoi prtition tht preserves the lineEsegments nd their juntions is then reted y inserting nhors t spei( lotions @etion PFSAF ightX the oronoi prtition is homogenized y point proess @etion PFTAF 2.2 Review of image partitioning he review of previous work relted to imge prtitioning overs two min fets of our prolem sttementX segmenttion into superpixels nd shpe detetionF

  generted y P is the set of the oronoi ells {V (p 1 ), ...V (p n )}F oronoi digrms hve ppeling geometri propertiesD in prtiulr they entirely prtition the domin K without region overlpF fy using the iuliden distne in iqF PFID oronoi ells re gurnteed to e onvex polygonsF he dul grph of oronoi digrm lso orresponds to the heluny tringultion of its seedsD nd gives the djeny reltion etween regionsF pinlly the lgorithmi omplexity to uild oronoi digrm when dim K = 2 is only in O(n log n)F ptil point proesses n e used to generte the seeds of oronoi digrmF sn prtiulrD oissonEdisk smpling onstitutes fst nd e0ient wy to rete prtitions of homogeneous oronoi ellsF 2.4 Shape detection he (rst step of our lgorithm onsists of extrting lineEsegments from the input imgeD nd then onsolidting them to ring sptil ohereneF Line-segment extraction. es mentioned in etion PFPD mny methods hve een proposed in the litertureF yur hoie fouses on the vineEegment hetetor @vhA qtwIH for the detetion qulityD the running times nd the flse detetion ontrolF he miniml length of lineEsegments is (xed to εF xote tht our lgorithm is not restrited to vh nd n e used with other lineEsegment or polyline extrtion methodsF Consolidation. he extrtion of lineEsegments is lol proess tht n generte hep of shpes with noise nd outliersF uh rw deteted lineEsegments is sometimes hrdly exploitleF husD onsolidtion proedure is proposed to ring sptil oherene mong the lineEsegmentsF en djeny grph is uiltX two lineEsegments l i nd l j re onsidered s djent if d(l i , l j ) ≤ εD where d(., .) is the miniml euliden distne etween ny pir of points of the two lineEsegmentsF es illustrted in pigure PFQD sets of djent lineEsegments re onsolidted using three types of opertorsX ! Merging. he merging opertor tests whether two djent lineEsegments re nerEollinerD ndD if vlidD reples them y one lrge lineEsegment tht ovE ers their lengthF ! Removing. e smll lineEsegment is removed when djent to lrge nerE prllel lineEsegmentF Chapter 2. Polygonal partitioning ! Concurrence. he onurrene opertor tests whether the insried irle of three mutully djent lineEsegmentsD iFeFD of simple yle of order Q in the djeny grphD is smllD ndD if vlidD trnsltes the three lineEsegments onto the enter of the insried irleF xote the djeny grph is updted fter eh e'etive opertionsF wergingD reE moving nd onurrene opertors re suessively pplied over the lineEsegments using greedy proedureF removing merging concurrence pigure PFQX vineEsegment onsolidtionF hree di'erent opertions pplied greedily over the djeny grph @dshed grey linesA ring sptil oherene etween the deteted lineEsegmentsF uh onsolidtion proedure lso redues the prolem omplexity s the numer of lineEsegments eomes lowerF 2.5 Shape conforming Voronoi partition yur ojetive is now to rete oronoi prtition tht onforms to the deteted lineEsegmentsF id di'erentlyD the lineEsegments must not ross the oronoi ellsD ut must e inluded onto the oronoi edgesF wnipulting oronoi prtition to mke the ells lign with some geometri shpes or rdiometri informtion is delite opertion euseD for the displement of single seedD even smllD the whole group of onneted ells is usully strongly perturedF his explins why the use of oronoi digrms in vision hs minly e restrited to the retion of si isotropi prtitionsD eFgFD in texture segmenttion tvVVF snspired y reent work in surfe reonstrution to onform Qh heluny tringultion to plnes veIQD mehnism is proposed to rete oronoi prtition tht onforms to the lineEsegments y onstrutionF Shape anchoring. he key ide onsists in smpling pirs of seedsD lled s anchorsD loted on eh side of lineEsegmentF es illustrted on pigure PFRD eh nhor is positioned so tht the oronoi edge seprting the ells indued y the two seeds is extly on the lineEsegmentF he two verties of n nhor re re)etively symmetri to the lineEsegment distnt y εF he nhors relted to the sme lineEsegment re regulrly positioned with distne of 2εF his strtegy preisely preserves the dherene of the oronoi edges generted y the nhors to the lineEsegment in onsistent wyF et the sme timeD the density nd regulrity of nhor distriution long lineEsegment void in)uene from nhors of other lineEsegmentsF Junction preservation. he smpling of nhors is lol proedure on individul lineEsegments tht does not preserve their juntionsF hus junctionanchors re reted y positioning pirs of seeds on irleD lled the junction-circleD entered t the intersetion of the djent lineEsegmentsD nd of rdius 2εF enhors loted inside juntionEirles re (rst removedF henD juntionEnhors re inserted onto the juntionEirle s explined in pigure PFSF xote tht three mutully djent lineEsegments re neessrily interseting in one point s onsequene of the onsolidtion proessF por juntions etween two djent lineEsegmentsD the (rst juntionEnhor is positioned t the intersetion of the juntionEirle with the isetor of the lineEsegment pir hving the smller ngleF hen the other two juntionEnhors re reted y orthogonl symmetry with respet to the two lineE segmentsF sn term of juntions etween three djent lineEsegmentsD the two lineE segments hving the smllest ngle re seleted to position three juntionEnhors s desried eforeF hen two more juntionEnhors re symmetrilly positioned to the third line segment without disturing existing juntionEnhorsF sn suh linee set of nhors is positioned orthogonlly to eh lineE segmentD eh seed of n nhor eing t the sme orthogonl distne ε from the lineEsegmentF wo djent nhors relted to the sme lineEsegment re distnt y 2εFwyD the oronoi edges generted from these juntionEnhors extly preserve the juntion nd lie on the lineEsegments within the juntionEirleF he nhoring proedure is entirely ontrolled y the prmeter εF xote tht ells generted from juntionEnhors hve typilly tringulr shpe tht redue hree @respF (veA juntionEnhors re positioned to preserve juntions etween two @respF threeA lines @topAF he strting juntionE nhor (p 0 , p 0 ) is positioned t the intersetion of the juntionEirle with the isetor of the lineEsegment pir hving the smller ngleF hen the other juntionEnhors e reted y orthogonl symmetry with respet to the lineEsegments @ottomAF the glol omptness of the prtitionF his is the prie to py for preserving the ext intersetion of the lineEsegments into the prtitionF tuntions etween t lest four lineEsegments re mrginl in prtieX this se is not hndled y our lgorithmF 2.6 Spatial homogenization he oronoi prtition from nhors genertes ells of heterogeneous sizeF sn prtiulrD lrge ells poorly ptures the homogeneous res of the input imgeF sf lineEsegments pture well the min imge disontinuitiesD they re less dpted to seondry oundriesD s those formed y the sil frmes of the windmill on pigure PFTF reneD the oronoi prtition is re(ned y smpling point proess for etter sptil homogeniztion of polygonsF Sampling domain. e smpling domin is (rst de(ned so tht the oronoi edges supporting lineEsegments nd their juntion will not e 'eted y the insertion of new seedsF his domin is de(ned s the omplementryD over the imge dominD of the umulted disks entered on eh seed nd of rdius 2εFPoisson-disk sampling. xew seeds re then distriuted over this domin using oissonEdisk smplingD the disk rdius eing equl to εF snsted of onsidering homogeneous smplingD the seed distriution is guided with sptil densityD similrly to fhHWF he density is de(ned s proportionl to the inverse of the imge grdientD s detiled in pigure PFUF he intuition ehind tht is to void new seeds to e positioned on imge disontinuitiesF his proedure does not gurntee to produe oronoi edges tht perfetly lign with seondry oundriesD ut it enourges the positioning of seeds t the enter of lol homogeneous resD s illustrted on pigure PFTD ottom middleF xote tht other types of sptil densiE ties n lso e usedD eFgFD texture or distne mps depending on the study ontextF gradient-driven sampling uniform sampling pigure PFTX ptil homogeniztionF snitil oronoi prtition from nhoring @top leftA is re(ned into prtition @top rightA with regulrEsized ells @see histogrms of the distriution of the iuliden distne etween oundry pixels nd region entroidAF hen no lineEsegments re deteted in n reD our oissonEdisk smE pling driven y the imge grdient llows the preservtion of seondry oundries ontrry to uniform smpling @see loseEupAF 2.7 Comparison with superpixel methods he lgorithm is implemented in gCCD using the gomputtionl qeometry elE gorithms virry 1 for the oronoi digrm struture s well s for the si geE ometri opertions s the omputtion of the lineEsegment distneF ell timings re mesured on n sntel gore iU loked t PqrzF ixperiments with size imges from the ferkeley dtset re onduted to show the performne of the proposed lgorithm ompring with stteEofEtheErt superpixel methodsF he min prmeter of our lgorithmD εD llows the ontrol of the ell sizeF his prmeter steps in the di'erent stges our systemF pour dditionl prmeters smpling with nonEhomogeneous sptil distriutionF ih new disk to insert is positioned into irulr domin of width ε @lue ontourAF he smpling is guided y the inverse of the imge grdient @grey sleAD here from the loseEup of pigure PFTF re used during lineEsegment onsolidtion @etion QFRAX mximl ngle nd mximl distne to de(ne the ner prllelism nd nerEolinerity of lineE segmentsD s well s mximl rdius of insried irle of three lineEsegmentsD nd miniml lrge to smll lineEsegment length rtioF hese four prmeters re (xed respetively to 5 o D 0.5εD 0.5ε nd 5 in ll the experimentsF Flexibility. feuse of the nture of the geometri shpesD our lgorithm is prtiulrly suitle for mnEmde environments in whih oundries re often urtely desried y lineEsegmentsF st lso produes onvining results on freeEform oundry imges s illustrted on pigures PFP nd PFW @top rowAD even if the pieewiseEliner pproximtion of ojet ontours n e penlizingF diometri informtion re exploited t two di'erent levels in the lgorithmD iFeFD during lineEsegment extrtion nd oissonEdisk smplingF he former plys more importnt role s its onditions the positioning of the oronoi edges onto the min imge disontinuitiesF Comparison with superpixel methods. elthough the proposed lgorithm produes polygonl regions di'erent from superpixelsD it n e evluted using the stndrd qulity riteri required for superpixel methodsF pour qulity riE teri re tken into ountX oundry rell e + IPD undersegmenttion error vu + HWD omptness pIPD nd running timesF yur lgorithm is ompred on the ferkeley dtset wpwHI with three stteEofEtheErt superpixel methodsX vsg e + IPD iih dff + IP nd i vgIIF por mesuring the qulE ity riteri on our methodD the edges of the polygonl regions re disretized into pixelEsed oundriesF

