Titan, Saturn's largest moon, hosts lakes and seas of liquid hydrocarbons at its poles [START_REF] Stofan | The lakes of Titan[END_REF] . General circulation models demonstrate that regional evaporation and precipitation rates of methane are likely to change with the seasons (Titan's year is 29.5 Earth years) and evolve on a geological timescale (~10 [START_REF] Hayes | Transient surface liquid in Titan's polar regions from Cassini[END_REF] Earth years) [START_REF] Lunine | lakes, dunes, and rain: crustal processes in Titan's methane cycle[END_REF][START_REF] Lora | Simulations of Titan's paleoclimate[END_REF][START_REF] Mitchell | The climate of Titan[END_REF] . Cassini observations suggest shoreline recession at a few south polar lakes during local summer [START_REF] Hayes | Transient surface liquid in Titan's polar regions from Cassini[END_REF] , but similar seasonal changes have yet to be observed at the north pole where lakes are larger and more numerous [START_REF] Hayes | Hydrocarbon lakes on Titan: distribution and interaction with a porous regolith[END_REF][START_REF] Birch | Geomorphologic mapping of Titan's polar terrains: constraining surface processes and landscape evolution[END_REF] . We present three 'phantom lakes' that appear to be north polar surface liquids in winter observations by Cassini RADAR but that are inconsistent with lakes in infrared images obtained up to seven years later, after vernal equinox, suggesting that the liquids were removed in between. If this were the case, the phantom lakes could be interpreted as shallow ponds, with either a pure methane composition or a regolith porous enough to remove the less volatile ethane. These phantom lakes provide observational constraints on removal timescales for surface liquids at Titan's north pole. The location, size and longevity of surface liquid reservoirs affect sediment processing [START_REF] Birch | Geomorphologic mapping of Titan's polar terrains: constraining surface processes and landscape evolution[END_REF] , seasonal weather [START_REF] Tokano | Impact of seas/lakes on polar meteorology of Titan: simulation by a coupled GCM-Sea model[END_REF] , climate evolution [START_REF] Lora | GCM simulations of Titan's middle and lower atmosphere and comparison to observations[END_REF] , and even, perhaps, their habitability [START_REF] Tokano | Limnological structure of Titan's hydrocarbon lakes and its astrobiological implication[END_REF] . As solubility of the possible non-polar mixtures is generally low, short-lived lakes might be nutrient-poor [START_REF] Tokano | Limnological structure of Titan's hydrocarbon lakes and its astrobiological implication[END_REF] and thus have low astrobiological potential.

Complete emptying of small or shallow lakes may be the easiest shoreline change to identify in Cassini data, given that the largest predicted evaporation and infiltration rates peak at metres per year [START_REF] Hayes | Hydrocarbon lakes on Titan: distribution and interaction with a porous regolith[END_REF][START_REF] Mitri | Hydrocarbon lakes on Titan[END_REF][START_REF] Newman | Simulating Titan's methane cycle with the TitanWRF general circulation model[END_REF] . For example, although observations of Ontario Lacus, Titan's largest south polar lake, were interpreted as evidence of kilometres of shoreline recession over four years [START_REF] Hayes | Transient surface liquid in Titan's polar regions from Cassini[END_REF][START_REF] Turtle | Shoreline retreat at Titan's Ontario Lacus and Arrakis Planitia from Cassini Imaging Science Subsystem observations[END_REF] , later analysis [START_REF] Cornet | Edge detection applied to Cassini images reveals no measurable displacement of Ontario Lacus' margin between 2005 and 2010[END_REF] contested that such change was within the uncertainty of spatial sampling. The difficulty in identifying even the most dramatic liquid level change lies in establishing a long enough baseline between observations with sufficient spatial resolution. Data from a single instrument are rarely able to produce suitable comparisons for this purpose. But, by combining data from RADAR, the Visual and Infrared Mapping Spectrometer (VIMS) and the Imaging Science Subystem (ISS), we can take advantage of 13 years of Titan-targeted flybys at the cost of added complexity. Each instrument's dataset is unique in spatial and temporal resolution and coverage, making precise comparison between them nontrivial. Furthermore, the instruments probe different properties of the surface. VIMS and ISS are sensitive to composition and grain size on the scale of a few micrometres while Synthetic Aperture RADAR (SAR) images convey information about dielectric properties and surface roughness on the centimetre scale.

