Maria Biosca

Merce Coll

Florian Lagarde

Emma Bremond

Lucie Routaboul

Eric Manoury
email: eric.manoury@lcc-toulouse.fr.

Oscar Pamies

Rinaldo Poli

Montserrat Dieguez
email: montserrat.dieguez@urv.cat.

Mercè Coll

Emma Brémond

Oscar Pàmies

Montserrat Diéguez

Chiral ferrocene-based P,S ligands for Ir-catalyzed hydrogenation of minimally functionalized olefins. Scope and limitations

come

Introduction

One of the most challenging tasks of organic chemistry is the synthesis of chiral compounds, which are necessary intermediates in the preparation of a wide range of pharmaceutical, agrochemical, fine chemical and natural products. 1 Up to date, asymmetric hydrogenation, the atom-economical addition of H2 to a C=X (X = C, N or O) bond to obtain chiral compounds is one of the most efficient, sustainable and straightforward chirality-generating process.1 ,2 For the enantioselective hydrogenation of minimally functionalized olefins, Ir complexes with chiral P,N ligands have shown to be effective catalysts that complement the well-developed Rh/Ru catalysts for functionalized olefins. 3 Since the application of Ir-phosphine-oxazoline PHOX chiral catalysts in 1998 by Pfaltz and coworkers, 4 researchers have focused on Ir-catalysts based on a wide range of P-oxazoline ligands. 5 These new Ir-catalysts have significantly broadened the substrate scope. Despite the advances in Ir-based P-N catalysts, their activity and selectivity for reducing some significant minimally functionalized olefins still needs to be improved, especially since the demand for new optically active chiral centers has moved researchers into the Ir-catalyzed asymmetric reduction of more "exotic" substrates. This will require novel, highly efficient chiral ligands that are easier to handle, readily accessible, and that enhance the application range. In this respect, research has progressed to heterodonor P,X-ligands bearing more robust X-donor groups than oxazolines (pyridines, 6 amides, 7 thiazoles, 8 thiazolines, 9 oxazoles, 10 etc.). Some of us have recently described the successful use of non-N-donor heterodonor ligands, the phosphorus-thioether ligands, for the enantioselective Ir-catalyzed reduction of minimally functionalized olefins. 11 Ir-complexes modified with two families of Pthioether ligands efficiently catalyzed the hydrogenation of a large range of olefins, with results comparable to the best ones reported in the literature. Despite this success, other thioether-P ligands have not yet been reported and research is in progress to study the possibilities of this new class of ligands for this process. Some of us have been involved for several years in the development of chiral ferrocene-based ligands for asymmetric catalysis. 12 Ferrocene-based ligands have been successfully employed in asymmetric catalysis for more than three decades. 13 They are particularly interesting because of the facile introduction of different chiralities (planar and central), their particular stereoelectronic properties and their high stability.

Although they have emerged as a privileged ligand structures for asymmetric catalysis, their use in the Ir-catalyzed hydrogenation of minimally functionalized olefins has been scarce. 14 Because we are interested in more versatile and robust Ir-catalysts, we took one further step and tested ligands that incorporate the advantages of ferrocenes and the robustness of the thioether moiety. To this end, we tested a family of modular ferrocene phosphine-thioether ligands 1-12 (Figure 1) in the Ir-catalyzed hydrogenation of 34 minimally functionalized alkenes, including concrete examples with neighboring polar groups. The selection of chiral ligands contemplates systematic variations of the electronic and steric properties of the thioether moiety (ligands 1-9), [START_REF]These ligands have been applied in allylic substitution reactions, methoxycarbonylation and hydrogenation of alkynes, imines and ketones[END_REF] the removal of the methylene spacer between the ferrocene and the thioether groups (ligand 10), [START_REF] Arrayas | Fesulphos ligand 10 has been successfully used in several asymmetric metalcatalyzed reactions (i.e. 1,3-dipolar cycloadditions, aza-Diels Alder and Mannich reactions, allylic substitution[END_REF] as well as introducing a second stereogenic center in the methylene spacer (ligands 11-12) [START_REF] Zeng | These ligands have been applied in hydrosilylation, [3+2] cycloaddition and allylic substitution reactions[END_REF] .

Figure 1. Ferrocene-based phosphine-thioether ligands 1-12

Results and discussion

Synthesis of Ir-catalyst precursors

The Ir-catalyst precursors were prepared in a two-step, one-pot procedure (Scheme 1). In the first step, the appropriate ligand reacts with 0.5 equivalent of [Ir(-Cl)(cod)]2 for 1 h at reflux. Then, Cl -/BArF -counterion exchange was achieved by a reaction with sodium tetrakis [3,5-bis(trifluoromethyl)phenyl]borate (NaBArF) (1 equiv) in the presence of water at room temperature. The iridium catalyst precursors were isolated in pure form as air-stable orange solids in excellent yields (89-91%).

Scheme 1. Preparation of Ir-catalyst precursors [Ir(cod)(1-12)]BArF

The elemental analyses were in agreement with the assigned structures. The HRMS-ESI spectra of [Ir(cod) (1-12)]BArF displayed the heaviest ions at m/z which correspond to the loss of the BArF anion from the molecular species. Crystals suitable for X-ray diffraction analysis of [Ir(cod)(4)]BArF complex were also obtained in order to determine the coordination mode of the ferrocene-based phosphine-thioether ligands (Figure 2). The six-membered chelate ring adopted a boat conformation, with the thioether substituent in an equatorial position and the sulfur in an R configuration as has already been observed for similar complexes. The 1 H, 13 C, and 31 P NMR spectra show the expected pattern for these C1-complexes.

The VT-NMR spectra in CD2Cl2 (+35 to -75 °C) indicate the presence of a single isomer in all cases except for [Ir(cod) (8)]BArF and [Ir(cod) (12)]BArF that were mixtures of two isomers in equilibrium at a ratio of 1:2 and 1:6, respectively. These isomers may be attributed to the two possible diastereoisomers formed when the thioether coordinates to the metal atom (note that the coordinated S atom is a stereogenic center), to different conformers for the six-membered chelate ring, or to both. To obtain the spatial orientation of the thioether substituent and the conformation adopted by the sixmembered chelate ring we initially performed NOESY experiments of [Ir(cod)(4)]BArF and [Ir(cod) (12)]BArF. Since the NOE contacts for Ir/4 were not conclusive, we studied the [Ir(cod) (9)]BArF analogue instead.

For complex [Ir(cod) (9)]BArF and the major isomer of [Ir(cod) (12)]BArF, the NOE indicated interactions between one of the methyl groups of the thioether xylyl substituent and the phenyl group of the phosphine moiety and of that same methyl group with either the methyl substituent (for Ir/12) or one of the hydrogen atoms (for Ir/9) at the alkyl backbone chain (Figure 3a). In addition, the NOE indicated interactions of the other xylyl methyl group with the other hydrogen of the alkyl backbone chain and with the unsubstituted cyclopentadiene ring. These interactions can be explained assuming an equatorial disposition of the thioether group and a boat conformation of the six-membered chelate ring with an R configuration of the sulfur atom (Figure 3a), as in the X-ray structure of [Ir(cod)(4)]BArF (see Figure 2). For the minor isomer of [Ir(cod) (12)]BArF, we found NOE interactions between one of the xylyl methyl groups and the phenyl group of the phosphine moiety and with the hydrogen at the alkyl backbone chain (Figure 3b). We also observed NOE contacts between the methyl substituent at the alkyl backbone chain and the substituted cyclopentadiene ring. All these NOE contacts are in agreement with a boat conformation of the six-membered chelate ring and the thioether substituent in an equatorial disposition but, in contrast to previous isomers, with an S configuration of the sulfur atom (Figure 3b). The assignments of the isomers of [Ir(cod) (12)]BArF were further confirmed by DFT studies. Figure 4 shows these calculated structures and the relative values of the formation enthalpy, being the isomer with an R configuration of the sulfur atom the most stable. Complexes [Ir(cod)( 8)]BArF and [Ir(cod) (12)]BArF are the first examples of incomplete control of the sulfur chirality upon coordination for ferrocenyl phosphine-thioethers with this type of backbone: only one diastereoisomer was observed for all previously reported complexes, whatever the metal or the oxidation state. 18,19 Major isomer (0 KJ/mol)

Minor isomer (11.8 KJ/mol) Figure 4. Calculated structures (DFT) for cationic species of complex [Ir(cod)( 12)]BArF and their relative formation enthalpies.

Asymmetric Ir-catalyzed hydrogenation

Asymmetric hydrogenation of minimally functionalized olefins is highly sensitive to the steric demands of the substrate.3 Unlike trisubstituted olefins, 1,1-disubstituted olefins have not been successfully hydrogenated until very recently.3 e,h This is because the catalyst must control not only the face selectivity coordination (only two substituents compared with the three in trisubstituted olefins), but also the isomerization of the olefins to form the more stable E-trisubstituted substrates, which are hydrogenated to form the opposite enantiomer. Tetrasubstituted olefins also remain an unsolved class of substrate.3 f,h The only Ir-catalysts that react with them with high yields and enantioselectivities contain the less bulky phosphanylmethyloxazoline ligands reported by Pfaltz. 20 In order to evaluate the efficiency of ferrocene-based P-S ligands 1-12 in the hydrogenation of olefins with different steric demands, we initially tested them in the asymmetric reduction of the model tri-, di-and tetrasubstituted substrates S1-S3 (Table 1).

Although low-to-moderate enantioselectivities were achieved in the reduction of tetrasubstituted substrate S3, high enantioselectivities were obtained in the hydrogenation of model tri-and disubstituted substrates (ee's up to 85% and 82% for S1 and S2, respectively). The results also indicated that the ligand components need to be properly tuned for each substrate to maximize the enantioselectivities. For instance, while for S1 the best enantioselectivities were obtained with ligand We next evaluated the new Ir/1-12 catalyst precursors in the hydrogenation of a selected range of trisubstituted substrates, most of them with neighbouring polar groups.

The reduction of substrates with neighbouring polar groups has a large interest because they are relevant intermediates for the synthesis of highly valued chemicals. The most remarkable results are shown in Figure 5 (see SI for a complete set of results). We first considered the reduction of aryl/alkyl substrates with Z-geometry S4-S6, which are usually hydrogenated less enantioselectively than E-trisubstituted olefins like S1. 3 Unfortunately, as previous studies had already suggested, enantiocontrol was only moderate (ee's up to 46%). On the other hand, [Ir(cod)(4)]BArF was very efficient in the reduction of several ,-unsaturated esters S7-S11. 21 The ee's were between 95-98% and quite independent on the electronic nature of the substrate phenyl ring and on the substituent cis to the ester group. Being able to hydrogenate ,-unsaturated esters at such high ee's is of great importance because chiral carboxylic ester derivatives with tertiary benzylic aliphatic stereogenic centres are found in many fragrances, pharmaceuticals and natural products. 22 This methodology represents a more sustainable route for producing these chiral carboxylic esters than other common methods such as the Co-catalyzed asymmetric conjugated reduction of ,-unsaturated esters using sodium borohydride 23 and the Cu-and Rh-catalyzed 1,4-reduction using very moisturesensitive hydrosilane reagents 24 . We then studied the reduction of alkenylboronic esters u,v,25 The hydrogenation of the model -unsaturated enone S14 proceeded with moderate enantiocontrol (ee's up to 47%). However, it was very interesting to find that enantioselectivities increased up to 85% in the hydrogenation of more challenging cyclic enones S15 and S16.5 v These latter results prompted us to focus on the hydrogenation of other difficult olefins, such as enamide S17, 26 lactone S18 27 and enol phosphinates S19-S23 28 . Very few catalytic systems can provide high enantioselectivities for these substrates so it was remarkable that we could achieve highto-excellent enantioselectivities in all of them by carefully tuning the ligand components. Thus, in the reduction of enamide S17 and lactone S18, the highest enantioselectivities (up to 90%) were achieved using [Ir(cod)(11)]BArF and [Ir(cod) (10)]BArF, respectively. [Ir(cod) (10)]BArF was also extremely efficient in the reduction of a range of sterically demanding enol phosphinates, including examples of pure alkyl-substituted enol phosphinates (Figure 5; S19-S23), providing comparable high enantioselectivities to those achieved with the best ones reported (ee's between 92-99%). The effective hydrogenation of this type of substrates opens up an appealing route for obtaining chiral organophosphinates, which can be easily transformed into high-value compounds such as alcohols and phosphines.