  of fhSHH with mnEmde ojets pigure PFVX untittive evlution on ferkeley dtsetF foundry rellD underE segmenttion errorD omptnessD runtimeD eeD nd preisionErell re given for the entire dtset @AD nd for suset of QH imges @A from ferkeley dtset in whih mnEmde strutures re dominntD with some smples t the ottom leftF method is glolly 1% less urte thn the est sore of the three superpixel methodsF pigure PFW shows some visul omprisons with these three superpixel methodsF yur method ompetes wellD speilly for indoor nd urn senesF sf the other methods typilly perform etter for pturing thin irregulr detils with lrge region sizeD our method ompenstes y higher region omptnessD some geometri gurntees on the resultD nd region oundries under the pixel sle s shown in pigure PFIHF Limitations. he proposed lgorithm is designed to prtition imges with polygonl pproximtion of region oundriesF sf this pproximtion is usully relevnt for mnEmde environmentsD it might e of lower interest for imges with weker geometri signturesF he ury of our results is lso dependent of the qulity of the deteted lineEsegmentsF he stteEofEtheErt lineEsegment detetor qtwIH is employedX it produes urte lineEsegments ut still lks of glol regulriztion to get lineEsegment on(gurtion of very high qulityF 2.8 Conclusion sn this hpterD novel lgorithm is proposed to prtition imges into onvex polygonsF gontrry to superpixel methodsD the proposed method opertes t the sle of the geometri shpe nd not diretly t the pixel sleF yur lgorithm hs demonstrted severl interesting properties in terms of geometri gurnteesD region omptness nd slilityD nd hs shown potentil for prtitioning imges with strong geometri signturesD typilly mnEmde environmentsF he key tehnil ingredient of our work is n nhoring proedure to onform oronoi digrms to geometri shpesD orD to e more preiseD to lineEsegmentsF his work rings geometri dimension to trditionl superpixel segmenttion methodsF sed s preproessingD it is expeted to serve ision to exploit more e0iently the geometri knowledge disseminted into imgesD for instne y polygE onlyzing ojets with region groupingD lssifying senes t supixeli sle or SLIC SEEDS ERS ours pigure PFWX isul omprisonF he proposed lgorithm produes ompetitive reE sults for mnEmde ojets or environments @four middle rowsA in whih the geoE metri strutures re preservedF ynly vsg presents regions of the sme order of omptness thn our lgorithmD ut with more outliers @see the histogrms repE resenting the distriution of the iuliden distne etween oundry pixels nd region entroidD for the medium region sizeAF SLIC SEEDS ERS ours pigure PFIHX egion oundryF gontrry to trditionl superpixel methods suh s vsgD iihD nd iD the regions produed y the proposed lgorithm re polygons le to preserve the geometri signtures of imges t supixeli sle shown t the loseupsF 3.1 Introduction smge understnding sed on imge semntis hs een n importnt reserh topi in gomputer ision for mny yersF emnti lssi(tion plys vlule role in retrievl of meningful informtion in imgesD espeilly in urn senesF rE ditionl lssi(tion pprohes mostly rely on the mthing of visul feturesD suh s textureD intensity nd olor informtionD to lssify pixels into semnti lsses rHSD xHWD uyuITF gontextul lssi(tion methods integrte sptil onsisteny nd neighoring informtion to etter pture ojetElevel trgets in high resolution imgeryD while su'ering from omplex feture design nd the size of ontext regions wniIQF woreoverD intrElss vritions n e lrge in stellite ity senesD suh tht the ontrst mong prts of roof n e higher thn the ontrst etween the roof nd its surroundings eeIHF ynly relying on Ph pperne lues is not su0iently e'etive to lssify urn ontext from stellite imgeryF enother useful potentil lue is height informtion providing Qh interprettion of senes uwfHWF roweverD stereo mthing of stellite imges produes sprse elevtion mps tht re inomplete nd rough for semnti extrtion s explined in etion IFRF e joint strtegy is proposed to retrieve semntis nd estimte elevtions siE multneouslyD y interting rdiometri nd Qh geometri informtion oth from the left nd the right imgesF he output onsists of polygons leled with semnE ti lssesX roof nd otherD nd enrihed with n elevtion vlue for eh polygon determined s roofF he overview is illustrted on pigure QFPF 3.2 Review of region-based stereo matching xumerous works hve een proposed in stereo mthing HPF hile wellE estlished methods s the qw lgorithm rirHV reson t the sle of pixelD some works fous on mthing imge regions to more urtely preserve ojet oundE ries uHUD HVF feyond oundry uryD regionEsed stereo mthE ing methods n o'er high slility nd timeEe0ieny fqIRF ome works @of the joint lssi(tionF snput stereo imges @A re (rst deE omposed into tomi onvex polygons @A using the lgorithm desried in ghpter PF eondlyD the initil elevtion of eh polygon is lulted y the qw rirHV with douleEheking @AF sn the lst step detiled in etion QFRD the semnti lss nd the elevtion of eh polygon re simultneously retrieved in the two sets of prtitions @dAF he olor re)ets the orresponding elevtion vlue in proportion to the elevtion rnge of the seneD whih is di'erent in @A nd @dA sine elevtions re quntized in @dAF fu + IID v + IP lso omine ojet segmenttion or lssi(tion with stereo mthing in uni(ed frmeworksF snferene for these models isD howeverD omplex tsk tht requires timeEonsuming optimiztion proeduresF yverllD most of these methods re not dpted to stellite imges whose wide selines typilly produe severe olusion prolems tht re not spei(lly hndledF he dditionl use of geometri primitives s lineEsegments usully helps to etter interpret oluded prts of imges fpqHSF 3.3 Elevation assignment to polygonal partitions he lgorithm in ghpter P is pplied independently on oth stellite stereo imges with polygon size (xed to 5 pixelsD iFeFD verge distne of polygon edges to its polygon entroidA in our experimentsF es illustrted on pigure QFQD it pE tures geometri regulrities in imges y ligning ontours of tomi polygons with liner strutures suh s roof edgesF xote tht the lineEsegments emedded into the polygonl prtitions will e used further in our pprohF he polygons re enrihed with n elevation estimate whih orresponds to the ltimetri distne etween the oserved surfe ptured in the polygon nd the groundF por eh polygonD its elevtion estimte is de(ned s the di'erene etween the men of the pixel depths ontined inside the polygon @omputed y qw rirHV with doule hekingAD nd the depth of the ground @omputed y stndrd higitl errin wodel @hwA estimtion method fhHPAF feuse of the wide seline of our stereo pirsD polygons without elevtion estimtes re frequentD espeilly when ssoited to fde elements s illustrted in pigure QFQF sn returnD elevtion estimtes re reltively urte nd present on very lrge mjority of roofsF yur strtegy is thus to ouple these elevtion estimtes with the geometri informtion ontined in the polygonl prtitions to retrieve uilding ontours even for prtilly oluded roofsF he polygonl prtitions produed y the lgorithm in ghpter P re denoted y P l nd P r for the left nd the right imges respetivelyF P l ⊂ P l represents the set of polygons in P l with elevtion estimtesF e polygon i ∈ P l ∪ P r ssoited with n elevtion estimte d i is projeted in Qh using the trditionl tionl olynomil goe0ients @gA model rWUF wo polygons i ∈ P l nd j ∈ P r with respetive elevtion estimtes d i nd d j re sid to e imbricate if the orthogrphi projetions into the horizontl plne of the Qh polygons overlpF sn this seD τ ij ∈ [0, 1] denotes the overlpping rtio of the orthogrphi projetionsD iFeFD the intersetion re to union re rtioF hese nottions re illustrted in pigure QFRF H IHH ilevtion estimte @in meterA pigure QFQX olygonl prtitioning nd elevtion estimtesF veft nd right polygonl prtitions pture liner strutures ontined in input imgesD nd in prtiulr uilding edgesF ilevtion estimtes sprsely over the polygonl prtitions @see olored polygonsAF ih roof ontins t lest few elevtion estimtesF left polygonal partition P l right polygonal partition Pr horizontal plane i j (j, d j ) (i, d i ) pigure QFRX yrthogrphi projetion of polygonsF olygons i nd j with respetive elevtion estimtes d i nd d j re projeted in Qh using the g modelF hese two polygons re imrite s their orthogrphi projetions into the horizontl plne overlp @see yellow reAF 3.4 Joint classication and elevation recovery trting from the two polygonl prtitions nd sprsely distriuted elevtion estimtesD our gol is now to retrieve simultneously the semnti lss nd the elevtion of eh polygon of the prtitionsF wo semnti lsses of interest re onsideredX roof nd otherF glss other minly refers to ground nd fde elementsF feuse of the wide selineD most of these elements re only visile in one imgeF es our min ojetive is to reonstrut uildingsD onsidering only these two lsses is su0ient under the ssumption tht fdes re vertilF gontrry to lss otherD lss roof is ssoited with n elevtion vlueF fy onsidering the lssi(tion prolem s leling formultionD the set of possile lels n then e de(ned s L = {z 1 , ..., z n , other} where z 1 , ..., z n re the n possile elevtion vlues of roofF o set z 1 , ..., z n D the set of elevtion estimtes re lustered y uEmens with K = n + 1D nd ssoite the n highest entroids to themF es the ground flls into the lss otherD the entroid with the lowest vlue is reset to zeroF e σ(z k ) denotes the stndrd devition of the k th lusterF he qulity of on(gurtion of lels l ∈ L card(P) is mesured through n energy U of the formX