Lakes are identifiable due to their lacustrine morphology and characteristic darkness in each dataset. Light specularly reflects off the surface of the smooth lakes [START_REF] Wye | Electrical properties of Titan's surface from Cassini RADAR scatterometer measurements[END_REF][START_REF] Soderblom | Modeling specular reflections from hydrocarbon lakes on Titan[END_REF] , often away from the direction of Cassini. In the infrared (IR), diffuse scattering off haze in the atmosphere also provides some illumination, making lakes appear dark grey to ISS (0.93 μm) and dark blue to VIMS (0.9-5 μm) in the colour scheme of Figs. 1 and2. At 2.17 cm, the observed RADAR signal is unaffected by the atmosphere [START_REF] Rodriguez | Impact of aerosols present in Titan's atmosphere on the Cassini radar experiment[END_REF] and is a combination of quasispecular backscatter and diffuse backscatter [START_REF] Wye | Electrical properties of Titan's surface from Cassini RADAR scatterometer measurements[END_REF] . For lakes, SAR observes low signal return resulting from little to no quasispecular contribution (due to the smooth lake surface); weak diffuse contribution from volume scattering within the liquid (if it is nearly homogenous liquid); and reduced scattering off the lake floor boundary (due to the small Fresnel reflection coefficient between liquid and solid organics) [START_REF] Hofgartner | Titan's "Magic Islands": transient features in a hydrocarbon sea[END_REF] . Attenuation within a liquid column begins to affect the signal when path lengths are greater than tens of metres [START_REF] Mastrogiuseppe | The bathymetry of a Titan sea[END_REF][START_REF] Mitchell | Laboratory measurements of cryogenic liquid alkane microwave absorptivity and implications for the composition of Ligeia Mare[END_REF] (Supplementary Fig. 1). Each instrument is sensitive to liquid depths of at least a few wavelengths.

The location and extent of Titan's lakes and seas are thus some of the strongest cases of agreement between RADAR, VIMS and ISS datasets. Three surface features, however, defy that agreement. These phantom lakes appear liquid-filled and lacustrine in shape to RADAR but not to the IR instruments in later observations. Observed by RADAR in SAR mode on 22 July and 9 October of 2006 1 (top panel of Fig. 2), the phantom lakes are dark in both the denoised 21 images (Fig. 1) and raw images (Fig. 2). Their normalized radar cross-sections (σ 0 ) are more consistent with nearby lakes than dry surfaces. In Fig. 3 we show the σ 0 of the phantom lakes relative to empirical fits of empty lakes (red) and partially filled lakes (blue); shading represents 95% confidence intervals [START_REF] Hayes | Transient surface liquid in Titan's polar regions from Cassini[END_REF] . A second observation on 23 May 2013 (Fig. 2 inset) shows that phantom lake B remained dark enough to agree with the lake fit, although is brighter than predicted.

Of course, RADAR darkness does not a lake make. We do not definitively rule out that some combination of smoothness or reduced volumetric scattering [START_REF] Paillou | Models of synthetic aperture radar backscattering for bright flows and dark spots on Titan[END_REF] makes these features RADAR-dark dry surfaces. However, the lacustrine morphology of each candidate makes the presence of liquids a more likely explanation, especially given the phantom lakes' locations within the lake district and far from, for example, the dark dunes of the equatorial region. While phantom lake A lacks the sharp edges seen at some lakes [START_REF] Birch | Raised rims around Titan's sharp-edged depressions[END_REF] , it is locally confined at a scale similar to neighbouring lakes and has diffuse boundaries like those seen at Jingpo and MacKay Lacus; A is therefore unlikely to be a dark plain (examples of which are plotted as grey circles in Fig. 3).