Then we focused our attention on extending the range of disubstituted substrates (Figure 6). Our results with several -alkylstyrenes bearing decreasingly sterically demanding alkyl substituents (S2, S24 and S25) indicated that enantioselectivity is affected by the nature of the alkyl chain (ee's ranging from 14% to 82%). A plausible explanation is the competition between direct hydrogenation and isomerization. This is supported by the fact that the hydrogenation of substrate S2 bearing a tert-butyl group, which cannot isomerize, provides the highest enantioselectivity. We then tested a wide range of α-tert-butylstyrene type substrates (S26-S32) to evaluate how the electronic and steric properties of the aryl group of the substrate affected the catalytic performance. The highest enantioselectivities (up to 90%) of the series were achieved in the reduction of substrates containing electrondonating groups at the para-position of the aryl group (substrates S26 and S27). Finally, we studied whether the excellent enantioselectivities obtained in the hydrogenation of trisubstituted enol phosphinates (S19-S23, Figure 5) are maintained for the even more demanding disubstituted analogues S33 and S34. Again,

[Ir(cod) (10)]BArF was able to successfully hydrogenate these substrates with excellent enantioselectivities comparable to the best ones reported. 29

Conclusions

Stable cationic iridium(cod) complexes with different P,S ligands proved to be good precatalysts for the asymmetric hydrogenation of minimally functionalized olefins in terms of activities and enantioselectivities. For many substrates, the ligand fine tuning, thanks to its high modularity, enabled achieving good to excellent levels of enantioselectivity, underlining their promising potential. Therefore, these new Ircatalysts compete well with the state of art not only for model trisubstituted ,unsaturated esters S7-S11, 21 but also for demanding di-and tri-substituted enol phosphinates S19-S23 28 and S33-S34 [START_REF] Cheruku | Only two catalytic systems have provided high enantioselectivities[END_REF] . In addition promising high enantioselectivities have been achieved for challenging cyclic enones S15-S16,5 v and alkenes bearing benzyl amide 26 (S17) and -lactone 27 (S18) groups.

Experimental Section

General considerations

All reactions were carried out using standard Schlenk techniques under an argon atmosphere. Solvents were purified and dried by standard procedures. Phosphine-thioether ligands 11 17b and 12 30 were prepared as previously reported. 1 H, 13 C, and 31 P NMR spectra were recorded using a 400 MHz or a 300 MHz spectrometer. Chemical shifts are relative to that of SiMe4 ( 1 H and 13 C) as internal standard or H3PO4 ( 31 P) as external standard. 1 H and 13 C assignments were made on the basis of 1 H-1 H gCOSY and 1 H-13 C gHSQC. Geometries of isomers of [Ir(cod) (12)]BArF were optimized using the Gaussian 09 program, [START_REF] Frisch | Revision A.02[END_REF] employing the B3LYP 32 density functional and the LANL2DZ 33 basis set for iridium and iron and the 6-31G* basis set for all other elements. 34 Solvation correction was applied in the course of the optimizations using the PCM model with the default parameters of dichloromethane. 35 The complexes were treated with the charge +1 and in singlet state. No symmetry constraints were applied.

The energies were further refined by applying dispersion correction using the DFT-D3 36 model. All energies reported are Gibbs free energies at 298.15 K and calculated as Greported = G6-31G* + EDFT-D3

General procedure for the preparation of ligands 1-9

Ligands 1-4 and 6-7 were prepared as previously reported. 15a The ligands 5, 8 and 9

were prepared using the same method from enantiomerically pure (R)-(2diphenylthiophosphinoferrocenyl)methanol (100 mg, 0.23 mmol) 12c and the corresponding thiol in protecting form 5-S, 8-S and 9-S as thiophosphine-thioethers.

The deprotected (P,S) ligands were obtained by reaction of the protected forms with P(NMe2)3 15a and immediately engaged in the coordination reaction.

5-S:

Yield 131 mg (97%). [START_REF] Frisch | Revision A.02[END_REF]

5:

Yield 114 mg (92%). [START_REF] Frisch | Revision A.02[END_REF] P NMR (162 MHz, CDCl3), δ: -23.5. 1

8-S:

Yield 110 mg (83%). [START_REF] Frisch | Revision A.02[END_REF] of the solvent gave a brown-orange solid, which was purified by flash chromatography on neutral silica (dichloromethane/petroleum ether (1/1) as eluent) to produce the corresponding complex as an orange solid.

[Ir(cod)(1)]BArF: Yield 105.9 mg (89%). [START_REF] Frisch | Revision A.02[END_REF] P NMR (162 MHz, CDCl3), : 9.5 (s);

18

 18

Figure 2 .

 2 Figure 2. X-ray structure of [Ir(cod)(4)]BArF (CCDC 1033867) (the hydrogen atoms and BArF -anion have been omitted for clarity)

Figure 3 .

 3 Figure 3. Main NOE contacts for (a) [Ir(cod)(9)]BArF (X= H) and major isomer of [Ir(cod)(12)]BArF (X= Me) and (b) minor isomer of [Ir(cod)(12)]BArF.

Figure 5 .

 5 Figure 5. Selected results for the hydrogenation of trisubstituted olefins S4-S23 using [Ir(cod)(1-12)]BArF catalyst precursors. Reaction conditions: 1 mol % catalyst precursor, CH2Cl2 as solvent, 100 bar H2, 4 h. a Reaction carried out for 18 h.

S12

  and S13 which would form versatile chiral C-B bonds that can later become C-N, C-O and C-C bonds. The hydrogenation of alkenes containing one or two pinacolatoboron groups proceeded smoothly with enantioselectivities as high as 76%. Another important class of substrates that is receiving much attention are the -unsaturated enones. The hydrogenation of these substrates is an elegant path for obtaining ketones with a stereogenic center in the  position of the carbonyl moiety. Nonetheless, they have been less studied and less successfully hydrogenated than other trisubstituted olefins.5 i,

Figure 6 .

 6 Figure 6. Selected results for the hydrogenation of 1,1-disubstituted olefins S24-S34 using [Ir(cod)(1-12)]BArF catalyst precursors. Reaction conditions: 1 mol % catalyst precursor, CH2Cl2 as solvent, 1 bar H2, 4 h. a Reactions carried out for 18 h.

  P{1 H} NMR (121 MHz, CDCl3), δ: 41.7.1 H NMR (300 MHz, CDCl3), δ: 1.63(m, 6H, CH2, Ad), 1.75 (m, 6H, CH2, Ad), 1.97 (m, 3H, CH, Ad), 3.72 (s, 1H, CH=, Cp), 3.90 (br d, 1H, CH2, 2 JH-H = 13.0 Hz),3.98 (br d, 1H, CH2, 2 JH-H = 13.0 Hz), 4.29(s, 1H, CH=, Cp), 4.36 (s, 5H, CH=, Cp), 4.66 (s, 1H, CH=, Cp), 7.55- 7.35 (m, 6H, CH=), 7.66 (m, 2H, CH=), 7.86(m, 2H, CH=).13 C{ 1 H} NMR (75 MHz, CDCl3), δ: 23.7 (CH2), 29.7 (CH, Ad), 36.3 (CH2, Ad), 43.3 (CH2, Ad), 44.8 (C, Ad), 69.0 (d, JC-P = 10.5 Hz, CH=, Cp), 70.9 (Cp), 73.4 (d, JC-P = 9.3 Hz, CH=, Cp), 74.0 (d, JC-P = 94.6 Hz, C, Cp,) 74.2 (d, JC-P = 12.7 Hz, CH=, Cp), 90.2 (d, JC-P = 12.0 Hz, C, Cp), 128.0 (d, JC-P = 12.4 Hz, CH=), 128.1 (d, JC-P = 12.5 Hz, CH=), 131.1 (d, JC-P = 3.0 Hz, CH=), 131.2 (d, JC-P = 3.0 Hz, CH=), 132.1 (d, JC-P = 10.6 Hz, CH=),1 32.3 (d, JC-P = 10.6 Hz, CH=), 133.6 (d, JC-P = 86.0 Hz, C), 134.6 (d, JC-P = 87.1 Hz, C). HR/MS (ESI) m/e: 582.1273 (M, 100 %; calculated for C33H35PS2Fe: 582.1267).

  9 (C, Ad), 69.5 (CH=, Cp), 70.0 (CH=, Cp), 71.1 (d, JC-P = 3.8 Hz, CH=, Cp), 71.5 (d, JC-P = 3.8 Hz, C, Cp,) 75.7 (d, JC-P = 10.2 Hz, CH=, Cp), 91.3 (d, JC-P = 25.1 Hz, C, Cp), 125.4 (C), 127.8 (CH=), 128.0 (d, JC-P = 6.0 Hz, CH=), 128.3 (d, JC-P = 7.6 Hz, CH=), 128.4 (C), 129.2 (d, JC-P = 6.2 Hz, CH=), 132.6 (d, JC-P = 17.5 Hz, CH=), 135.3 (d, JC-P = 21.3 Hz, CH=), 137.7 (d, JC-P = 8.3 Hz, C), 140.0 (d, JC-P = 9.1 Hz, C). TOF-MS (ESI+): m/z = 550.1546, calcd. for C33H35FePS [M] + : 550.1547).

  Hz, C, Cp), 90.4(d, JC-P = 25.9 Hz, C, Cp), 127.8(CH=), 127.9(CH=), 128.0 (CH=), 128.1 (CH=), 128.2 (CH=), 129.1 (CH=), 132.5 (d, JC-P = 18.2 Hz, CH=), 134.2 (C), 135.2 (d, JC-P = 21.3 Hz, CH=), 137.6 (d, JC-P = 8.3 Hz, C), 139.7 (d, JC-P = 9.1 Hz, C), 143.1 (C). TOF-MS (ESI+): m/z = 520.1074, calcd. for C31H29FePS [M] + : 520.1077).General procedure for the preparation of [Ir(cod)(1-12)]BArFThe corresponding ligand (0.074 mmol) was dissolved in CH2Cl2 (5 mL) and [Ir(µ-Cl)(cod)]2 (25.0 mg, 0.037 mmol) was added. The reaction mixture was refluxed at 40 ºC for 1 hour. After 5 min at room temperature, NaBArF (77.2 mg, 0.080 mmol) and water (5 mL) were added and the reaction mixture was stirred vigorously for 30 min at room temperature. The phases were separated and the aqueous phase was extracted twice with CH2Cl2. The combined organic phases were dried with MgSO4. Evaporation

( d , 2 (

 d2 JC-P = 5.2 Hz, CH=, Cp), 70.9(CH=, cod and CH=, Cp), 72.3 (CH=, cod), 73.CH=, Cp), 76.0 (d, JC-P = 7.0 Hz¸CH=, Cp), 84.3 (d, 2 JC-P = 15.5 Hz, C, Cp), 90.5 (d, JC-P = 14.6 Hz, CH=, cod), 90.7 (d, JC-P = 14.6 Hz, CH=. cod), 117.4 (b, CH=, BArF), 120.4-134.2 (aromatic carbons), 134.7 (b, CH=, BArF), 161.7 (q, 1 JC-B = 48.8 Hz, C-B, BArF). TOF-MS (ESI+): m/z = 745.1336, calcd. for C65H49BF24FeIrPS [M-BArF] + :

Table 1 .