  djenyF wo types of pirwise intertions etween polygons re tken into ount in the leling formultionX within the sme prtition nd in etween prtitions @leftAF vineEsegments emedded into the prtitions prevent neighoring polygons from interting @rightAF

  using the αEβ swp lgorithm fuHRF pigure QFT shows the impt of the di'erent terms of the energyF sn the sequelD the term enriched prtition is de(ned to repreE sent polygonl prtition whose polygons hve reeived lss nd eventully n elevtion vlue y this energy minimiztionF Joint classication of urban cities. he proposed joint lssi(tion lgoE rithm hs een pplied to severl ities with di'erent lndspesF pigure QFU shows lssi(tion results of dense downtown in eoulD outh uoreD downtown in xew ork gityD the D nd ntique ity in elexndriD igyptF fuildings re glolly well deteted with estimted elevtion vluesF entique ities suh s elexndri re hllenging for the nrrow streets tht ring di0ulties in seprting them in lssi(tionF xote thtD semntis nd elevtions re simultneously retrieved in the lssi(tionD llowing for roustly hndling olusion res @see rops in xew ork gity in pigure QFUAF3.5 Conclusionhis hpter proposes joint lssi(tion method for semnti ojet leling nd elevtion estimting from stellite stereo imgesF emntis nd elevtion esE timtes re jointly retrieved to e roust for hndling low imge qulityD limited resolution nd olusion res in stellite imgesF emntis in lrgeEsle urn pigure QFTX smpt of the di'erent energy termsF oofs re sprsely leled using the dt term only @β 1 = β 2 = 0D 2 nd olumnAF edding the smoothness potentil propgtes roof lels while preserving uilding edges @β 2 = 0D 3 rd olumnAF he leling oherene etween the left nd right prtitions is enfored onsidering the omplete energy formultion @4 th olumnAF senes re e'etively lssi(ed y integrting elevtion informtionF ooftops re extrted nd simultneously enrihed with elevtion vluesF he integrtion of semntis nd elevtionsD nd the intertion of informtion from the left nd the right imgesD improve the roustness to the low x nd the olusion prolems in stellite imgeryF wo preliminry Qh models in vyhI n e generted y projeting the enrihed polygons in Qh using the g modelsF xote tht lerned rdiometri prior to distinguish roofsD rodsD vegettion nd othersD hs een evluted for the joint lssi(tionF roweverD the results show tht lol rdiometri fetures of polygonl regions re not su0iently relile for roust lssi(tion of urn senesD espeilly when fdes nd rods hve very similr ppernes with roofsF por the future workD more semnti lsses n e inluded into the lssi(lssi(tion of di'erent itiesF prom the left to the right olumns reX the lssi(tion of ity with elevtion estimted on rooftopsD nd rops of the lssi(tion respetively from the left nd the right imgesF he joint lssi(tion lgorithm is performed on worldwide ities in di'erent urn lndspesD inluding dense downtown with lose residentil uildings @topAD downtown with lrgeD tll uildings nd olusions @middleAD nd ntique ity with nrrow streets nd smll uildings @ottomAF in prtiulr rods nd vegettionF verning priors with nonlol feturesD suh s pirEwise feture desriptors involving neighorhood informtionD show potentil to improve the lssi(tion performneF Chapter 4 Model fusion wo sets of enrihed prtitions re produed y the joint lssi(tion lgorithm proposed in ghpter QD respetively from the left nd the right imges in stellite stereo pirF rojeting these enrihed prtitions into Qh y the g models results in two di'erent modelsD euse of di'erent interprettions of the shpes of ojetsX ! ome roof prts re frequently oluded etween the two imgesF ! he shpes of polygons etween left nd right prtitions do not neessrily orrespondF ! he smooth term of iqution QFI depends on the rdiometri pperne whih is di'erent in eh individul imgeF ! he oupling term of iqution QFI is soft onstrint tht does not gurntee tht imrite polygons hve the sme elevtionF pigure RFI shows n exmple of the two di'erent Qh interprettions of uildingF sn this hpterD model fusion method is proposed to produe ompt nd geometrilly urte Qh ity models from the two preliminry models generted y the joint lssi(tion lgorithmF st relels the polygons y integrting onstrints of rdiometri disontinuities nd geometri shpe regulritiesF 4.1 Introduction qeometri ury of Qh models is n importnt evlution metri for high qulity ity reonstrutionF he qulity of the two preliminry models from the joint lssi(tion is not su0ient for pplitions tht require high omptness nd geometri uryF ih of the models my pture prts of the geometri shpes wellD ut neither gives preise or omplete ojet ontoursF pigure RFIX wodels from the joint lssi(tion of the left nd right imgesF he proE jetion in Qh of the left nd the right enrihed prtitions is not neessrily oherent with eh other in terms of ojet shpesF op row shows the interprettion proE dued y the joint lssi(tion lgorithm from the left imgeD in whih the uilding in the middle is prtilly oludedF his Qh model ptures well the oundry of the higher roof lyer in the middleD ut is inomplete due to the olusion reF fottom row shows the results from the right imgeD in whih the Qh model gives omplete ontour of the rooftopD ut misses the top left ornerF sn vyhI interprettionD roofs re represented y )t horizontl primitivesD nd ontours in the footprint indite the orders of di'erent height lyersF reneD high qulity vyhI model re)ets accurate ojet ontours in the orthogonl projetion sine fdes re vertilF o unify suh two preliminry models into unique geometrilly urte Qh representtionD ll enrihed polygons re projeted into the horizontl plneD nd relel elevtions inside the new indued horizontl prtitionF his method reE trieves geometry nd semntis simultneouslyD improving geometri uryD nd roustness to olusion resD low imge qulityD nd model on)itsF pigure RFP illustrtes the fusion proess from the joint lssi(tion of the two input stereo imges @enterAF pigure RFPX yverview of model fusionF fsed on the joint lssi(tion of the input stereo pirD polygons re enrihed with semnti lels nd elevtions vluesD lled rough models @2 nd olumnAF he fusion of these two models opertes on their projetions to horizontl plne @3 rd olumn ottomAD nd genertes the ompt nd geometri urte Qh model @3 rd olumn topAF 4.2 Review of object contouring he review of previous work overs two min fets of the model fusion prolemX ojet polygonliztion nd ontour optimiztionF Object polygonalization. gpturing ojets y polygonl shpes provides ompt nd strutureEwre representtion of the ojet ontoursF st is prtiulrly dpted to representing regulr ojets s roofs from imgesF yjet polygonlizE tion methods typilly deprt from the detetion of lineEsegments whih re then ssemled into polygonsF his seond step n e doneD for instneD y serhing for yles in grph of lineEsegments p + IPD or y onneting lineEsegments with gp (lling strtegy gpIRF qrouping tomi regions vhIH is lso posE sile pprohD espeilly when the numer of ojets is highD nd the input imge is igF st requiresD howeverD postEproessing step to vetorize hins of pixels into polygons with typilly loss of uryF Path optimization. erhing for optiml ontoursGpths provides tehnique for formulting mnEmde ojet shpesF sn urn itiesD footprints of ojetsD suh s uildings nd rodsD mostly onsist of regulr geometri primitives inluding stright lines nd urvesF qiven grph whose edges indite possile pths to onstrut ojet ontoursD pth optimiztion prolem n e formulted to explore the optiml ontourF orks suh s gpIR reonstrut regulr shpes from freeE spe evidene y solving shortest pth prolem through dynmi progrmming insted of hijkstr9s lgorithmF riors n lso e introdued to is the pth serhing s desried in vrHTD exploring optiml pths to formulte footprints of uildings in spe of oundry pointsF wost of the works re foused on extrting outlines of ojetsD ut hve less onsidertions on internl struturesD for instneD elements onstruted inside the outline of roofsF 4.3 Fusion of enriched partitions por ity reonstrution in vyhID urte shpes of rooftops re the most ritE il trgetsF he proposed model fusion method optimizes ojet ontours on the orthogonl projetion of the enrihed polygons in PhF he edges of djent polygE onl projetions who hve di'erent elevtion vlues form the ontours of rooftopsD inluding outlines nd shpes of their interior height lyersF Orthographic projection. ih polygon i ∈ P whose lss is not other is proE jeted into the horizontl plneF he superposition of projeted polygons from left nd right prtitions produes deomposition of the horizontl plne into new polyE gons lled cellsF xote tht the ells re not neessrily onvexF he set of ells is left enriched polygons P l right enriched polygons Pr pigure RFQX ilevtion inherenyF inrihed polygons iD j 1 D nd j 2 respetively with elevtion estimtes z i D z j D nd z j re projeted into Qh using the g modelsD nd then re orthogonlly projeted into horizontl plneF ih ell inherits set of elevtions from the polygons tht overlp with itF gell a shres no overlp with other polygonsD suh tht Z a = {z j }F olygons j 1 , j 2 overlp t ell b with identil elevtion vlue z j D so Z b = {z j }F por ell cD polygons i, j 1 with two di'erent elevtions z i nd z j overlpped with itD hene Z c = {z i , z j }F denoted s CF ih ell inherits the elevtions of the polygons tht overlp with itF he set of elevtions inherited y ell i ∈ CD is denoted s Z k F pigure RFQ explins the proess of elevtion inherenyF hi'erent types of ells n e distinguishedX ! Coherent cells re ells tht inherit two identil elevtionsD one from the left prtition nd one from the rightF he elevtion vlue of these ells is not modi(ed furtherF ! Conict cells re ells tht inherit t lest one elevtionD nd tht re not oherent ellsF ! Empty cells re ells without inherited elevtionF heses ellsD whih typiE lly (ll in the holes in the ell deompositionD minly orresponds to ground or smll roof prtsF hese three sets of ells re respetively denoted y C coherent D C conf lict nd C empty D illustrted in pigure RFRF coherent cells conict cells empty cells pigure RFRX pusion of enrihed prtitionsF rojeting the enrihed prtitions @topA into the horizontl plne produes ell deomposition in whih three groups of ells n e distinguished @middleAF he releling of the elevtion of on)it nd empty ells gives uni(ed Qh model @rightAF Cell relabeling. por fusing enrihed prtitionsD eh on)it or empty ell must e ssoited with unique elevtionF hose ells re releled using n energy formultion with stndrd formX