Phantom lake B is a dark area along the southern shoreline of Oneida Lacus, a lake confirmed to have liquids by echoes in the April 2017 altimetry pass (which unfortunately ends before reaching phantom lake B). Overlap between SAR swaths T19 and T91 indicates that the rim extends partially along the southern shore, separating half of the phantom lake terrain from the liquid of Oneida. Thus, phantom lake B's morphology suggests a plain in contact with a lake shoreline, potentially a flood plain. Finally, C's boundaries resemble those of neighbouring sharp-edge depressions [START_REF] Birch | Geomorphologic mapping of Titan's polar terrains: constraining surface processes and landscape evolution[END_REF] .

Because the ISS and VIMS cameras could not observe Titan's north pole until the Sun rose with northern spring (August 2009) and the winter clouds dissipated [START_REF] Mouélic | Dissipation of Titan's north polar cloud at northern spring equinox[END_REF] , ISS first glimpsed the lake district on 13 October 2013. In that image, phantom lake A was not dark like a lake while phantom lakes B and C were not resolved. A month later (Fig. 2 middle), phantom lakes A and C appear bright, inconsistent with the presence of surface liquids. The observation of phantom lake B is less conclusive due to its proximity to Oneida Lacus.

VIMS followed up on 1 December 2013 (Fig. 2 bottom). At as fine as 4 km pixel -1 , at least four spectral units-surface materials with similar reflectance properties in the IR-are evident. Evaporites [START_REF] Barnes | Organic sedimentary deposits in Titan's dry lakebeds: probable evaporite[END_REF][START_REF] Mackenzie | Evidence of Titan's climate history from evaporite distribution[END_REF] appear bright pink/orange in our IR colour images because of their diagnostic brightness at 5 μm; they surround some of the dark blue lakes. (The blue and green materials are spectrally distinct but not yet geomorphologically interpreted.) VIMS pixels covering phantom lakes A and B do not behave as a single unit as they do in RADAR.

In Fig. 4 we show that the southern pixels of A (black square) are darker than the northern pixels (grey square). Similarly, the western half of B (black star) is darker than the eastern (grey star). These bright western pixels of B parallel the raised rim of Oneida Lacus.

Although the outline of the phantom lakes is unmistakable in RADAR, A and C do not show these boundaries in VIMS. Phantom lake B's two VIMS units do correspond to the RADAR boundaries, providing morphological evidence that this RADAR-dark patch is a unique and isolated feature. Phantom lake C's spectrum most closely resembles the evaporites of Ypoa and Suwa Lacus, nearby lakes that appear liquid-filled in all datasets.

Subsequent VIMS observations are too coarse for in-depth analysis but appear consistent with a lack of surface liquids. ISS images from February 2014 and July 2017 show that the phantom lakes are bright even in the final Cassini glimpses of the lake district.

Thus, the phantom lakes scatter like nearby solid surfaces in the IR. They cannot be open bodies of liquid at the time of VIMS or ISS observations. How then can we reconcile the liquid RADARdarkness with an IR bright surface? We put forth three possible explanations for the phantom lake observations: (1) constant liquid level with a RADAR-invisible topmost layer; (2) an IR scattering layer developing between observations; and (3) liquid removal from at least the top few micrometres of the surface. In all cases, the RADAR-darkness arises from liquids on or saturating the surface at the time of the RADAR observations.

In scenario (1), no surface change occurs. Rather, the difference between the RADAR and IR observations stems from the difference in wavelengths observed by the RADAR mapper and the IR imagers. For example, the diffuse scattering off suspended Rayleigh particles much smaller than a RADAR wavelength with dielectric constants near that of liquid methane could contribute a small enough σ 0 that the lake would appear RADAR-dark [START_REF] Hofgartner | Titan's "Magic Islands": transient features in a hydrocarbon sea[END_REF] . In this case, the scattering layer must be less than a RADAR wavelength (2.17 cm) to be effectively transparent to the instrument.