 1 12 (entry 12), containing both planar and central chirality and a bulky 2,6-dimethylphenyl thioether substituent, the highest enantioselectivities for S2 were achieved with ligands 4 and 10 Ir-catalyzed hydrogenation model substrates S1-S3 a

	(entries 4 and 10), containing only planar chirality and a bulky tert-butyl thioether
	group. Interestingly, for disubstituted substrate S2 both enantiomers of the
	hydrogenated products could be obtained in high enantioselectivity by simply selecting
	the planar chirality. We also studied the reaction of model substrates S1 and S2 at low
	catalyst loading (0.25 mol%) using ligand 12, and the enantioselectivities and
	conversion (95% for S1 and 99% for S2) were maintained (entry 13).
	Entry Ligand	% Conv b % ee c	% Conv b % ee c	% Conv b % ee c
	1	(Rp)-1	100	25 (S)	100	22 (S)	75	9 (R)
	2	(Rp)-2	100	0	100	30 (S)	<5	nd
	3	(Rp)-3	100	10 (S)	100	33 (S)	<5	nd
	4	(Rp)-4	100	50 (R)	100	81 (S)	70	32 (R)
	5	(Rp)-5	100	46 (S)	100	73 (S)	60	34 (R)
	6	(Rp)-6	100	11 (S)	100	34 (S)	85	6 (R)
	7	(Rp)-7	100	30 (S)	100	16 (S)	35	8 (R)
	8	(Rp)-8	100	24 (S)	100	32 (S)	65	6 (R)
	9	(Rp)-9	100	50 (R)	100	26 (S)	49	10 (S)
	10	(Rp)-10	100	15 (S)	100	82 (R)	95	4 (R)
	11	(Rp,S)-11	100	29 (S)	100	3 (R)	100	9 (R)
	12	(Rp,S)-12	100	85 (S)	100	46 (R)	100	12 (S)
	13 d (Rp,S)-12	95	84 (S)	99	46 (R)	-	-

a Reactions carried out at room temperature using 0.5 mmol of substrate and 1 mol% of Ir-catalyst precursor at 100 bar of H2 (for substrates S1 and S3) and 1 bar (for S2) with dichloromethane (2 mL) as solvent.

b

Conversion measured by

1

H-NMR after 4 h (for S1 and S2) and after 18 h (for S3).

c

Enantiomeric excess determined by GC.

d

Reactions carried out at 0.25 mol% of Ir-catalyst precursor.

  NMR (400 MHz, CDCl3), : 1.12 (t, 3H,3 JH-H = 7.6 Hz, CH3), 1.56 (m, 1H, CH2, cod),1.71 (m, 1H, CH2, cod), 2.06 (m, 1H, CH2, cod), 2.32 (m, 1H, CH2, cod), 2.45 (m, 3H, CH2, cod), 2.64 (m, 1H, CH2, Et), 2.78 (d, 1H, 2 JH-H = 12.4 Hz, CH2-S), 2.91 (m, 1H, CH2, Et), 3.47 (m, 1H, CH=, cod), 3.57 (m, 1H, CH=, cod), 4.00 (d, 1H, 2 JH-H = 12.4 Hz, CH2-S), 4.05 (s, 1H, CH=, Cp), 4.41 (m, 1H, CH=, Cp), 4.47 (s, 6H, CH=, Cp), 4.63 (m, 1H, CH=, cod), 4.94 (m, 1H, CH=, cod), 7.3-7.8 (m, 22H, CH=); 13 C NMR (100 MHz, CDCl3), : 14.6 (CH3), 27.4 (CH2, cod), 29.2 (CH2, cod), 31.2 (CH2),31.6 (CH2, cod), 33.7 (CH2, Et), 35.0 (CH2, cod), 63.7 (d, 1 JC-P = 63.6 Hz, C, Cp), 68.8

1 H

H NMR (400 MHz, CDCl3), : 1.09 (s, 9H, CH3, t Bu), 1.68 (m, 1H, CH2, cod), 1.84(m, 1H, CH2, cod),

2.16 (m, 2H, CH2, cod), 2.32 (m, 1H, CH2, cod), 2.42 (m, 1H, CH2,

Acknowledgements

We thank the Spanish Government for providing grant CTQ2013-40568, the Catalan Government for grant 2014SGR670, and the ICREA Foundation for providing M.

Diéguez and O. Pàmies with financial support through the ICREA Academia awards.

We also thank the Centre National de la Recherche Scientifique, the Institut Universitaire de France, and the Laboratoire Européen Associé "Laboratoire Trans-Pyrénéen: de la Molécule aux Matériaux" for additional support.

General procedure for the hydrogenation of olefins

The alkene (0.5 mmol) and Ir complex (1 mol %) were dissolved in CH2Cl2 (2 mL) in a high-pressure autoclave, which was purged four times with hydrogen. Then, it was pressurized to the desired pressure. After the desired reaction time, the autoclave was depressurized and the solvent evaporated off. The residue was dissolved in Et2O (1.5 ml) and filtered through a short Celite plug. The enantiomeric excess was determined by chiral GC or chiral HPLC and conversions were determined by 1 H NMR. The enantiomeric excesses of hydrogenated products from S1-S5, 10a S6, 37 S7, 10a S8-S9,5 o S10, 38 S11,5 o S12, 39 S13, 40 S14,5 i S15-S16,5 v S17, 26a S18, 27b S19-S23, 28a S24, 41 S25, 10a S26-S32, 42 S33, 29a S34, 28a were determined using the conditions described previously.


Jean-Baptiste Bordes

Henri Maître

Automatic Semantic Network Construction for Multi-Layer Annotation of Satellite Images

A novel method is presented for annotating satellite images. The labels used for annotation are given by a user with a set of example images. A learning step is then applied to learn the model. The originality of the method is to formulate the problem of semantic annotation to a further extent than a mere probabilistic classification task. The method takes into account the semantical relationships between the concepts by considering a duality between the structure of the model and the structure of the set of labels. The semantical structure of the labels is represented by a semantic network containing three semantical relationships: synonymy, meronymy, and hyponymy. The semantic network is constrained in a hierarchy induced by the links of hyponymy and meronymy. By a procedure of MDL model selection, it is possible to find the optimal semantical structure of the set of labels.

Introduction 1.State of the art

The last two decades have seen the emergence of large image databases of various types. The spread of digital cameras and the increase of power and archiving ability of the computers have resulted in a growing need for the efficient handling of large databases of personal images. As for the field of remote sensing, a large variety of space-borne and air-borne sensors provide every day a huge quantity of information about the surface of the Earth, and this amount is getting even more enormous with the arriving generation of high-resolution satellite sensors.

Reliable image retrieval and indexing has thus become a major problem to efficiently access this information, driving an important amount of studies on 1 the topic of content-based image retrieval. As a response to this demand, the early works made a direct use of low-level features extracted from the images [START_REF] Newsam | Using texture to analyze and manage large collections of remote sensed image and video data[END_REF][START_REF] Smith | Querying by color regions using visualseek content-based visual query system[END_REF][START_REF] Faloutsos | Efficient and effective querying by image content[END_REF][START_REF] Hafner | Efficient color histogram indexing for quadratic form distance functions[END_REF] and focused on the "query-by-example" request. Low-level descriptors computed from the documents are compared to those extracted in the user provided example images, and the images returned to the user are those with the least distance in the feature space. But it is now widely acknowledged that significative improvements in indexing systems require to build a bridge over the so-called semantic gap existing between the low-level features extracted in the images and semantic concepts [START_REF] Hare | Mind the gap: another look at the problem of the semantic gap in image retrieval[END_REF].

In recent systems, image indexation and retrieval are based most of the time on the annotation of the database by a set of words describing the content of each image, enabling the user to specify the query through a natural language description of the concepts of interest. The earliest researches focused mainly on supervised learning schemes of specific semantics: differentiating indoor from outdoor scenes [START_REF] Szummer | Indoor-outdoor image classification[END_REF], photographs from paintings [START_REF] Cutzu | Distinguishing paintings from photographs[END_REF], bodies of humans and animals [START_REF] Forsyth | Body plans[END_REF], cities from landscapes [START_REF] Vailaya | On image classification: City vs. landscape[END_REF], natural scenes [START_REF] Maron | Multiple-instance learning for natural scene classification[END_REF]. In these studies, a set of training images with and without the concept of interest was collected and a binary classifier trained to detect this concept. This classifier was then applied to the images of the whole database which were therefore annotated with respect to the presence or absence of the concept.

More recent researches tackle the problem differently by posing the problem of annotation as the inference of latent variables that encode the hidden semantic classes. They were encouraged by the results of topics extraction in textual data [START_REF] Hofmann | Probabilistic latent semantic indexing[END_REF][START_REF] Blei | Latent dirichlet allocation[END_REF][START_REF] Rosen-Zvi | The authortopic model for authors and documents[END_REF] and draw an analogy with retrieval in textual data by considering visual words. Visual words belong to a discrete collection obtained by quantization of low-level features and processed as the words of a text [START_REF] Zisserman | Video google: a text retrieval approach to object matching in videos[END_REF]. In [START_REF] Kang | Regularizing translation models for better automatic image annotation[END_REF][START_REF] Duygulu | Object recognition as machine translation: Learning a lexicon for a fixed image vocabulary[END_REF], the annotation process is considered as translating the content from a visual language to a set of textual words and the learning process is identical to learning a lexicon from an aligned bitext. In [START_REF] Jeon | Automatic image annotation and retrieval using cross-media relevance models[END_REF], annotation is made through a cross-media relevance model, inspired by the relevance models introduced for cross-lingual retrieval [START_REF] Lavrenko | Cross-lingual relevance models[END_REF]. In [START_REF] Monay | On image auto-annotation with latent space models[END_REF][START_REF] Monay | Plsa-based image auto-annotation: constraining the latent space[END_REF], an exchangeability assumption is applied for the visual words and the pLSA model is applied for annotation. In [START_REF] Blei | Modeling annotated data[END_REF], three probabilistical models of annotation are presented, inspired from various text models like LDA [START_REF] Blei | Latent dirichlet allocation[END_REF].

During training, a set of labels is assigned to each image, the image is segmented into a collection of regions (either using a regular block-based decomposition [START_REF] Mori | Image-to-word transformation based on dividing and vector quantizing images with words[END_REF], or using a traditional segmentation method using directly the low-level features computed in the image [START_REF] Barnard | Matching words and pictures[END_REF]) and an unsupervised learning algorithm is run over the entire training set to estimate the joint density of semantic labels and visual features.

In these studies, the semantic labelling is thus seen as a problem of classification. Classes correspond to latent variables which have no semantic relationship between them. The semantic is introduced by the user during the annotation stage when providing a vocabulary for annotation and example images for each annotation label. Stochastic models for each model are built independantly for each label, and the semantic relationships among labels are not taken into account. Moreover, the labels are treated similarly for learning and annotation even if they are often very different in terms of semantic complexity and specificity and even if they can correspond to areas of various typical sizes.