  the set of pirs of djent ells in C tht hve t lest one ell elonging to C F E d D E r nd λ re respetively the unry dt termD the pirwise potentil nd the weighting prmeter etween the two termsF A k nd L kk re respetively the re of ell kD nd the length of the ommon edge etween ells k nd k X they re introdued to normlize the energy with respet to the size of ellsF

  kEprojetion mesure of the ommon edge t elevtion x k into the left @respetively the rightA imgeF sn prtieD the kEprojetion mesure is de(ned s the solute vlue of one minus the slr produt etween the imge grdients nd the grdients of the kE projeted edgeF o verge the impts of kEprojetion mesures G(x k ) nd G(x k )D sum opertion is de(ned to mesure the kEprojetion qulity of the ommon edges into one imgeF sn theoryD projetions in two di'erent perspetives re neessry for verifying the (delity of Qh geometryF sdellyD oth the two kE projetions t x k nd x k (t well the disontinuities in imges if the elevtion vlues re urteF roweverD in order to over the se of inomplete ontours of oluded resD min opertion is pplied to de(ne the totl kEprojetion mesure of the left nd the right imgesD insted of medin funtionF en explntion is shown mesure E r F he top left shows the projetion of ll enrihed polygons on horizontl plneY the right is rop of ell k nd ell k projeted in Qh spe with lel x k nd x k D nd the line segment in red indites the ommon edge eY the 2 nd nd 3 rd row @leftA desries the kEprojetions of the ommon edge e respetively with elevtion x k nd x k into the left nd the right imgesF Optimization. por e0ieny resonsD the energy minimiztion is sptilly deE omposed into independent suprolemsF he onneted on)it nd oherent ells re regrouped into lusters while llowing empty ells to e insideF ih luster intuitively orresponds to uilding or uilding lokF he αEβ swp lgorithm fuHR is then operted over the set of on)it nd empty ells of eh lusterF xote thtD for eh lusterD the lel set Z is restrited to the inherited elevtions of its ellsF yptionllyD the optimiztion n e performed in prllel on eh lusterF Compact city model. he ground is represented in Qh y mesh surfe trinE gulted from the ltitude estimtes fhHPF prom the optiml lel on(gurtionD roofs re inserted y simply elevted ells to their elevtion lel from the groundF he fde omponents re (nlly dded y reting vertil fets etween the djent ells with di'erent lelsF 4.4 Conclusion his hpter presents model fusion lgorithm to extrt optiml ojet onE tours from the two sets of enrihed polygons produed y the joint lssi(tion in ghpter QF he fusion method produes geometrilly urte Qh representtions with high omptness y minimizing n energy funtion onstrined with geometE ri ury nd rdiometri disontinuitiesF st gins roustness to low resolution nd olusion prolems of stellite imgery y retrieving geometry nd semntis simultneouslyD nd rings e0ieny y operting on polygonsF Chapter 5 Experiments he works in ghpter PD ghpter Q nd ghpter R respetively desrie the three min steps of the proposed utomti pipeline for ity reonstrution from stellite imgesX polygonl prtitioningD joint lssi(tionD nd Qh model fusionF he polygonl prtitioning lgorithm deomposes imges into onvex polygons while preserving geometri shpesF he joint lssi(tion method relels the polygonl prtitions with semnti lsses nd elevtion estimtes simultneouslyF yur model fusion lgorithm genertes geometrilly urte Qh models y optimizing ojet ontours from two sets of enrihed polygonsF his utomti pipeline produes ompt nd geometri urte Qh models for ities worldwide in few minutesD with high slilityF sn this hpterD evlutions re presented to mesure the e0ieny nd the performne of the utomti pipeline for Qh ity reonstrution of di'erent types of ities round the worldF snput dt quisitions re stereo pirs from uikfird PD orldiew P nd leides stellite imges with sptil resolution t HFTD HFS nd HFS meter respetivelyF ell experiments re performed on n sntel gore iU loked t PqrzF5.1 Implementation detailshe reonstrution pipeline is implemented in gCC using the gomputtionl qeometry elgorithms virry @gqevA CgalIS for mnipulting geometri dt strutures in Ph nd QhD nd the qeosptil ht estrtion virry @qhevA qhe for proessing si opertions with stellite imgesF he oronoi digrm struture in etion PFS is produed y the dul of the heluny tringultionF por ll stellite imges in our experiments with sptil resolution round 0.5mD the prmeter ε is (xed to 5F he ell deomposition in etion RFQ is omputed using onstrined heluny tringultion whose onstrined edges orrespond to the orthogrphi projetion into the horizontl plne of the polygon edges of oth prtitionsF he numer of prmeters is lrgeD i.e., TD ut this is the prie to py for full pipeline omining semnti nd geometri onsidertions in n unsupervised mnnerF sn ll the experimentsD the weights of the two energies re (xed to β 1 = 0.2Dβ 2 = 10 nd λ = 2.5D nd the penlties to α = 0.05 nd γ = 2F he numer of possile roof elevtions is set to n = 50D exept for ities where skysrpers requires inresing its vlue to 100F he omptness of the output Qh model is minly ontrolled y the weight of model fusion energy λ in iqution RFQF st lnes the omptness of modelsD the qulity of ontoursD nd the ompleteness @totl reA of rooftopsF e igger vlue of λ leds the optimiztion solution to fvor omptness of shpes nd qulity of ontoursD while losing pthes tht penlize regulrity of shpes nd kEprojetion qulityF pigure SFI shows the impt of prmeter λ on the reonstrution of uildingF 5.2 Qualitative evaluation ixperiments re onduted to evlute the output qulities of the proposed lE gorithms from lrgeEsle stellite imgesF smge polygonl prtitioning nd Qh reonstrution from lrgeEsle ities re evluted in terms of geometri shpe preservtion qulity nd ltimetri uryF Large-scale satellite images partitioning. pigure SFP shows n use se in whih the lgorithm hrteristis re prtiulrly ttrtiveF feuse of the sle nd the geometri signture of the urn stellite imgesD the imge prtition well preserves the shpe of uildingsD in prtiulr the fde nd rooftop edgesD s well s uilding ornersF his knowledge is used in the geometryEwre joint lssi(tion of urn senesF λ = 0 λ = 5 λ = 10 λ = 400 pigure SFIX smpts of prmeter λF es λ inreses @γ is (xed to 2.0AD the model fusion method produes more ompt ojet ontours with higher kEprojetion qulityF yptimiztion using only the unry dt term in iqution RFQD genertes rough ojet ontours without onstrints on the regulrity of geometri shpes@1 st olumnAF e more ompt nd urte outline of the uilding is ptured y inresing λ to 5 @2 nd olumnAF hen inresing λ to 10D smll geometri detils n e otined @yellow irleD 3 rd imgeAD euse the ugmenttion of kEprojeting qulity ompenstes the smll inrese of ontour lengthF roweverD only smll pthes with regulr shpes remin when set λ to n extremely lrge vlue @the 4 th olumnAF Reconstruction of buildings. Qh models produed y the proposed pipeline re georeferenedF sf the model is urteD the kEprojetion into the input stereo imges of the roof edges from the output Qh model mthes well the disontinuities of imgesF sn vyhI representtionD high qulity kEprojetions of rooftops from oth the left nd right imges prove the ury of geogrphi lotion nd the preision of uilding elevtionsF pigure SFQ displys set of typil reonstrution of uildings of di'erent typesD suh s single roof with more thn one height lyerD uilding loksD nd freeform rhitetureF e visul omprison etween the kE projeted ontours nd the edges of rooftops in pigure SFQ gives n verge mthing distne of less thn 3 pixelsD whih mens 1.5m t 0.5m sptil resolutionF hue to the plnr ssumption of polygonl regionD urved roofs re pproximted y Denver Manhattan, NY pigure SFPX rtition of lrgeEsle stellite imgesF yur lgorithm deomposes 104wpixel @respetively QWwpixelA imge of henver @respetively wnhttnA into 0.8w @respetively 0.2wA onvex polygons in few minutesF he imge prtition niely preserves the fde edges nd rooftop juntions in spite of low imge ontrst onduted to show the geometri ury of the output Qh modelsF gomprison with hw methods nd vihe solutions shows the qulity of our output models on uildingsF o evlute the ury of the output Qh model in ityEsleD n ltimetri ury mesurement is omputed on henver ity using vihe dt s ground truthF Comparison with DSMs and LiDAR solutions. hile there is no utomti lgorithm produing ompt nd semntillyEwre lrgeEsle ity models from stellite imgesD the output models re ompred to trditionl higitl urfe wodE elsF he hws re generted from stereo mthing