In scenario (2), the scattering layer could develop in the time between the RADAR and IR observations. In this case, the IR bright layer need only be thick enough to obscure the liquid below. The scattering 'scum' layer could be bubbles, haze fallout, or suspended sediment atop a liquid layer. But, as even a few millimetres of liquid would show significantly decreased reflectance to VIMS [START_REF] Clark | Detection and mapping of hydrocarbon deposits on Titan[END_REF] , the overall IR brightness of the phantom lakes requires that the scattering layer be optically thick (a few millimetres). Furthermore, as no ethane absorption features are present in any of the phantom lakes' spectra, ethane cannot be present in the scattering layer (Supplementary Fig. 3). This, along with the fact that the phantom lakes do not exhibit the same boundaries in VIMS as they do in RADAR, suggests that bubbles, haze fallout, and suspended sediment are unlikely explanations for the IR brightness of the phantom lakes.

Alternatively, a dry rind sitting atop a saturated regolith would not necessarily show unique spectral boundaries and is thus the more likely no-change scenario. Huygens' observations [START_REF] Lorenz | Titan's damp ground: constraints on Titan surface thermal properties from the temperature evolution of the Huygens GCMS inlet[END_REF] suggest even Titan's equatorial desert has liquid methane close to the surface. Modelling Titan's climate with extensive surface liquid reservoirs better reproduces the observed distribution of seas and cloud activity [START_REF] Mitchell | The climate of Titan[END_REF][START_REF] Lora | GCM simulations of Titan's middle and lower atmosphere and comparison to observations[END_REF][START_REF] Newman | Simulating Titan's methane cycle with the TitanWRF general circulation model[END_REF][START_REF] Turtle | Titan's meteorology over the Cassini mission: evidence for extensive subsurface methane reservoirs[END_REF] . The phantom lakes could therefore be highly localized areas of near-surface-wetted regolith distinct from the surrounding features, an explanation perhaps more likely for phantom lake B given its morphological similarity to a flood plain of Oneida Lacus and less likely for A and C given their lacustrine morphologies and distance from other lakes. If the phantom lakes are the first Cassini identification of regolith saturated up to the top few millimetres, it is curious that such saturated regolith is limited to a few isolated locales given that lakes are widely distributed throughout the polar region.

We therefore currently favour scenario (3) in which liquids are responsible for the dark σ 0 and are removed to at least a few millimetres below the surface by the time VIMS and ISS observe the phantom lakes. A freshly exposed solid surface could explain both the IR brightness and the similarity between the phantom lakes' VIMS units and those of the surrounding terrain. Processes for emptying a lake on Titan include draining by channels, infiltration into a porous regolith and evaporation. Cassini could not resolve any channels feeding into the phantom lakes; if any such features exist they must be subpixel in size (<300 m).

For features A and C, the emptying process would have to take place within the seven years between observations, a timescale that easily fits within the estimates for emptying via a combination of evaporation and infiltration. If the phantom lakes are shallow, evaporation would empty them more quickly than a nearby deep lake-creating more easily resolvable shoreline change-and should pick up with increased insolation during northern summer, in line with the sequence of our observations. Infiltration can happen on relatively short timescales: even the least permeable regoliths hypothesized on Titan can drain lakes of 10 m to a methane table a few centimetres below the surface within several years 5 . Modelled evaporation rates for Titan range from ~0.01 mm per Earth year [START_REF] Newman | Simulating Titan's methane cycle with the TitanWRF general circulation model[END_REF] to metres per Earth year [START_REF] Mitri | Hydrocarbon lakes on Titan[END_REF] . The most conservative evaporation estimates (0.01 mm per Earth year) constrain the evaporated volumes of phantom lakes A and C to as small as 10 6 m 3 ; corresponding to depths too shallow to be sufficiently dark to RADAR. Thus, infiltration of about the same volume would have to have played a role.