In the KIM system [START_REF] Daschiel | Image information mining system evaluation using information-theoretic measures[END_REF], this hierarchy of the information is taken into account and modelized by a hierarchy distributed in five layers. Symbolic values, free of semantic, are infered by unsupervised learning at the four first layers. The semantic labels, introduced by the user, lie at the fifth layer and are linked to the symbolic values by the user interaction. The relation between layers is estimated using information-theoretic quantities. However, in this system, all the concepts lie on a single semantic layer and have no semantic relationship between them. There has been only few attempts to exploit the relationships between the semantic labels. Barnard and Forsyth, motivated by the statistical models proposed by Hoffman and Puzicha [START_REF] Hofmann | Statistical models for co-occurrence data[END_REF], adapted the hierarchical clustering for image annotation [START_REF] Barnard | Matching words and pictures[END_REF]. The hierarchy of models for generating words and image segments is derived from clustered images in the training set. Clusters capture contextual similarities while nodes capture generality of concepts. Words and blobs are then represented over the nodes of a hierarchy. Hierarchies induced by image clusters provide semantic interpretation for the models.

More generally, an efficient way to take into account the relationships between labels and to obtain a high-level scene description is the use of semantic net [START_REF] Srikanth | Exploiting ontologies for automatic image annotation[END_REF]. Semantic networks contain nodes and links and are defined as directional acyclic graphs. They have been widely used for multimedia annotation. Naphade proposed the MultiNet as a way to represent highlevel dependencies between concepts [START_REF] Milind | A factor graph framework for semantic indexing and retrieval in video[END_REF] and to take into account the mutual information between concepts. However, both classes and structure of the classification framework were decided by experts. Moreover the structure becomes very large when the number of classes increases. Benitez proposed a more general approach with MediaNet for video annotation in which the salient classes are automatically selected from annotated images and the relationships between concepts are discovered by using external knowledge resources from WordNet [START_REF] Shih | Medianet: A multimedia information network for knowledge representation[END_REF]. The relationships between concepts in MediaNet are divided in perceptual relationships (such as looks similar to) and semantic relationships (such as meronymy/holonymy).

For image interpretation, semantic networks describe stuctural relationships between the objects which are expected to be found in a scene and contain prior knowledge given by experts. For remote sensing images, literature provides several references of semantic networks application [START_REF] Liedtke | Aida: A system for the knowledge based interpretation of remote sensing data[END_REF][START_REF] Kummert | Control and explanation in a signal understanding environment[END_REF][START_REF] Tnjes | Knowledge based interpretation of remote sensing images using semantic nets[END_REF][START_REF] Niemann | Ernest: A semantic network system for pattern understanding[END_REF][START_REF] Buckner | Semantic interpretation of remote sensing data[END_REF]. Devoted to the understanding of remote sensing data, the GeoAIDA system [START_REF] Buckner | Geoaida-a knowledge based automatic image data analyser for remote sensing data[END_REF] represents explicitly the knowledge given by photointerpreters in a hierarchical semantic network. This network contains two different types of node: the generalization nodes (comparable to logic xor ) and the compound nodes (comparable to logic and ). Each node carries information about the type of area it represents and possesses attributes which are also a part of the knowledge (for example, a road junction consists of three to six interescting roads). The interpretation strategy relies on fixed control rules. In [START_REF] Han | Bottom-up/top-down image parsing by attribute graph grammar[END_REF], semantic concepts are structured by and/or graphs [START_REF] Zhu | A stochastic grammar of images[END_REF][START_REF] Yao | Introduction to a large-scale general purpose ground truth database: methodology, annotation tool and benchmarks[END_REF] which are used for annotation of various types of images: outdoor scenes, faces, remote sensing data. An and/or graph is set in correspondence with the structure of a stochastic grammar. Given a test image, a parsing graph is formed by the production rules of the stochastic grammar and is defined as the image interpretation.

In such systems, adding a new concept requires an expert to add manually a new node in the structure of the semantic network and to build the edges linking this concept to others. However, some studies tried to solve the problem in greater generality and with higher flexibility by extracting these links automatically. In [START_REF] Oder | Interactive learning and probabilistic retrieval in remote sensing image archives[END_REF], when the user introduces a new concept, the concept is linked by some probability distributions to the low-level features and a distance is computed between this distribution and the other concepts distributions. If the distributions are too similar, the new concept is not added to the system. In [START_REF] Wang | Construction of semantic network for videos[END_REF], an algorithm is elaborated to learn the structure of the semantic network based on Bayesian decision.

Paradigmatic Semantic Labelling

In this work, we show that it is possible to infer automatically the links between labels from their properties learnt during the training stage. Moreover, we show that this influence results in a hierarchy of labels well described by a semantic net. The nodes of the network contain the semantic labels and the arcs contain paradigmatic relationships between the labels ("meronymy/holonymy", "hyponymy/hyperonymy", "synonymy"). The structure of the network is constrained in a hierarchy naturally induced by the paradigmatic relationships of meronymy and hyponymy and decomposed in a finite set of layers. This Paradigmatic Semantic Labelling (PSL) makes possible to annotate the test images in several layers, corresponding to differ-ent levels of generality and complexity. It maintains an efficient correspondance between the structure of the semantic networks and the structure of a stochastic image model.

Each label of the network is associated with a probabilistic model used to compute the likelihood of an image annotated by this label. The models depend on each other according to the paradigmatic relationhips between the labels. At the training stage, an annotated database is provided by the user and the model optimaly fitting this database is estimated. Both parameters and structure are determined using the Minimization of Stochastic Complexity criterion [START_REF] Rissanen | Stochastic Complexity in Statistical Inquiry Theory[END_REF], and the semantic network is thus deduced without ambiguity from this optimal model. We prove that these paradigmatic links can be infered with a training database consisting in a set of example images provided for each semantic label. A substantial amount of semantic information can thus be extracted from a weakly labelled training set. Given a new concept, the structure of the model is updated easily and adding new concepts increases the descriptive power of the database by the model (property of extensivity). Each model is fitted by taking into account the whole knowledge acquired by the system. We prove that this increases greatly the descriptive power of the images by the model.

As in [START_REF] Monay | Plsa-based image auto-annotation: constraining the latent space[END_REF][START_REF] Blei | Modeling annotated data[END_REF] and many other works previously cited, the PSL is based on modelisations inspired from text retrieval. The statistical models which will be introduced are based on visual words lying at the lowest level of the hierarchy. This layer contains a discrete collection of textons obtained from quantization of the low-level features extracted from the image. Moreover, the generation models which are used to estimate the likelihood of the textons are inspired from text retrieval methods. On top of this texton layer, three layers are devoted to express the semantic description. The hierarchy between these upper layers derives naturally from the relationships of hyponymy and meronymy [START_REF] Lyons | Language and Linguistics: an introduction[END_REF][START_REF] Cruse | Lexical Semantics[END_REF].

From a theoretical point of view, we have to answer three questions:

• First, which semantic concepts will be used to describe the image?

We have chosen the usual vocabulary of remote sensing, as familiar to any application expert: "city", "forest", "fields", etc.

• Second, which relationships do we expect between nodes ?

We have chosen to use the paradigmatic relationships which link concepts in semantic languages. As the hyponymy relationship orders the words by their generality, the meaning of the words will be all the more general that they lie in the highest layer of the hierarchy. For instance, "forest" will lie in a lower layer when "vegetation" will lie in a higher layer. The meronymy relationship corresponds to a global/part-of hierarchy, and the words describe regions which are all the more structured that they lie in the highest layer of the hierarchy. For instance, "factory" will lie in a lower layer when "suburb" will lie in a higher layer.

• The third question is How to derive automatically a correspondance between the structure of the model and a semantic network?

Each label of the semantic network is associated with a probabilistic model which is used to express the likelihood of the database of example images associated to the label. The concepts which lie in the lowest layer of the network are associated to a Naive Bayes model of the texton generation. If a label lies in a higher level of the hierarchy and is linked to a set of other words, the likelihood of the database is expressed with the models associated to these words, according to the nature of the link. By model selection, it is possible to determine the semantic network corresponding to the optimal model in terms of the database coding.

Following Smeulders, when attempting to bridge the semantic gap, we should also take into account the context [START_REF] Smeulders | Contentbased image retrieval at the end of the early years[END_REF]. In this work, since we only deal with remote sensing images, we make the simplifying assumption that all the images of the database correspond to the same context.

The paper is organized as follows: Section 2. details the global formalism used for the approach. Section 3. deals with the probabilistic modelling. Section 4. explains the coding of the model. Section 5. details the annotation of a test image using the model. Section 6. is devoted to experimental results.

Semantic representation 2.1 Semantic relationships

Semantic, as a field of linguistic, is based on the assumption that the words lie in their own space which is structured by the semantic relationships. It is now commonly acknowledged that the lexical units are structured by four different kinds of paradigmatic relationships [START_REF] Lyons | Language and Linguistics: an introduction[END_REF]: the synonymy, the antonymy, the hyponymy/hyperonymy, and the meronymy/holonymy. We describe here briefly these relationships in their linguistical meaning:

The relationship of synonymy It is based on the possibility to exchange two lexical units in a minimal context while keeping a stable meaning.

The relationship of antonymy It determines a relationship of opposition between two terms. Like synonymy, it links lexical terms of the same grammatical category. However, at a semantic level, antonymy differs from synonymy by its binarity and the four kinds of dichotomical oppositions it corresponds to: contradictory ("inside"/"outside"), polar ("short"/"long"), inverse ("go up/ go down"), reciproc ("buy/sell").

The relationship of hyponymy/hyperonymy J. Lyons creates these terms to specify the vertical structuration of the lexical units [START_REF] Lyons | Language and Linguistics: an introduction[END_REF]. The relationship of hyponymy corresponds to a specification: "cat" is hyponym of "animal". Reciprocally, the relationship of hyperonymy corresponds to a generalization. The logical implication which is linked to this relationship is: "if it is a cat, then it is an animal". Hyponymy is often refered to, in semantic networks, by a kind-of relationship.

The relationship of meronymy/holonymy The term of meronymy has been introduced by A. Cruse [START_REF] Cruse | Lexical Semantics[END_REF] to differentiate the "overall/part-of" hierarchical lexical relationship with the hyponymic relationship. Indeed, even if these two relationships share the properties of inclusion and asymmetry, their semantical meaning is different and their hierarchies are not compatible. Meronymy is often refered to, in semantic networks, by a part-of relationship.

For PSL, we choose not to take into account antonymy.

Considered links 2.2.1 Link of Synonymy

Two words are supposed to be synonyms if they describe the same type of region. Abusively, we will consider it here as an equivalence relationship as we suppose it here to be symmetric, reflexive and transitive.

kind-of link

The kind-of link corresponds to the semantical relationship of hyponymy. If {c 1 , . . . , c k , c} is a set of labels belonging to a vocabulary Ω, the semantical link kind-of KO is denoted as:

• KO(c, {c 1 , . . . , c k }) means that "c 1 , c 2 ,..., et c k are kinds of c" (lexical semantic link of hyponymy), and conversely that c is more general than c 1 , c 2 ,..., and c k (lexical semantic link of hyperonymy).

The kind-of relationship is defined here in an exclusive meaning: KO(c, {c 1 , ..., c k }) means that a region is annotated by the label c if and only if it is annotated by the label c 1 or c 2 ... or c k .

From this relationship, a set of semantic networks S ko Ω is defined as a set of semantic networks whose nodes are the elements of Ω submitted to the following constraints:

• The nodes of the semantic networks are assumed to be located in a hierarchy of a finite number of layers. The layer containing a label c is denoted l(c). The set of concepts such as l(c

) = i is denoted C i (S ko Ω ).
• The only semantic link existing between two links is the link kind-of

• A label c a can be linked to a label c b by the kind-of relationship only if l(c b ) = l(c a ) + 1. • If c is a label such as l(c) = i, i > 1, ∃{c 1 , . . . , c k } ∈ C i (S ko Ω )\KO(c, {c 1 , . . . , c k })

part-of link

The part-of link corresponds to the semantical relationship of meronymy/holonymy. If {c 1 , . . . , c k , c} is a set of labels belonging to a vocabulary Ω, the semantical link part-of P O is denoted: More precisely, P O(c, {c 1 , ..., c k }) means that, given a set of images, if a region R is annotated by the concept c, R admits a partition in one or several subregions which are annotated by concepts belonging to the set {c 1 , ..., c k }. It is important to note that the part-of relationship is defined here in a weak sense as all the concepts {c 1 , ..., c k } do not have to be necessarily represented in the partition of R, and, contrary to the kind-of network used in [START_REF] Buckner | Geoaida-a knowledge based automatic image data analyser for remote sensing data[END_REF], no constraint is imposed on the occurrence number of a same label inside region R.