following y struture reovE ery lgorithms suh s oronoi lustering from the polygonl prtitioning method @ghpter PA nd mesh simpli(tion in veISF es shown in pigure SFRD the outE put model etter preserves the uilding struture while eing semntillyEwre nd omptF he geometri ury of the proposed method is lso mesured in pigure SFS nd is ompred with ury of n irorne vihe sed lgorithmF elthough the output is less urteD the gp is reltively low given the ontrst of dt ury etween irorne vihe nd stellite imgeryF Altimetric accuracy on city reconstruction. en ltimetri ury of the Qh ity reonstrution on henver is mesured in pigure SFTF he high qulity eirorne vihe representtion is onsidered s ground truthF rusdor' distnes re omputed from eh vihe point to the output Qh model from the proposed pipelineD nd ltimetri errors re displyed y projeting the rusdor' distne vlues in to gridF he proposed method genertes ompt Qh models within resonle verge error to the ground truthF wost of the devition onstitutes to prtiulr uildings missed euse of insu0ient numer of elevtion estimtesD rough ground pproximtion due to elevted rodsD nd presene of trees tht re not hndled y the proposed lgorithmF pigure SFQX eonstrution of uildingsF yn simple uildings @top rowsAD left nd right enrihed prtitions @left olumnsA re reltively similrF por more omplex uildings @middle rowsAD enrihed prtitions re more di'erentX their fusion llows us to (nd onsensul Qh output modelF ith freeform rhiteturl strutures @ottom rowsAD urved roofs re roughly pproximted y stepElike geometryF he kEprojetion into the input imges of the roof edges from the output Qh model shows good ury of oth uilding elevtions nd ontours @see red lines with higitl urfe wodelsF rditionl hw derived from stereo mthing rirHV t the pixel sle gives dense nd strutureEfree Qh modelsF fy postproessing hw with oronoi lustering proposed in ghpter P or with strutureEwre mesh simpli(tion veISD more ompt meshes re otinedD ut the uilding struture nnot e not restoredF he output model produed y the proposed pipeline is oth ompt nd strutureEwre @see the low numer of prinipl diretions in the distriution of output normlsAF 5.4 Robustness he output models provide fithful vyhI representtion of uildingsD s illusE trted in pigure SFQF ith the urrent stellite resolutionsD more detiled uilding representtion suh s vyhP is not relistiF gses tht hllenge our lgorithm re smll uildingsD typilly houses in residentil resD nd the textureless nd re)etive ojets whih in generl onstitute n importnt hllenge in stereovisionF H uryF eirorne vihe sns onstitute preise mesureE ments tht n e used s ground truth to evlute the geometri ury of the outputs of the proposed method @see the distriution of errors on the horizontl hisE togrmAF hile stteEofEtheErt irorne vihe method vwII produes more urte results with lower men error to vihe points @0.9m vs 1.7mAD the gp is reltively low given the di'erene of qulity etween the two types of inputsF he proposed method n hndle olusions where some prts of uildings re inE visile in one imgeD s shown in the top rows of pigure SFUF roweverD severe roof olusions where the oluded prts re lrge or roof is only visile in one imgeD nnot e reoveredD s shown in the ottom row of pigure SFUF H ≥ 10 error @meterA pigure SFTX eltimetri ury on henverF en ltimetri error mp @topA of our output Qh model on henver @see pigure IFIA is omputed yD (rstD mesuring the rusdor' distne from eh vihe point to the output Qh modelD ndD seondD projeting the distne vlues into gridF he loseups illustrte the min types of errors from insu0ient numer of elevtion estimtesD rough ground pproximE tion due to elevted rodsD nd presene of treesF pigure SFUX oustness to olusion resF prom the left to the right olumnsX the kEprojetions of the optimized ontours on the left nd right imgesD nd the reonstruted Qh modelsF por roofs tht re prtilly oluded in one imgeD the proposed pipeline n reover the olusion res @see the top three rowsAF roweverD lrge olusion res tht led to too few elevtion estimtesD my not e hndled properlyF sn the ottom rowD the highest prt of the roof is missing euse of the huge perspetive di'erenes indued y its nonE)t strutureD wheres its lowest @nd lrgestA prt is ompletely hidden in the left imgeD exept one orner tht is tully pturedF 5.5 Scalability he proposed pipeline hs een tested on severl ities presenting di'erent urE n lndspesD s shown in pigures RFP nd SFVF hense downtowns in ntique ities suh s elexndriD igyptD re prtiulrly hllenging with nrrow streets nd smll uildings mssively onnetedF he proposed lgorithm sometimes fils sepE rting loks in etween these nrrow streets s their width n e smller thn the size of our polygonsF fusiness distrits of ities s henver or xew ork re the opposite lndspeX uildings re lrgeD tll nd firly seprted from eh otherF he proposed lgorithm typilly performs etter on suh resF sn terms of lsE si(tionD uildings re glolly well detetedF yne of the min resons is euse the proposed method does not rely on pure rdiometri desription of uildingsF et the sle of ig itiesD the rdiometri vriility of uildings is too high to drw likelihoodsF fuildings n e missed when there re not enough elevtion estimtesF his sitution is reltively mrginl in prtieX visul omprison etween our output Qh model of henver nd the uilding footprints of dstrl mp give us less thn 5% of missed uildings nd 14% of invlid uildingsD iFeFD uildings with t lest 20% of their footprints missed or overEdetetedF ixperiments of more lrgeEsle ity reonstrution re shown in eppendix UFPD suh s welourne hrE or in eustrliD n prniso in the D wdrid downtown in pinD nd rgue downtown in the gzeh epuliF 5.6 Performance erformne of the proposed utomti reonstrution pipeline re mesured y severl stndrd metris inluding running timesD memory pekD nd output omE plexityF smpts of severl prmeters re lso evluted in terms of performneF Eciency and complexity. o evlute the performne of the proposed utoE mti pipelineD timings nd omplexity of output Qh models re given for di'erent ities in le SFIF snput stellite imges typilly hve round QHwpixelsF ih of the three steps of our method tkes few minutes from typil stereo pir of xew ork gityD elexndriD igypt eoulD outh uore pigure SFVX eonstrution of itiesF he proposed pipeline performs on di'erent types of urn lndspesD inluding dense downtown @top leftAD ntique ity @ottom leftAD nd downtown @ottom rightAF ih model ws otined from one stereo pir of stellite imgesF stellite imgesF por very dense itiesD fusion is the most timeEonsuming step s the high density of uildings genertes omplex ell deompositionsF por ities with more spe in etween the uildings suh s xew ork gity or henverD fusion is quite fstF unning times for joint lssi(tion nd elevtion reoveryD nd polygE onl prtitioning do not depend on the urn lndspeD ut on the input imge sizeF yverllD the use of ompt nd e0ient geometri dt strutures llow us to hve ompetitive timings with respet to irorneEsed methodsF New times nd output omplexity of the reonstrution pipelineF he output omplexity refers to the numer of tringulr fets in the output Qh modelF xote tht the fusion step hs een optimized sequentilly on eh uilding lusterF rtiulrlyD the polygonl prtitioning lgorithm performs well on ig size imges s shown in le SFPF pive minutes nd 0.8q of memory re required for IHHwpixel imgeF fy ontrstD the superpixel method i tkes 39 minutes nd 34q memoryD nd the relesed versions of vsg nd iih re not le to hndle suh imge sizeF wnipulting geometri shpes insted of pixels mkes our lgorithm prtiulrly slleF sn terms of storgeD our polygon prtition n e sved in very ompt wy s plnr grph where eh node refers to polygonF Impact of parameters. wo key prmetersD the prtitioning prmeter ε nd the numer of elevtions n re evluted to illustrte their impt on the reonE strution performneF es ε inresesD imges re prtitioned into lrger tomi regions ndD thusD lower numer of onvex polygonsF fut we re fing trdeEo'D s shown in pigure SFWF yn one hndD lower numer of polygons rings omE puttionl e0ienyY on the other hndD the higher sizes nd the onvexity of the polygons mke the preservtion of (ne detils in geometri shpes di0ultF sn the joint lssi(tion lgorithmD n possile elevtion vlues for the roofs re de(ned from the lustering of ll elevtion vlues in the seneF e greter vlue of prmeter n mens lrger lel spe of possile elevtion vluesD whih is more urte in elevtion estimtion ut is more time onsuming for optimiztionF he urve of