Feature B, on the other hand, would have a much shorter timescale for change. Although brief, the 6 months between observations may be enough time to remove liquid from the shallow depths of the surface that the IR instruments sense. Phantom lake B appears brighter to RADAR at higher incidence angles than would be expected for a shallow lake. Scattering off suspended particles can increase σ 0 , but so can looking through less liquid, that is, a decrease in the amount of liquid at phantom lake B. Furthermore, B is situated along the shoreline of Oneida Lacus, enhancing the likelihood of a shallow deposition of liquid (for example, lake overflow) or draining into a nearby reservoir (for example, deeper into the subsurface). As a raised rim separates the western half of phantom lake B from Oneida Lacus, it is more likely for liquid to overflow on the eastern half, consistent with the difference in VIMS units. Together, the phantom lakes suggest that observable change may have occurred at Titan's north pole during the Cassini mission at timescales (6 months-7 years) comparable to that observed for south polar lakes 5 of similar size. This seasonal timescale would also be consistent with the range of removal rates predicted for evaporation [START_REF] Mitri | Hydrocarbon lakes on Titan[END_REF][START_REF] Newman | Simulating Titan's methane cycle with the TitanWRF general circulation model[END_REF] and infiltration [START_REF] Hayes | Hydrocarbon lakes on Titan: distribution and interaction with a porous regolith[END_REF] when operating in conjunction. Barring substantial local (less than a few kilometres) differences in evaporation and/or infiltration properties, we expect that larger and deeper lakes are exchanging their liquids between the surface and atmosphere at similar rates, but their greater depths make their shoreline changes undetectable by Cassini.

Methods

After calibration (described below), we imported images into QGIS, an opensource GIS, for projection and mapping.

In SAR mode, the Cassini RADAR instrument mapped the surface at resolutions of ~350 m pixel -1 at 2.17 cm (ref. [START_REF] Elachi | Radar: the Cassini Titan radar mapper[END_REF] ). We used incidence angle, noise-subtracted and NLDSAR [START_REF] Lucas | Insights into Titan's geology and hydrology based on enhanced image processing of Cassini RADAR data[END_REF] swaths from T16, T19 and T91. Incidence and σ 0 values were extracted via polygon mapping and statistical tools within QGIS. The fits shown in Fig. 3 are taken directly from a previously published empirical fit to SAR data [START_REF] Hayes | Transient surface liquid in Titan's polar regions from Cassini[END_REF] .

ISS imaged Titan at 0.938 μm (ref. [START_REF] Porco | Cassini imaging science: instrument characteristics and anticipated scientific investigations at Saturn[END_REF] ). At this wavelength, haze particles in the atmosphere scatter most of the light before it reaches the surface. However, the shape of the haze phase scattering function [START_REF] Tomasko | A model of Titan's aerosols based on measurements made inside the atmosphere[END_REF] actually facilitates observation of the surface because some of that light forward scatters to the ISS detector. The resulting ISS maps are generally 1 km pixel -1 . Thus, ISS data have been used to identify the presence of liquid on Titan's surface [START_REF] Turtle | Shoreline retreat at Titan's Ontario Lacus and Arrakis Planitia from Cassini Imaging Science Subsystem observations[END_REF][START_REF] Turtle | Rapid and extensive surface changes near Titan's equator: evidence of April showers[END_REF] as well as monitor cloud activity in the atmosphere [START_REF] Turtle | Cassini imaging of Titan's high-latitude lakes, clouds, and south-polar surface changes[END_REF][START_REF] Turtle | Seasonal changes in Titan's meteorology[END_REF] . For this work, we used the global mosaic map available from the United States Geological Survey (USGS), as well as data from 13 October 2013 to 2 February 2014 available on the Planetary Data System (PDS). The latter were calibrated and mosaicked using USGS Integrated Software for Imagers and Spectrometers (ISIS).