• P O(c,
Given a vocabulary of labels Ω, we define S po Ω as a set of semantic networks whose nodes are the elements of Ω submitted to the following constraints:

• The nodes of the semantic networks are supposed here to be located in a hierarchy of a finite number of layers. The layer a concept c lies in is noted l(c). The set of concepts such as l(c

) = i is denoted C i (S po Ω ).
• The only semantic link existing between two links is the link part-of

• A concept c a can be linked to a concept c b by the part-of relationship only if l(c b ) = l(c a ) + 1. • If c is a label such as l(c) = i, i > 1, ∃{c 1 , . . . , c k } ∈ C i (S po Ω )\P O(c, {c 1 , . . . , c k })

General structure of the global semantic network

To tackle the problem of semantic representation of the labels to an extent that incorporates both kind-of and part-of networks presented in Section 2.2, a structure of a semantic network integrating the links of hyponymy and meronymy is defined here. But as seen in Section 2.1, the hierarchies induced by meronymy and hyponymy are of completely different types. The solution proposed here to integrate the links part-of and kind-of within a single network is to consider a kind-of network which is superimposed on a part-of network (cf fig 1). More formally, the global semantic network S Ω whose nodes are the elements of Ω is supposed to contain two partial networks S ko Ω and S po Ω . The first one verifies the network structure of type kind-of, and the second one verifies the network structure of type part-of previously described. To simplify the notations, each one of these networks is supposed not to contain more than two layers. Moreover, the nodes of the first layer of S ko Ω are supposed to be the nodes of S po Ω :

C 1 (S ko Ω ) = C 1 (S po Ω ) ∪ C 2 (S po Ω )
The choice to superimpose the kind-of structure on the two layers of the part-of structure is based on the fact that the words of the second layer of the kind-of relationship correspond to very general structures which can be of various complexity. For example, the word "urban" can correspond to small scale structures like "group of buildings", but can also correspond to a very large scale and complex areas which could be labelled by "suburb".

3 Probabilistic modelisation

Formalism

Let Ω = {c 1 , ..., c n } be the codebook of labels used for annotation. Each label c i is assumed to be linked to a set of example images X i provided by the user. The whole dataset is noted X = {X 1 , ..., X n }, where X ij stands for the jth learning image provided for label i. A semantic network S Ω whose nodes are the labels {c 1 , ..., c n } and the corresponding probabilistic model M Ω used to express the dataset likelihood P (X|M Ω ) are defined. The set of networks the nodes of which are the labels {c 1 , ..., c n } and verifying the requirements defined in section 2.2 is denoted S Ω , and the set of possible models to describe X is denoted M Ω .

The global model M Ω is decomposed in a set of models {M 1 , ..., M n }, M i modelling the database X i of the label c i . Each model M i contains a set of parameters θ i fitted on the database X i , and a location in the structure of M Ω . In Section 2.3, a surjective function defined from M Ω to S Ω associating each model M Ω to a semantic network S Ω will be specified.

Different layers of the model

The main idea of the association of a semantic network S Ω to an image model M Ω is to link each layer to a specific kind of probabilistic modelisation. For the sake of clarity, the number of layers of each partial network C 2 (S po Ω ) and C 2 (S ko Ω ) is constrained to be less than 2. The training sets X i are supposed to be generated independently conditionnaly to the image model M . The likelihood of the training database X can be written as:

P (X 1 , X 2 , ..., X n |M Ω ) = n i=1 P (X i |M Ω ) (1)
Each label c i in S Ω is associated to a model M i used for description of the learning set X i .

• If c i ∈ C 1 (S po
Ω ), M i is a naïve Bayes model over the low-level features of the image.

• If c i ∈ C 2 (S po
Ω ), M i is a model which has some similarity with LDA. The image is decomposed in regions which are then described by the models associated to the labels of C 1 (S po Ω ).

• If c i ∈ C 2 (S ko
Ω ), M i is defined as a mixture of unigrams over the models associated to the concepts of C 1 (S ko Ω ).

Layer 0: Low-level description of the images

The method detailed in this work takes place after a first stage of image processing where features have been extracted on a regular grid in the images of the database. A clustering algorithm is then applied on these features and a codebook of size n 0 is computed. Given an image of the database, the features previously extracted from it are quantized using the computed codebook to represent this image with a discrete collection of textons. A map, the pixels of which are the index of the textons, is thus obtained (cf image 2). This reduced image is used as the input of the modelling and the original image will no longer be used in the following lines.

Layer 1

Given a map I annotated by the concept a belonging to C 1 (S ko Ω ), its likelihood is expressed by a naive Bayes model [START_REF] Lowd | Naive bayes models for probability estimation[END_REF] and the number of textons in the map is coded by a Poisson's law. The likelihood of the map I conditionally to M a is thus written as:

P (I|M a ) = P oiss λ a ( n 0 j=1 x j ) n 0 j=1 (θ aj ) x j (2)
where θ aj stands for the probability for a texton of value j to be generated with model M a , and x j is the occurrence of texton j in map I. As this expression only depends on M a :

P (I|M ) = P (I|M a ) (3)

Layer 2 of the part-of network

Given a part-of network S po Ω , let a be a label in C 2 (S po Ω ) linked to a set of labels {c 1 , ..., c k } lying in C 1 (S po Ω ). If I is a map annotated by a, the generative model is detailed as:

• a number m ai is sampled with probability P oiss Λa .

• a partition of the map P = {R 1 , R 2 , ..., R m ai } is sampled with uniform probability.

• for j from 1 to m ai , a label c(R j ) is sampled among {1, ..., k} with probability {π a1 , ..., π ak } and the likelihood of the region is computed conditionally to the label c: P (R j |c(R j )).

The likelihood of the map is thus written as:

P (I, {R 1 , R 2 , ..., R m ai }, {c(R 1 ), c(R 2 ), .., c(R m )}|M a ) = P (I|M a , {R 1 , R 2 , ..., R m ai }, {c(R 1 ), c(R 2 ), .., c(R m )}) P ({R 1 , R 2 , ..., R m }, {c(R 1 ), c(R 2 ), .., c(R m )}|M a ) (4)
The first term of this product is expressed as:

P (I|M a , {R 1 , R 2 , ..., R m ai }, {c(R 1 ), c(R 2 ), .., c(R m )}) = P oiss Λa (m ai ) m ai j=1 P (R j |M c(R j ) ) (5)
where the term P (R j |M c(R j ) ) can be written using eq 2, and c(R j ) ∈ C 1 (S po Ω po ). Assuming independancy between the annotations and the partition of the image conditionally to the model M a , the second term of eq 4 can be written as:

P ({R 1 , R 2 , ..., R m }, {c(R 1 ), c(R 2 ), .., c(R m )}|M a ) = P ({R 1 , R 2 , ..., R m }|M a )P ({c(R 1 ), c(R 2 ), .., c(R m )}|M a ) (6)
The labels are also assumed independant conditionally to the model M a :

P ({c(R 1 ), c(R 2 ), .., c(R m )}|M a ) = m j=1 P (c(R j )|M a ). P (c(R i ) = c j )
is denoted π aj for every j ∈ {1, ..., k}. π aj and Λ a are parameters of the model a. A uniform law is assumed on the set of the map partitions.

P ({R 1 , R 2 , ..., R m }|M a ) = 1
K , where K is the number of possible partitions in the image with 4-connex regions. This number depends on the image, it is untractable for most images.

Layer 2 of the kind-of network

Given a vocabulary of labels Ω ko ⊂ Ω and a kind-of network S ko Ω ko , let a be a concept in C 2 (S ko Ω ko ) linked to a set of concepts {c 1 , ..., c k } ∈ C 1 (S ko Ω ko ) The concept a is associated with a latent variable L a taking its value in a finite vocabulary of size k: {1, ..., k}. The process of semantic specification from concept a to concept c j is modelled by the assignment of latent variable L a to value j.

Given an image I annotated by a:

P (I, L a = j|M ) = P (L a = j)P (I|L a = j, M ) (7)
Conditionnaly to the fact that the concept a has been specified to concept c j , the probability of the image is computed with the submodel M j :

P (x, L a = j|c(I) = a) = P (L a = j)P (I|M j )
Thus, the probability is computed as a mixture model:

P (x|c(I) = a) = k j=1 P (L a = j)P (I|M j )
The set of values {P (L a = j)} k j=1 are the parameters of the concept a and are noted: π aj = P (L a = j). The fact that each concept a in C 2 (S ko Ω ko ) is linked to at least one concept of C 1 (S ko Ω ko ) guarantees that k j=1 π aj = 1.

P a (x) = k j=1 π j P (I|M j ) (8)

Synonymy relationship

Let Ω = {c 1 , ..., c n } be a vocabulary and S Ω a semantic network the nodes of which are the elements of Ω. Let M Ω be a stochastic model which is set in relationship with S Ω . Let c i and c j be two labels, if they are synonyms in S Ω , they are linked to the same model in

M Ω . Thus, if M i is a model, c(M i )
is not a singleton but a set of words which are all synonyms.

Correspondance between a global stochastic model and a semantic network

Given a model M = {M 1 , . . . , M k }, the associated stochastic model S is built in two steps: • The labels are divided into the different sets C 1 (S po ), C 2 (S po ) and C 2 (S ko ) according to the model they correspond to.

• For all the labels c set in C 2 (S po ) and C 2 (S ko ), the semantic relationship part-of (if c ∈ C 2 (S po ) or kind-of (if c ∈ C 2 (S ko ) with the label corresponding to index i is created if π ci > 0.

Extensivity

Let M be a model the parameters and structure of which have been optimized by a maximum of likelihood of the training set X = {X1, ..., X n } among the set M of possible models:

M = arg max M∈M P (X|M)
If a new concept c n+1 is added to the initial set of concepts c 1 , ..., c n , and X ′ is the training set composed of X and a training set X n+1 associated to the concept c n+1 .

X

′ = X ∪ X n+1
Let M ′ be the model estimated by maximum of likelihood on the dataset X ′ among the set of models M':

M ′ = arg max M'∈M ′ P (X|M')
The following property holds:

P (X|M ′ ) ≥ P (X|M ) (9)
Proof: Let i ∈ {1, ..., n}, M i et M ′ i two sets of models fitting the dataset X i in each case. Models M i and M ′ i can be located in the first or the second layer of the network:

M i = C1(M i ) ∪ C2(M i ) M ′ i = C1(M ′ i ) ∪ C2(M ′ i )
The models of layer 1 are defined by direct modelisation on the textons of the image and their expression are not related to other models of the network (cf equation 3). The following property can thus be deduced:

C1(M i ) = C1(M ′ i )
As long as the second layer is concerned:

{C2(M ′ i )/π i,n+1 = 0} = C2(M i ) (10)
the following inclusion relationship can be infered:

∀i, M i ⊃ M ′ i Thus M' ⊃ M
The following property can be deduced:

max M ′ P (X|M ′ ) ≥ max M P (X|M )
This property means that, by adding a new concept to the vocabulary, the likelihood of the rest of the database can only increase. Thus, this method takes advantage of all the knowledge given by the user to improve the description of the database. By analogy with Statistic Physics, this property is called 'extensivity property" [START_REF] Lieb | The Stability of Matter[END_REF] as a physical state variable describing a system is said to be "extensive" if this variable grows with the size of the system.