5. 7

 7 Limitationshe reonstrution pipeline hs severl limittionsX ! he output Qh models of the utomti pipeline only ontin three semnti lels @groundD roof nd fdeAF he design of the lgorithm isD howeverD )exile enough to ount for new urn lsses in future worksF ! he limited qulity of stellite imges mkes the reonstrution of smll uildE ingsD typilly houses in residentil resD di0ultF ! he proposed system is roust to olusions of fdesD ground nd prts of roofsD ut nnot hndle severe roof olusions where roof is only visile in one imgeF he output vyhI representtion is lso less urte with freeform rhiteturl roofs s domes or peky struturesF sn suh sesD roofs re pproximted y stepElike geometry whose ury depends on the mount of elevtion estimtesF ! he polygonl prtitioning is designed to prtition imges with polygonl Error w.r.t. LiDAR (in meter) Runtime (in minute) of prmeter εF sing eirorne vihe sns s qround ruthD geometri errors re mesured y omputing rusdor' distnes from eh vihe point to the output Qh modelF ith smller εD the output Qh models pture (ne geometri shpes with higher uryD otining vergely lower geometri errors ut longer runtimeF pproximtion of region oundries tht is usully relevnt for mnEmde environmentsF he ury of the prtitions is lso dependent on the qulity of the lineEsegments deteted y the vh qtwIHF st produes urte lineEsegmentsD howeverD still requires glol regulriztion to get lineEsegment on(gurtion of very high qulityF sn future worksD the use of )exile geometri shpes tht pture etter freeform ojets n e exploredD nd udris or fEsplines re potentil solutions ssuming oronoi digrm n e uilt in nonEiuliden spe tht onforms to these shpesF Error w.r.t. LiDAR (in meter) Runtime (in minute) of prmeter nF he higher the vlue of nD the lrger the lel spe L = {z 1 , ..., z n , other} of the possile evlution vluesF he elevtion estimtes of roofs ontined in the Qh models otined with lrger vlue of n get higher uryD t the ost of loss in time sn this thesisD fully utomti pipeline of Qh ity reonstrution from stellite imgery hs een proposedF gontriutions re summrizedD with disussion of limittionsF Automatic city reconstruction. hue to the high diversity nd omplexity of urn ontextsD trdeEo' etween reonstrution ury nd lgorithmi )exE iility generlly exists in mny Qh ity modeling methodsF epprohes tht rely on more prede(ned ssumptions hieve higher ury of output ity modelsD ut lose )exiility to dpt to di'erent types of urn senesF por reonstrution from stellite imgeryD the hllenge is even greter euse of its limited resolutionD low imge qulity nd long seline prolemsF en utomti pipeline of urn ityreonstrution from stellite stereo pir is proposed in this thesisF st produes omptD semntillyEwre nd geometrilly urte Qh ity models with high slility nd time e0ieny y operting on polygonl tomi regionsF qeometry nd semntis re retrieved simultneously in order to hndle olusion res nd low imge qulity roustlyF heres the qulity of the output models is not s urte s irorne vihe solutionsD the proposed method outlsses trditionl hw representtionsD nd o'ers new perspetives in utomti ity modelingF Geometry-aware image partitioning. smge prtitioning is vlule tehE nique to improve slility nd e0ieny for lrgeEsle ity modeling from imgery dt souresF eduing rdiometri redundnies y prtitioning imges into tomi regions rings dvntges in terms of lgorithmi omplexity nd sptil onsistenyF sn urn senesD the most oserved semnti ojets re mnEmde strutures with strong geometri signturesF e novel lgorithm hs een proposed in ghpter P to deompose imges into onvex polygons while preserving geometri shpes of urn ojetsF st provides geometri gurntees on onnetivity nd onvexity of polygons nd is suited well for mnEmde environmentsF ith suh geometryEwre imge prtitioning tehniqueD ity modeling from imgery n e proessed t the sle of polygons e0ientlyF Joint exploration of semantics and elevations. wny ity modeling strteE gies re either imgeEsed or depthEsedF he omintion of them o'ers n interesting diretion to exploreF sn this thesisD joint lssi(tion lgorithm is proE posed to retrieve semntis nd estimte elevtions simultneously through glol optimiztionF he Ph rdiometri nd Qh geometri lues re exploited in omE mon frmeworkD gining roustness to low imge qulity nd olusion prolemsF his joint strtegy is not restrited to stellite imgeryD ut n e lso pplied to other stereo imgery pplitionsF Limitations. everl restritions remind us tht mny hllenges still remin in ity reonstrution (eldF Freeform-roof buildings. he proposed pipeline is not well dpted to the reonE strution of uildings with freeform roof shpesF pirstD the polygonl prtitioning relies on deteted lineEsegments nd pproximtes urves y polylinesF egulr geE ometri shpes re ptured y dhering edges of polygons to the lineEsegmentsF his strtegy is not dptive to freeform shpe preservtion due to loss of uE ry when represented with limit numer of stright edgesF eondlyD the output vyhI representtion is less urte with freeform rhiteturl roofs suh s domes or spiresF sn suh sesD roofs re pproximted y stepElike geometry whose E ury depends on the numer of elevtion estimtesF Residential buildings. he limited qulity of stellite imges rings di0ulties in the reonstrution of smll uildingsD typilly houses in residentil resF st is hllenge for polygonl prtitioning lgorithm to preserve suh smll size shpes of residentil uildings y homogeneous polygonsF ilevtion dt omputed y the qw from stellite stereo pir is sprse nd esy to miss smll uildingsF sn dditionD undesired ojets suh s vegettion nd vehiles lso mke di0ulties in urte uilding detetionF Severe occlusion. glues for reovering oluded res minly onsist of rdioE metri informtion ompenstion from the two imges nd elevtion vlues in their ommon prtsF he proposed systemD while roust to olusions of fdesD ground nd piees of roofsD nnot hndle severe roof olusions where roof is only visile in one imgeF 6.2 Perspectives smportnt hllenges remin in Qh ity modelingF he following res re posE sile venues for future worksF Modeling from higher resolution satellite imagery. ith the fst dvne of quisition tehniquesD higher resolution stellite imgery eomes villeF he newly lunhed orldiew Q stellite provides imges with 0.31m sptil resoE lutionD insted of 0.5m nd 0.6m s used in this thesisF he gp etween stellite imgery nd eril imgery or vihe sns still exists while eoming smller nd smller in terms of sptil resolutionF he long seline prolem my eome the (rst hllenge for dpting erilEsed pprohes diretly to ity reonstrution from stellitesF fig di'erene in perspetives rings di0ulties in high qulity dense mthing tht gives urte detils of urn ojetsF he seond hllenge my lie in the qulity of stellite imgesF righer resolution imges provide riher inforE mtion for reonstrution of geometri detils of urn ojetsD ut lso introdue more noise nd undesired ojetsF Public domain and crowd-sourced data. huring the lst twenty yersD difE ferent dt soures suh s irorneGstellite stereosopi imgery or lser snning re pplied to tkle geometri modeling issues on urn senesF he essiility of this dt hs eome ville to nonEspeilized people working in di'erent omE munitiesF iven uiquitous smrtphones provide lrge mount of photos tht re ville on the snternetD providing potentil dt soure for Qh ity reonstrutionF his everEexpnding dtD together with everEinresing omputtionl resoures onstitute gret opportunity to explore e0ient solutions for Qh ity reonstruE tionF pirstD puli domin nd rowdEsoured dt provide muh wider overge of worldwide ities ompred the speilized dtF eondD the onstrints of singleE soure dt re redued suh tht existing modeling methods n e dpted to other dt souresF his rings opportunities for multiEsouredD puliD lower ostD nd worldwide urn ity reonstrutionF Learning characteristics of urban landscape. wny lerningEsed lgoE rithms o'er impressive performne on ojet reognitionD dt lssi(tion nd semnti extrtionF rior knowledge lerned from nnotted orGnd leled smE ples n e integrted to enhne the roustness to undesired ojetsD eFgFD vegetE tion nd vehilesF heep lerning pprohes do not require prior feture extrtion ut lern them diretly from trining proessF he lerned networks is possile to desrie the hrteristis of urn lndspes well if the trining dtset onE tins su0ient smples tht depit vrious types of trget semnti ojets wniIQF ghllenges still exist to dpt deep lerning to urn reonstrution for the huge diversity nd intrElss vrition of semnti lssesD nd the di0ulties in extenE sive nnottion of trining dtF por high qulity ity reonstrutionD one promising diretion to explore is hyrid system omining relile lerningEsed semnti lssi(tion nd Qh geometri shpe reonstrutionF rgeted ojets retrieved from lssi(tion provides vlule lues in Ph perspetives for shpe reovery in QhF enother promising diretion is lerningEsed proedurl modelingD whih lerns to enode omplex onstrints using genertive methodsF he omintion of lerning pprohes with grmmrEsplitting n e n interesting step to explore wITF Joint city modeling. he gol of semnti ity modeling is to reonstrut