Coding of the model

The principle of minimization of the stochastic complexity has been introduced by Rissanen in 1978 [START_REF] Rissanen | Stochastic Complexity in Statistical Inquiry Theory[END_REF]. The notion of stochastic complexity substitutes to the complexity of Kolmogorov [START_REF] Gammerman | Kolmogorov complexity: Sources, theory and applications[END_REF] the number of bits necessary to code a sequence with an entropic code, and also the number of bits which are necessary to code the probabilistic model.

Coding of the system

The code length is traditionnaly made in two parts ( [START_REF] Rissanen | Modeling by shortest data description[END_REF]):

C(X, M ) = C(M ) + C(X|M )
the first term corresponding to the coding of the model, the second term corresponding to the length of the code which is necessary to code the data using the model. The set of example images are supposed to be independant for each label. The description length can thus be summed on the labels:

C(X, M ) = n c=1 [C(X c |M ) + C(M c )] (11)

Layer 1

The layer 1 models are assumed to generate directly the textons of example images. Thus, C(X c |M ) = C(X c |M c ) and if X cj is the j-th example image associated to the concept c, by using Shannon formula [START_REF] Shannon | A mathematical theory of communication[END_REF], the term CS(X c |M c ) is written as:

CS(X c |M c ) = -log P (X c |M c )
the images X cj of the database provided for concept c are supposed to be independant. The stochastic complexity of the database can be written as:

CS(X c |M c ) = - j log P (X cj |M c )
by defining card(X cj ) = n 0 j=1 x cj as the total number of textons in X cj , and by introducing the expression 2 in the last equation:

CS(X c |M c ) = λ c -card(X cj ) log λ c + card(X cj )s j=1 log j - n 0 j=1 x cj log(θ c ) (12)
To code the model M c , the layer it belongs to has to be coded first.

Here, a model which can have a maximum of two layers is presented, the index of the layer can be coded by a single bit with value 0 or 1. Then, the generation parameters of textons θ c and the size parameter Λ c have to be coded. Rissanen formula [START_REF] Rissanen | Modeling by shortest data description[END_REF] linking a vector of parameters of size T estimated with N ech samples provides the code length:

T 2 log N ech (13)
Vector θ c has size n 0 . The number of samples it is estimated with is equal to the total number of textons of the database X c . The vector Λ c has size 1 and is estimated with a number of samples equal to the total number of images in the database X c , defined as N c .

CS(M

c ) = n 0 2 log( Nc j=1 n 0 k=1 x cjk ) + 1 2 log N 1 (14)
The stochastic complexity CS(X c |M c ) is therefore:

CS(X c |M c ) = λ c -card(X cj ) log λ c + card(X cj )s j=1 log(j) - n 0 j=1 x j log(θ c ) + n 0 2 log( Nc j n 0 k x cjk ) + 1 2 log N 1 + 1 (15)

Layer 2 of the 'Kind-of" network

Let c stand for a label lying in C 2 (S ko Ω ), the term C(X c |M ) can be written as:

C(X c |M ) = -log P (X c |M )
Applying the independence assumption of the images of the database X c and by introducing the expression of P (X c |M c ) written in eq 8, the following expression can be written as:

CS(X c |M ) = - Nc j=1 log( k i=1 π i P oiss λc ( n 0 k=1 x k ) n 0 k=1 θ x k c )
For the coding of the model, it is necessary to code the generation parameters π c . Using expression 13:

CS(M i ) = n 1 2 log N c (16)

Layer 2 of the part-of network

Let c stands for a label lying in C 2 (S po Ω ), and i for the index of a map in the database X c and P i = {R i1 , R i2 , ..., R im ci } stand for an annotated partition of this image, the term C(X ci |M, P i ) is written:

C(X ci |M, P i ) = -log P (X ci |M, P i )
This probability being expressed as a sum on the joint probability of the image and the labels on all possible annotations of the image given a partition, becomes:

P (X ci |M, P i ) = {c(R 1 ),c(R 2 ),...,c(Rm ci )} P (X ci , {c(R 1 ), c(R 2 ), ..., c(R m ci )}|M, P i ) (17)
The term P (X ci , {c(R 1 ), c(R 2 ), ..., c(R m ci )}|M, P i ) is decomposed as:

P (X ci , {c(R 1 ), c(R 2 ), ..., c(R m ci )}|M, P i ) = P (X ci |{c(R 1 ), c(R 2 ), ..., c(R m ci )}, M, P i ) P ({c(R 1 ), c(R 2 ), ..., c(R m ci )}|M ) (18)
The first term of this product is expressed by equation 5, and the second by equation 6.

P (X ci |M, P i ) = {c(R 1 ),c(R 2 ),...,c(Rm ci )} P oiss Λc (m ci ) m ai j=1 π c(R j ) P (x(R j )|c(R j )) (19)
However, this expression may become untractable for a high number of regions. Some approximations can be used to find a lower bound of this expression. In this work, we just use the following very coarse bound:

P (X ci |M, P i ) = max {c(R 1 ),c(R 2 ),...,c(Rm ci )} P oiss Λ c (m ci ) m ai j=1 π c(R j ) P (x(R j )|c(R j )) (20)
For each model, the index of the layer and the generation parameters of the labels of C 1 (S po Ω ) π c have to be coded.

CS(M

i ) = n 1 2 log N c ( 21
)
The point is, as for the concepts of layer 1, to code the values of the textons with a minimal code length. Thus, the partition P i for each image of index i is not coded and the code length C(X, M ) is expressed as:

C(X, M ) = min P,M (C(X|M, P ) + C(M ))

Optimization procedure

Given a database X, we wish to find the model M minimizing the stochastic complexity C(X, M ) among the set of possible models in terms of parameters and structure. Given a vocabulary Ω of cardinal n, the labels are separated in three subsets: C 1 (S po Ω ), C 2 (S po Ω ) and C 2 (S ko Ω ). The number of possible structures thus corresponds to the total number of possible repartitions of the n labels in these three subsets, that is to say 3 n . As a global exploration is untractable for high values of n, we propose here a greedy algorithm leading to a local minimum of the stochastic complexity CS(X, M ).

Initialization The initialization configuration of the algorithm is the one containing all the n concepts in layer 1.

Iterations At each step, and for each label c j of layer 1, the stochastic complexity associated with the configuration where the label c j is located in layer 2 is computed. The model parameters of the first layer are first estimated by likelihood maximisation.

For each label c of layer 1, the parameters are estimated using the following equations:

∀j ∈ {1, ..., n 0 }, θ cj = occ X c (j) card(X c ) λ c = 1 N c N c j=1 card(X cj )
card(X cj ) stands for the number of textons in the image X cj , card(X c ) = Nc j=1 card(X cj ). occ Xc (L c = j) stands for the number of occurrences of the texton of value j in the database X c .

For every concept c of layer 2, we have the following expressions:

∀j ∈ {1, ..., n 1 }, π cj = Nc i=1 P c j (x i ) Nc i=1 n k=1 P c k (x i )
Once the parameters are estimated, the global stochastic complexity is computed using equation 11. The model minimizing the stochastic complexity is set in layer 1 if the corresponding complexity is less than the complexity obtained at last step.

Stopping the algorithm The algorithm stops when the stochastic complexity algorithm increases. The last model is taken as the optimal model. Discussion To put a label c from layer C 1 (S po Ω ) to layer C 2 (S po Ω ) or C 2 (S ko Ω ) has two main impacts: an impact on the complexity term C(X c |M c ) as the likelihood of X c will be expressed by a different model, and an impact on the complexity terms corresponding to the labels belonging to layers C 2 (S po Ω ) or C 2 (S ko Ω ). This latter impact results in an increase of the stochastic complexity due to the decrease of the number of possible modelisations according to the models belonging to C 1 (S po Ω ).

Annotation of a new image

Once the structure of the model has been learnt and the parameters have been estimated, test images can be annotated using the model. The step of annotation extracts semantic information from the image by annotating it with the vocabulary Ω provided by the user. Our method is focused here on large databases of remote sensing images. As these images are very large, annotate a whole image to semantic labels seems not relevant, and we present a method which provides annotated regions of the test image.

Annotation method

The first step of the annotation stage is to decompose the test image I in regions annotated by concepts existing in the model. This process is modelled as a part-of network where the third layer is constituted of a virtual label c scene annotating the test image. In the stochastic model corresponding to this semantic network where c scene is added, the generation probability of each label c ∈ C 2 (S po Ω ) is unknown. Thus, we consider a uniform distribution on the elements of C 2 (M ):

∀c ∈ C 2 (M ), P cscene (c) = 1 |C 2 (M )|
The test image is represented as a region R annotated by the virtual concept c scene . This region is decomposed as an annotated partition

G 2 = {R 2 1 , R 2 2 , ..., R 2 N 2 } where each concept of annotation c(R 2 i ) ∈ C 2 (S po Ω ). Then, each region R 2
i is decomposed in a partition of regions annotated by concepts of C 1 (S po Ω ). The result is an annotated partition

G 1 = {R 1 1 , R 1 2 , ..., R 1 N 1 }. Given an image I, the annotations G 1 et G 2 are taken as maximizing the probability P (G 1 , G 2 |I): max G 1 ,G 2 P (G 1 , G 2 |I) (22)
Let us write:

P (G 1 , G 2 |I) = P (I, G 1 , G 2 ) P (I)
As the maximisation does not depend on I, we just operate the maximization of the joint probability P (G 1 , G 2 , I):

P (G 1 , G 2 , I) = P (G 2 )P (G 1 |G 2 )P (I|G 1 )

Optimization algorithm

As the space of joint configurations of G 1 and G 2 is too large, the complexity is reduced by applying two steps of inference. The maximum G 1,opt of P (I|G 1 ) is determined in the space of all the possible annotated partitions G I 1 . Then, given the partition G 1,opt , the maximum G 2,opt of P (G 1,opt |G 2 )P (G 2 ) is determined in the space of all the possible annotated partitions G

G 1,opt 2
where each region is a union of regions of G 1,opt .

For each inference step, the optimal annotated partition has to be found among a huge set of configurations. A path is thus explored through the space of annotations starting from a complex partition and finishing to a single region containing the whole image. Initialization is performed by annotating each texton with a label considering its value and the value of its neighbours on a small window.

First inference step

• Initialisation of the algorithm:

A first partition is created using the estimated models M c associated with the concepts c ∈ C 1 (S po Ω ) in the following way: at each texton of the image of coordinates (k, l), the following histogram vector of size n 0 is computed:

U (k, l) = (i,j)∈I E I(k,l) g k,l,σ (i, j)
where E i stands for the i-th base vector, g m 1 ,m 2 ,σ (x, y) stands for the 2D Gaussian function of mean m 1 , m 2 and of variance σ 2 . σ is a parameter of the algorithm. This vector is a representation of the neighbourhood of the texton (k, l).

Then, for i ∈ {1, . . . , n 1 }, the following probability functions is computed:

P (U (k, l)|θ i ) = n 0 j=1 p U (k,l) ij (j)
and texton (k, l) is annotated with label c verifying:

P (U (k, l)|θ c ) = min i∈{1,...,n 1 } P (U (k, l)|θ i )
An annotated partition G 0 1 is then created by building a region annotated with concept c for each 4-connex area of textons which has been linked to the concept c during the previous step.

• Let i be the number of iterations done in the loop. While the number of regions in the image contained in G i 1 is more than 1:

-for all possible merging of adjacent regions: * we consider the n 1 possible annotations for the new region.