n nnotted Qh modelD leling ojets s uildingsD vegettionD groundD rod netE works nd wter resD etF elted literture shows growing trend to fuse proE lems of segmenttionD lssi(tionD nd reonstrution ltogether pr + ISF smge segmenttion plys n importnt role in reduing rdiometri redundny nd omE puttionl omplexityF glssi(tion is useful for deling with olusions in modern urn reonstrutionD prtiulrly in long seline stereo visionF st is still n open question how to est tkle segmenttionD lssi(tionD nd reonstrution from imE gery in ommon frmeworkD iming t utomti reonstrution of urn ities in n urte nd e0ient wyF6.3 Conclusion (version française) gette disserttion dérit un lgorithme de reonstrution de villes en Qh à prtir d9imges stellitesF xous résumons iEdessous nos ontriutions priniples et en exposons les limittionsF Reconstruction automatique de villes. in rison de l diversité et de l omplexité des grndes villes du mondeD les lgorithmes de modélistion urine en Qh sont générlement sés sur un ompromis entre préision et )exiilité lgoE rithmiqueF ves pprohes s9ppuynt sur des hypothèses prédé(nies délivrent des résultts quiD pour ertines villesD o'rent un on niveu de préisionD mis éhouent à triter onvenlement ertins types de sènesF eve l9imgerie stelliteD le dé( est d9utnt plus grnd que les imges sont de plus file résolution et de moindre qulitéD ve en outreD une plus longue droite épipolireF our répondre à es proE lèmesD ette disserttion proposé un lgorithme de reonstrution urine à prtir de deux imges stéréosopiquesF ves modèles Qh de villes en sortie de et lgorithme sont omptsD préisD et ses di'érents ojets sont lssés selon une sémntique prE tiulièreF sl se rtérise pr un on pssge à l9éhelle et une ertine rpiditéD en opérnt à une éhelle géométrique élémentireF v desription géométrique des ojetsD et leur identité sémntiqueD sont extrites simultnément (n de gérer de mnière rouste les prolèmes liés ux phénomènes d9olusion et à l file qulité des imgesF fien que l qulité des modèles en sortie de l9lgorithme ne soit ps ussi préise qu9ve les solutions sées sur des données vihe ériennesD l soluE tion proposée surpsse les représenttions hw trditionnelles et ouvre de nouvelles perspetives dns l modélistion utomtique de villesF Partitionnement géométrique de l'image. ve prtitionnement d9une imE ge est une tehnique intéressnte pour modéliser e0ement des villes à grnde éhelle et à prtir de di'érentes soures de donnéesF v rédution des redondnes rdiométriques pr le prtitionnement en régions tomiques proure de préieux vntges en termes de omplexité lgorithmique ou de ohérene sptileF eu sein d9une sène urineD l pluprt des ojets oservés sont des onstrutions huminesD ve des signtures géométriques fortesF n lgorithme de prtitionnement d9une imge en polygones onvexesD préservnt l forme géométrique des ojetsD été dérit u hpitre PF geluiEi fournit d9importntes grnties géométriques sur l onnetivité et l onvexité des polygonesD et s9dpte ien ux environnements réés pr l9hommeF gette tehnique permet de triter e0ement le prolème de l reonstrution Qh en trnsformnt l9imge d9origine en simples polygones pturnt l forme géométrique des ojetsF Processus commun de classication sémantique et d'estimation des hauteurs. he nomreuses strtégies de modélistion sont soit sées sur une nlyse des imgesD soit sur des rtes de profondeurF v ominison des deux o're une piste intéressnte de ré)exionF hns ette thèseD un lgorithme est proposé pour lsser sémntiquement les ojets et estimer leur huteur de fçon simultnéeD à l9ide d9un proessus d9optimistion glolF ves signux rdiométriques Ph et les formes géométriques Qh sont exploités dns un proessus ommunD onférnt insi de l roustesse à notre lgorithme fe ux prolèmes d9olusion et de file qulE ité des imgesF gette doule pprohe ne onerne ps seulement les prolèmes liés à l9imgerie stelliteD mis peut ussi être ppliquée à d9utres prolèmes en lien ve l9imgerie stéréosopiqueF Limites. lusieurs di0ultés renontrées pr et lgorithme nous rppellent que de nomreux dé(s doivent enore être relevés dns le domine de l reonstrution urineF Formes de toits libres. v hîne de tritement proposée n9est ps dptée à l reonstrution de âtiments possédnt des toits non pltsF remièrementD le prtitionnement polygonl s9ppuie sur les segments retournés pr un lgorithme de détetion de ontoursD et pproxime les formes inurvées pr des oures 0nes pr moreuxF ves formes géométriques régulières sont pturées à l9ide de segmentsD positionnés le long des rêtes des polygonesF gette strtégie n9est ps dptée ux formes liresD en rison d9une perte de préisionD elleEmême due à l représenttion d9une oure à l9ide d9un nomre (ni de segmentsF heuxièmementD le modèle vyhI est peu préis ve des formes de toits non pltesD telles que les dômes ou les spiresF he tels ojets sont en fit pproximés à l9ide de oures en eslierD dont l préision dépend du nomre d9estimtions de huteursF Quartiers résidentiels. v qulité limitée des imges stellites pose prolème pour l reonstrution de âtiments de petite tilleD typiquement les misons des qurtiers résidentielsF sl est rdu pour l9lgorithme de prtitionnement de préserver l forme de tels âtiments dns des ensemles de polygones homogènesF v rte des disprités lulée pr le qw à prtir de deux imges est reuseD et il rrive souvent de mnquer les âtiments les plus petitsF in outreD l présene d9ojets non désirés tels que des rres ou des véhiules rendent di0ile l détetion de âtimentsF Occlusions. ves indies dont nous disposons pour retrouver les portions de âE timents 'etées pr un phénomène d9olusion onsistent priniplement en une ompenstion rdiométrique et des estimtions de huteurs onernnt les zones ommunes ux deux imges d9un ouple stéréoF fien que rouste fe ux oluE sions onernnt les fçdesD le sol ou ertines portions de toitsD l9lgorithme ne prvient ps à gérer les s d9olusions sévèresD lorsqu9un toit de âtiment of polygonal partitioning ome short experiments re onduted on two onrete vision prolemsD iFeFD ojet polygonliztion nd orner detetionD to illustrte the pplitive potentil of our lgorithmF Object polygonization. trting from polygonl prtition omputed y our lgorithmD we used inry wrkov ndom pield to lel eh polygon s inside or outsideF he interfe etween inside nd outside regions diretly forms polygonl ontoursD ontrry to existing ojet polygoniztion methods tht require omplex lgorithms in prtieD eFgFD gpIRF he wp formultion is sed on stndrd PEterm energy tking into ount imge onsisteny @rdiometri informtionA nd pirwise intertions @smoothness vi otts modelAF pigure UFI illustrtes the potentil of this strtegy ompred to gpIR for extrting roof ontours from eril imgesF Corner detection. e lso tested our lgorithm for deteting orner points in imgesD more preisely vE nd EjuntionsF his n e done y simple lol nlysis of the juntionEnhors from polygonl prtition of our lgorithmF sn prtiulrD we detet vEjuntions @respetively EjuntionsA when juntionEnhor is generted from P lineEsegments @respF Q lineEsegmentsAF es illustrted in pigure UFPD the proposed method otined detetion rte of similr order of mgnitude thn speilized lgorithm hqIR on oth syntheti nd rel imgesF groundtruth convex partition by our algorithm ours contour by [SCF14] pigure UFIX yjet polygoniztionF isul omprison of polygonl ontour exE trtion y our method nd y gpIR from eril imgesF he lss of interest orresponds to uilding roofsF groundtruth ACJ ours pigure UFPX gorner detetionF isul omprison of orner detetion y our method nd egt hqIRF yur method produed similr results on oth syntheti nd rel stellite imgesF sn prtiulrD for mnEmde ojets s uildingsD importnt orners of the roofs re orretly deteted y our methodF 7.2 Additional large-scale city reconstruction eonstrution of severl dditionl ities is presented in this setionF hi'erent types of urn itiesD suh s welourne in eustrliD n prniso in the D wdrid in pinD nd rgue in the gzeh epuliD re reonstruted from stelE lite stereo pirs into ompt nd urte Qh modelsD y the proposed utomti pipelineF he produed Qh models of these ities re respetively shown in pigures UFQD UFRD UFS nd UFTF pigure UFQX eonstrution of welourne hrorD eustrliF yur lgorithm interE prets elevted rods nd ridges s uildingsF iher urn semntis re neessry to solve this prolemF por evluting the reonstrution ury with visul onE sidertionsD roof edges of the output Qh model hve een kEprojeted into the input stereo stellite imges @topD see red linesAF his disply sheme is lso used for pigures UFR DUFS nd UFTF pigure UFRX eonstrution of n industril distrit in n prnisoF yur vyhI representtion is well suited to industril res whih re minly omposed of )t plnr struturesF xote tht our lgorithm is roust to uilding size vritionD s we n see with oth smll houses nd lrge industril sites within the sme seneF pigure UFSX eonstrution of wdrid downtownF fuildings of iuropen ities s wdrid typilly hve sloping roofs tht re etter desried y vyhP represenE ttionF elthough our lgorithm orretly extrts uilding loksD high resolution irorne quisition is reommended for pturing suh roofs with etter uryF