If two regions are adjacent and are annotated with the same label, they are merged. For these n 1 configurations G 1 , the likelihood P (I|G 1 ) is computed.

-the configuration maximizing the likelihood is kept and denoted

G i 1 •
The final annotated partition G opt 1 is the configuration verifying:

P (I|G opt 1 ) = max i P (I|G i 1 )
At each step of the loop, at least two regions are merged. As a consequence, the algorithm finishes in less iterations than the number of regions in the initial partition G 0 1 . The higher σ, the fewer regions are in G 0 1 . The process of the second step of the algorithm is similar to the first step. A path is explored in the space of the annotated partitions by creating an initial partition G 0 2 and by merging regions iteratively until just one region remains in the image.

Second step of inference

• Initialisation of the algorithm:

A first partition is created using the estimated models M c associated with the concepts c ∈ C 2 (S po Ω ) in the following way: for each region R k of G 0 1 , the following histogram vector of size n 1 is computed:

U (R k ) = j/adj(R j ,R k ) E c(R j )
Then, for i ∈ {1, . . . , n 2 }, the following probability functions are computed:

P (U (R k )|θ i ) = n 1 j=1 p U (R k ) kj (j)
and region R k is annotated by the label c verifying

P (R k |θ c ) = min i∈{1,...,n 2 } P (R k |θ i )
An annotated partition G 0 2 is then created by building a region annotated by the concept c for each 4-connex area of textons which have been linked to the concept c during the previous step.

• Let i be the number of iterations done in the loop. While the number of regions in the image contained in G i 1 is over 1:

-for all possible merging of adjacent regions * the n 2 possible annotations for the new region are considered.

If two regions are adjacent and are annotated with the same label, they are merged. For these n 2 configurations G 2 , the likelihood P (G opt 1 |G 2 ) is computed. -the configuration maximizing the likelihood is kept and noted G i

2

• The final annotated partition G opt 2 is the configuration verifying:

P (I|G opt 1 ) = max i P (G opt 1 |G i 2 )

Semantic representation of the image

The previously detailed algorithm output consists in two annotated partitions of the test image. the fusion of these two partitions in a single set of regions is denoted

P po = {G 1 , G 2 }
. This is the minimal interpretation of the image, to get it richer:

• For every region R belonging to P po , of the word c(R) is linked by an hyponymic relationship to the word c ′ belonging to C2(S ko ), we create a new region the localisation of which is the same as R and th annotation of which is c ′ .

• For every pair of regions R and R ′ belonging to P ko and annotated by the same concept, if R and R ′ are adjacent or if their intersection is not empty, these regions are merged.

• For every region R belonging to the set P = P ko ∪P po , all the synonyms of c(R) are added to the set of annotations of R Each region has an outer boundary. Regions with holes also have inner boundaries to represent the holes. Fuzzy modeling is used for pairwise relationships between regions to represent the following high-level user concepts:

Perimeter-class relationship Given two regions R i et R j , to find the relationship between a pair of regions R i and R j , the following quantities are first computed:

• Perimeter of the first region π i ,

• Perimeter of the second region π j ,

• Common perimeter between the two regions π ij ,

• Ratio of the common perimeter to the perimeter of the first region:

r 1 ij = π ij /π i ,
• Surface of the first region σ i ,

• Surface of the second region σ j ,

• Common surface between the two regions σ ij ,

• Ratio of the common surface to the surface of the first region:

r 2 ij = σ ij /σ i ,
• Closest distance between the boundary of the first region and the boundary of the second region d ij .

Then, each pair is assigned a degree of their spatial relationship using the fuzzy class membership functions given in figure 4. Then, these pairwise relationships are combined using an attributed relational graph [START_REF] Haralick | Computer and Robot Vision[END_REF]. The attributed relational graph represents regions by the graph nodes and their spatial relationship by the edges between such nodes. Nodes are labeled by concepts and the corresponding confidence values (likelihood) for the label assignment. Edges are labelled with the spatial relationship classes (pairwise relationship names) and the corresponding degrees (fuzzy membership values) for these relationships.

Experimentations

Construction of semantic networks

Two different sets of data will be used: synthetic data will confirm case by case the adequacy of the PSL algorithm and real data will demonstrate its robustness.

Synthetic data

Synonymy relationship A Gaussian probability function on gray values of range from 1 to 256 is defined. Two databases X 1 and X 2 associated with two concepts c 1 and c 2 and containing N images of size 200 × 200 are generated pixel by pixel using this distribution. These images are supposed to correspond to the textons map mentioned in Section 3.2.1. Two models M and M ′ are estimated considering two different cases:

• model M corresponds to the case where c 1 and c 2 are supposed to be not synonyms. Two vectors of parameters θ 1 and θ 2 of dimension 256 were estimated over X 1 and X 2 respectively. • model M ′ corresponds to the case where c 1 and c 2 are supposed to be synonyms. A single vector θ ′ of dimension 256 is estimated over

X 1 ∪ X 2 .
The stochastic complexity was computed in each case:

C(X, M ) = -log P (X 1 |M 1 ) -log P (X 2 |M 2 ) + C(M 1 ) + C(M 2 ) C(X, M ′ ) = -log P (X 1 |M ′ ) + C(M ′ )
The ratio R syn = C(X,M C(X,M ′ ) obtained according to the size of the database is shown on figure 6. As expected, R syn converges to 1 when the size of the database increases. Indeed, C(X, M ) contains the coding of two vectors of parameters as C(X, M ′ ) contains one. As the databases X 1 and X 2 are generated by a single distribution, the vectors θ 1 and θ 2 converge to θ asymptotically when the size of the database increases. Though, the terms C(θ 1 ), C(θ 2 ), C(θ ′ ) have a logarithmic dependence in N but the terms C(X 1 |θ 1 ), C(X 2 |θ 2 ) evolve in a linear way.

Hyponymy relationship k Gaussian distributions g i of mean m i = i 256 , i ∈ {1, . . . , 256} and of same variance σ 2 are considered. k training sets X i associated with each label c i are generated pixel by pixel from distribution g i and contain N images of size 200×200. These images are supposed to correspond • For every i ∈ {1, . . . , N } -a number j is sampled with uniform probability in {1, . . . , 256}.

-the image X (k+1)i is generated by sampling independantly each pixel with probability g i .

Two models M and M ′ are estimated for the two cases corresponding respectively to two different structures:

• {c1 , ..., c k } and c k+1 are all located on layer 1. The model M k+1 is estimated by maximum of likelihood on X k+1 as the other models.

• {c1 , ..., c k } are supposed to be hyponyms of c k+1 , and c k+1 is linked with {c1 , ..., c k } by kind-of links. The model M k+1 is thus built as a mixture of models over the distributions P c j and the vector of parameters λ k+1 is estimated on X k+1 .

Figure 7 shows the ratio R hyp = C(X,M C(X,M ′ ) according to the variance σ of the Gaussian distributions. As expected, R hyp converges to 1. Indeed, increasing Figure 7: Ratio R hyp versus σ (the higher σ, the less discriminative the features) for different values of k for the hyponymy relationship. R hyp is always greater than 1, and decreases for increasing σ the variance of the Gaussians amounts to saying that the features are less discriminative. This experience shows that the kind-of link between labels provides all the more reduction of stochastic complexity that the features describe efficiently the data.

Meronymy relationship k Gaussian distributions g i of mean m i = i 256 , i ∈ {1, . . . , 256} and of same variance σ 2 are considered. k training sets X i each associated with label c i are generated from distribution g i and contain N images of size 200 × 200. These images are supposed to correspond to the textons map mentioned in Section 3.2.1. Then, a database X k+1 associated to a label c k+1 is generated in the following way:

• for every i ∈ {1, . . . , N }, the image X i , of size 200×(200 * k) is separated in k regions R 1 (X i ), ..., R k (X i ) of size 200 × 200
-for every i ∈ {1, . . . , k} -each region R j (X i ) is generated by sampling independantly the textons with distributions g j .

• {c1 , ..., c k } and c k+1 are all located on layer 1. The model M k+1 is estimated by maximum of likelihood on X k+1 as the other models. Figure 8 shows the ratio R mer = C(X,M C(X,M ′ ) according to the variance σ of the Gaussian distributions. As expected, R mer converges to 1. Indeed, increasing the variance of the Gaussians amounts to saying that the features are less discriminative. This experience shows that the part-of link between labels provides all the more reduction of stochastic complexity that the features describe efficiently the data.

Real data

The reliability of the automatic learning of the model structure has been tested for real data on a database of SPOT5 images at 2,5m resolution. A training set has been created by annotating extracted images with a set of concepts listed on Table 2.

Synonymy relationship

To evaluate the role of synonymy on stochastic complexity, the following protocol is applied for every label c listed on Table 6.1.2:

• The training set X c associated to label c is split in two subsets denoted X a and X b of similar sizes (for us, X a and X b are therefore synonyms) • Two models M a and M b are estimated on X a and X b respectively. The stochastic complexity C(X c , M ) is computed, where M is defined as

M = {M a , M b }.
• A single model M ′ is also estimated on X a ∪X b = X c , and the stochastic complexity C(X c , M ′ ) is computed.

The ratio C(Xc,M ) C(Xc,M ′ ) is computed for the different labels and the results are shown on Table 6.1.2. The ratio is higher than 1 for all the labels. This means that the synonymy link is detected for every label.

Hyponymy/hyperonymy relationship To evaluate the evolution of stochastic complexity caused by introducing hyponymy (a label corresponds to the generalisation of a set of other concepts), the following protocol is applied:

• A set of k concepts {c 1 , . . . , c k } associated respectively to k training sets X 1 , . . . , X k is considered. Then, each set X i is split in two subsets X 1 i and X 2 i . A concept c is introduced and is supposed to annotate a database X 1 k+1 defined by X 1 k+1 = k i=1 X 2 i .

• The k + 1 models M i associated to each concept c i are supposed to lie on a single layer and are estimated separately on each database X 1 i .

• The concept c k+1 is linked with {c1 , ..., c k } by kind-of links. The model M k+1 is thus built using the corresponding model described in Section 3.4.

An experience has been made with the label "vegetation", which is built as a generalization of the labels "grass", "fields", and "forest". A second experience has been made with the label "urban", which is built as a generalization of the labels "residential area", "town center", and "industrial area".

To test the ratio R hyp = C(X,M ) C(X,M ′ ) according to the discriminative power of the low-level features, a noise is added on the textons of X i in the following way:

Every texton of the map is changed with probability p ∈ [0, 1] into another texton of value randomly chosen in {1, . . . , n}. The ratio R hyp is computed for p varying from 0 to 0,4. The results are shown on figure 9. As on the synthetic data, the ratio is decreasing with the value of the noise. With about 15% of noise, the ratio R hyp goes under 1, this means that the hyponymic relationship is no longer identified by the system. The reduction of stochastic complexity induced by the introduction of a hyponymic relationship in the network thus directly depends on the discriminative power of the low-level features. Under a certain level of discriminative power, the hyponymic relationship cannot be infered.

Meronymy/Holonymy relationship To evaluate the evolution of stochastic complexity caused by introducing a link of hyponymy (a label corresponds to the generalisation of a set of other concepts), the following protocol is applied:

• A set of k concepts {c 1 , . . . , c k } associated respectively to k training sets X 1 , . . . , X k is considered. Then, a concept c is introduced and is supposed to annotate a training set X 1 k+1 . • The k + 1 models M i associated to each concept c i are supposed to lie on a single layer and are estimated separately on each database X 1 i . • The concept c k+1 is is linked with {c1 , ..., c k } by part-of links. The model M k+1 is thus built using the corresponding model described in Section 3.4

An experience has been made with the label "urban area", which is built as a generalization of the labels "town center", "residential area", and "cemetery". A second experience has been made with the label "rural area", built as a generalization of the labels "sparse housing", "fields", "carrier", and "residential area".

To test the ratio R mer = C(X,M ) C(X,M ′ ) according to the discriminative power of the low-level features, a noise is added on the datasets on the textons of the datasets X i in the same way as in previous Section. The ratio R mer is computed for several values of p. The results are also shown on figure 9. As on the synthetic data, the ratio is decreasing with the value of the noise. With about 20% of noise, the ratio R mer goes under 1, meaning that the hyponymic relationship is not identified by the system. The reduction of stochastic complexity induced by the introduction of a hyponymic relationship in the network thus directly depends on the discriminative power of the low-level features. Under a certain level of discriminative power, the hyponymic relationship cannot be infered. Construction of a complete semantic network Experiences have been made on the database of SPOT5 images.

Annotation

In this section, the annotation performance of our method is evaluated. In the literature, a number of proposals for semantic image annotation and retrieval have appeared but it is quite difficult to compare the relative performances of the resulting algorithms with our method due to the lack of a proper experimental protocol. We thus decided to compare our method to the classical MPM segmentation method which has proved successfull for remote sensing segmentation [START_REF] Masson | Sem algorithm and unsupervised segmentation of satellite images[END_REF].

Database

SPOT5 images of Paris, Marseille, Nice and Angers at 2,5m of resolution have been manually annotated and used to apply quantitative evaluation of the performance of semantic annotation. This database contains 24 images of size 6000 × 6000. The concepts used for annotation are those listed in Table 2 and are put in a two layer semantic network. Each image of the database is associated with two annotated partitions corresponding to each layer. The database has been split in three parts where each part contains a representative sampling of the landscapes existing in the whole database. A cross validation has been performed by applying three permutations on the three sets. Each time, two sets of the annotated database are used for the learning stage and one set for the test stage. Notice that as the structure is fixed, only the parameters are to be estimated. The parameters of the Markovian model are learnt using the method of the stochastic gradient.

Industrial area

Used metric

To evaluate the quality of the annotation of test images, the concepts of C 2 (S ko ) are not taken into account as they depend deterministically of the annotations using S po . The result of the annotation process using layer j of the model is an annotated partition P sys = {R j 1 , R j 2 , ..., R j m j } of this image where each region R j i is annotated using the concept c(R j i ) ∈ C j (S po ). To evaluate the quality of a multi-layer annotation, we compare the annotation result for each layer to the ground truth P gt = {R jr 1 , R jr 2 , ..., R jr m r j } where each region R jr i is annotated with the concept c(R jr i ) ∈ C j (S po ). We assume that, in each layer, the set of annotation concepts used for ground truth is the one used by the system. For multi-layer annotation, we compare individually the segmentation of each layer. If the Vinet's distance [START_REF] Vinet | Segmentation et mise en correspondance de régions de paires d'images stéréoscopiques[END_REF] can be used to compare the produced segmentation, it is also relevant to use natural language processing tools as the goal of image annotation is to set images in relationship with words from natural language.

Indeed, the World Error Rate metric [START_REF] Hunt | Figures of merit for assessing connected-word recognisers[END_REF], used for evaluation of speech recognition systems, can be applied here by posing that a region R 1 of the system partition P sys and a region R 2 of the ground truth partition P gt can be matched if their overlap satisfy some given threshold:

|R 1 ∩ R 2 | |R 1 ∪ R 2 | > 0.8 (23)
where |R| corresponds to the number of textons of region R.

Given a matching between P sys and P gt , we define the following metric:

IAW ER = |El| + |Add| + |Sub| N
Where N is the number of words in the reference. We define here:

• An elision (El) is a region of P gt that has not been matched to any region of P sys .

• An adding (Add) is a region of P sys that has not been matched to any region of P gt .

• A substitution (Sub) is a region of P sys that has been matched to a region of P gt but is not annotated by the same label.

For each layer, the matching is processed in order to minimize the IAWER. We use a greedy algorithm to find a minimum IAWER:

• For i ∈ {1, . . . , m j }. For each region R j i of P sys , the overlap (cf eq 23) with all the regions of P gt annotated with c(R j i ) is computed. Let R jr i,opt be the region of P gt with optimal overlap.

-In case of conflict, if R jr i,opt is matched already with a region R j k , R jr i,opt is matched with the region corresponding to the higher overlap.

-In other case, R j i is matched with R jr i,opt .

Results

The images are annotated using the method described in Section 5.1. The performances are evaluated by comparing the ground truth with the output of the system using the two metrics: Vinet's measure and IAWER. These two metrics are complementary as the Vinet measure evaluates the output of the system as a segmentation result, and the IAWER evaluates the output of the system as an annotation result.

As it can be seen on Table 3, the two algorithms provide rather similar results with the Vinet metric for the annotation with the labels of the first layer. A similar conclusion holds for the evaluation with IAWER criterion. The annotation results are much different as far as the second layer is concerned. The Markovian method is outperformed by PSL. A clear difference can also be noted with the results obtained by the Markovian method compared with the annotation of the first layer. This can be interpreted by the fact that the semantic gap cannot be crossed by a direct inference from low-level to high-level. This leads us to conclude with the relevance of our method making the inference in several steps by using several layers. Example of annotation are shown on fig 12 and3

Conclusion

In this work, we use semantic networks to take into account the semantical relationships between the concepts and to tackle the problem with high generality. We took advantage of a correspondance between the structure of the semantic networks and the structure of the probabilistical models. By considering the semantic relationships of hyonymy/hyperonymy and meronymy/holonymy, the concepts can be handled by the system considering their level of generality or complexity. This makes possible a good estimation of the density of high level concepts by expressing this density with the densities of concepts lower in the hierarchy. Moreover, the use of the semantic network requires no expert knowledge, as the semantic network is built automatically through an algorithm of model selection which infers the paradigmatic relationships from a weakly training set. Experiments prove the reliability of the construction of the semantic network, and the efficiency and richness of the annotation of semantic labeling and retrieval.

  {c 1 , ..., c k }) means that: "c 1 , c 2 ,..., et c k are parts of c", and conversely that c is composed of c 1 , c 2 ,..., et c k .

Figure 1 :

 1 Figure 1: Illustration of the global semantic network

Figure 2 :

 2 Figure 2: (a) SPOT5 image of size 6000 * 6000 at 2,5m of resolution @CNES (b) image of size 150 × 150 whose pixels are the index of the textons. Each texton is computed on a 40 × 40 window. The codebook of textons contains 90 labels.

Figure 3 :

 3 Figure3: Representation of the models kind-of (upper graph) and part-of (lower graph). A box corresponds to the iterative and independant sampling of random variables which are inside the box. The number of sampling is wirtten at the bottom-left of the box. A colored disc corresponds to an observable random variable. A non-colored disc corresponds to a non observable random variable.

•

  disjoined : Regions are not bordering each other • bordering: Regions are bordering each other • invaded by: Smaller region is surrounded by the larger one at around 50% of the perimeter • surrounded by: Smaller region is almost completly surrounded by the larger one Surface-class relationship • overlapping: Regions are overlapping each other • contained by: Smaller region is almost completly surrounded by the larger one Distance-class relationship • Near : Regions are close to each other • Far : Regions are far from each other

Figure 4 :

 4 Figure 4: Fuzzy spatial relationships (a) Perimeter-related relationships (b) Surface-related relationships (c) Distance-related relationships

Figure 6 :

 6 Figure 6: Ratio R syn versus the number N of images in X 1 et X 2 . R syn converges to 1 when N increases.

Figure 8 :

 8 Figure 8: Ratio R mer versus σ for different values of k for the meronymy relationship. Similar conclusions can be drawn than in fig 7.

Figure 9 :

 9 Figure 9: Ratio R hyp and R mer versus the percentage of noise. As long as the ratio is above 1, the relationships are recognized. When the noise increases, the recognition is lost.

Figure 10 :

 10 Figure 10: Part-of links between first and second layer

Figure 11 :Figure 12 :

 1112 Figure 11: (a) Initial 6000 × 6000 SPOT5 image of "Marseille" @CNES (b) Ground truth mask of layer 1 (c) Misannotated pixels (d) Annotation by PSL method. Classes are: industrial area, sparse housing area, residential area and mountain,

Table 1 :

 1 Ratio of stochastic complexity obtained by the introduction of the

	synonymy relationship on image databases corresponding to different con-
	cepts
	Labels Forest Town Center Mountain Residential Area	Sea
	R syn 1.00031	1.00042	1.00061	1.00012	1.0064

Table 2 :

 2 Concepts used for semantic network

			Residential area
			Fields
			Mountainous area
			Forest
			Water
			Sparse housing area
			Town center
			Rural area
			Refinery
			Urban area
			Industry
			Cemetery
			Carrier
			Moutain
			Airport
			Maritim area
	Concepts	of	Concepts of first layer
	second layer
	Rural area		Carrier, Forest, Sparse
			housing area, Fields, Resi-
			dential area
	Urban area		Town center, Residential
			area, Cemetery
	Inudstrial com-	Refinery, Residential area,
	plex		Industrial area
	Moutainous area Mountain, Carrier, Forest ,
			Sparse housing area
	Maritim area		Water, Residential area ,
			Forest, Industrial area

  .

			Layer 1. Layer 2
	PSL	Vinet's	83,27 % 86,14%
	measure
	MPM	Vinet's	84,26%	68,27%
	measure
	PSL IAWER	9,79 %	12,44%
	MPM IAWER	8,91%	29,14%

Table 3 :

 3 Annotation evaluation method using Vinet's measure (a good score is close from 100%), and using IAWER (a good score is close from 0%)

Acknowledgment

This work has benefitted from fruitful discussions with M. Datcu (DLR), Véronique Prinet (INRIA/Liama), Régis Behmo (Centrale Paris/Liama), O. Cappé (CNRS/LTCI). We thank CNES for providing the SPOT database.


Marc Vandeputte

Selective breeding for better farmed fish: how to be more efficient ?

Aquaculture: a growing challenge

 The increase in consumption is and will be met by aquaculture pressing

Growth remains the #1 trait

With an average genetic gain in growth rate of 12.5% per generation, production may be dramatically increased if genetically improved animals are used

But is it growth that we really need to improve?

  Chavanne et al., 2016 Aquacult. Int. 24: 1287-1305

-

  Density 230 kg/m 3 -N-NH 3 : 40 kg/day 500t/yr, 1.35€/kg • FCR is always profitable • TGC is profitable only if density is the limiting factor • Extension to other systems show similar results Besson et al. 2014, J Anim. Sci. 92:5394-5405. Highly profitable but not selected for  Individual feed intake on long periods not measurable  candidate FE not measurable  Indirect criteria:  FE of individually housed fish  X-ray point FI measurements  Weight loss at fasting  Growth ?? Conclusion  Efficiency is both economically and environmentally beneficial  Major traits: feed efficiency, processing yields, disease resistance, adaptation to alternative diets  Some (little ?) progress may be expected by correlated response to selection for growth  Specific research needed on phenotyping, genetic and genomic bases of efficiency traits  A major key for sustained growth of aquaculture production in a finite world

Selecting « vegetarian » rainbow trout Sel.

Con.

V-gain= (S-T)/T M-gain= (S-T)/T

Efficiency also reduces environmental impact

Life Cycle Analysis

Emissions Resources

Emissions

Resources Besson et al., 2016, J. Cleaner Prod. 116: 100-109 What are the limits to selection for efficiency ?

 Ever faster growing fish is (probably) possible  But an immortal fillet block growing without feed will not be possible…  What are the limits ?  Will efficient fish be less robust ? Nestor et al.1996Poult Sci 75: 1180-1191