  Photogrammetry and Remote SensingD STXPTW!PVPD PHHPF @gited on pge IVFA

  + IPD IPD + IID re usully time nd memory e0ient nd pture oundries wellF ome methE ods ddress the prolem with more glol strtegiesD in prtiulr with energy minimiztion on grphs vgIID tyIQF esults re usully of higher qulity ut require more lgorithmi e'ortsF qlolly spekingD eh method hs its own = {p 1 , ..., p n } in ontinuous ounded set KD in our se the Ph domin of the input imgeF he numer of points n is itself rndom vrile tht typilly

	2.3 Mathematical background
	wo mthemtil tools tht ply entrl role in our lgorithm re rie)y
	introduedX ptil point proesses nd oronoi higrmsF heeper presenttions
	of these tools n e found in fvWQD yfgHHF
	Spatial point process. e point proess desries rndom on(gurtions of
	points P
	the imge disontinuitiesD in prtiulr for mnEmde environmentsF snterpreting
	lineEsegments from imges n ring preious informtion for disovering the sene
	struture vruHW or reognizing people enHUF sf the rough detetor hs een
	widely used in the litertureD reent lgorithms deeply improved the qulity of
	lineEsegment detetion while gurnteeing fst running times hrrIID nd even
	flse detetion ontrol qtwIHF glosely relted to lineEsegmentsD textons
	qHS lso provide ompt representtion of the imge struture in etween
	the pixel nd geometri shpe slesF

dvntges nd drwksD nd sores di'erently on the (ve riteri mentioned oveF xeverthelessD dherene to oundries is usully fvored t the expense of region omptness y lrge mjority of methods pIPF eprt from ertin lgorithms s vsg e + IPD no ontrol on the shpe of regions is possileF Geometric shape detection. he utomted detetion of geometri shpes is n instne of the generl prolem of (tting prmetri funtions to dtF here is wide vriety of shpes in ll dimensionsD the most ommon one in imge proessing eing lineEsegmentsF his prmetri shpe is known to pture well follows disrete oisson distriutionF ht mkes point proesses ppeling is the possiility to rete sptil intertions etween pointsD in prtiulr using the wrkovin propertiesD iFeFD points intert only in lol neighorhoodF he most ommon proess using wrkovin intertions is the truss proess in whih repulsion domin is loted round eh point to void points to e too lose to eh otherF hen dim K = 2D this domin is disk whose rdius is model prmeterF he smpling of point proesses is usully fstidious opertion relying on wonte grlo methods vIRF roweverD fst smpling mehnisms exist for ertin types of point proessesF his is the se of truss proesses for whih e0ient oissonEdisk smpling llows the rndom genertion of points either homogeneously distriuted hrHTD or following n ritrry density fhHWF Voronoi diagram. qiven on(gurtion of points P in KD lled seedsD the oronoi ell ssoited to the seed p i ∈ P D denoted s V (p i )D orresponds to the region in whih the points re loser to p i thn to ny other seed in P

  SFPX erformne of the polygonl prtitioning lgorithm on di'erent imge sizes @hurh from pigure PFID nd wnhttnGhenver from pigure SFPA in terms of running time nd memory onsumptionF xote tht the totl exeution times for wnhttn nd henver re di'erent from those listed in le SFI euse hereD the input imges re the entire ity senes insted of the overlpped res of stereo

		church (154Kpixels) Manhattan (39.1Mpixels) Denver (104Mpixels)
	line extraction	36ms	29.9s	114.2s
	consolidation	3ms	9.1s	107.4s
	anchoring	3ms	2.7s	32.7s
	homogenization	32ms	10.2s	48.4s
	total time	72ms	51.9s	302.7s
	memory peak	12.63Mb	372.20Mb	756.26Mb

le pirF prmeter n is shown in pigure SFIHF

www.cgal.org

mthing regions for stereoF ome pplitions presented in eppendix UFI illustrte the potentil of our pproh in isionF he use of lineEsegments is however not fully dpted to imges with wek geometri signturesF sn the future workD it is possile to investigte the use of