VIMS observed Titan in the near-IR windows at which methane absorption that of trace gases) is weak enough to allow light to penetrate through the atmosphere and interact with the surface [START_REF] Baines | The atmospheres of Saturn and Titan in the near-infrared: first results of Cassini/VIMS[END_REF][START_REF] Brown | Observations in the Saturn system during approach and orbital insertion, with Cassini's visual and infrared mapping spectrometer (VIMS)[END_REF] : 0.93 μm, 1.0 μm, 1.3 μm, 1.6 μm, 2.0 μm, 2.7 μm, 2.8 μm and 5 μm. Although specific chemical composition is difficult to identify [START_REF] Mccord | Titan's surface: search for spectral diversity and composition using the Cassini VIMS investigation[END_REF][START_REF] Mackenzie | Compositional similarities and distinctions between Titan's evaporitic terrains[END_REF] , the diverse surface can be divided by spectral reflectance properties into spectral units [START_REF] Barnes | Global-scale surface spectral variations on Titan seen from Cassini/VIMS[END_REF] .

VIMS data were calibrated and coloured [START_REF] Barnes | Global-scale surface spectral variations on Titan seen from Cassini/VIMS[END_REF] for initial identification of spectral units, shown in Figs. 1 and2. We identified four spectral units in the high-resolution cube-lake, evaporite, blue and green-based on the unique behaviour of the band ratios. These endmember representative spectra were created by averaging over pixels within the identified units. To rule out atmospheric phenomena, we applied an empirical correction [START_REF] Mouélic | Global mapping of Titan' s surface using an empirical processing method for the atmospheric and photometric correction of Cassini/VIMS images[END_REF] and also modelled the spectra with the radiative transfer model [START_REF] Hirtzig | Titan's surface and atmosphere from Cassini/VIMS data with updated methane opacity[END_REF][START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF][START_REF] Brossier | Geological evolution of Titan's equatorial regions: possible nature and origin of the dune material[END_REF] . In both datasets, the spectral behaviour of the phantom lakes shown in Fig. 4 is consistent and agrees with the raw data. The radiative transfer model, however, allowed us to significantly reduce the standard deviation of the spectral ratios with respect to the raw and empirically corrected data, thus reinforcing the conclusions that the phantom lakes are not liquid-filled in the VIMS data.

The radiative transfer model used is described in ref. [START_REF] Hirtzig | Titan's surface and atmosphere from Cassini/VIMS data with updated methane opacity[END_REF] with a look-up-table scheme [START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF] as described in detail in ref. [START_REF] Brossier | Geological evolution of Titan's equatorial regions: possible nature and origin of the dune material[END_REF] . Although the model relies on Huygens' ground truth from the equatorial region, the decreased standard deviation of the spectral ratios of all units indicates that the radiative transfer model fairly mitigated the atmospheric contributions, one of the main sources of data variability.

There are many IR bright phenomena in VIMS observations of Titan. Specular reflections off smooth surfaces [START_REF] Soderblom | Modeling specular reflections from hydrocarbon lakes on Titan[END_REF][START_REF] Stephan | Specular reflection on Titan: liquids in Kraken Mare[END_REF][START_REF] Barnes | Wave constraints for Titan's Jingpo Lacus and Kraken Mare from VIMS specular reflection lightcurves[END_REF] are bright at all wavelengths (especially 5 μm) but are only observed when Cassini images the surface at the same angle at which the light is incident. None of our phantom lakes were imaged at this geometry. Broad specular reflections from wavy surfaces can occur farther from the specular point but are also much brighter than the reflectance of the phantom lakes [START_REF] Barnes | Cassini/VIMS observes rough surfaces on Titan's Punga Mare in specular reflection[END_REF] . Furthermore, no specular reflections have been identified in ISS data to date, as the high optical depth at 0.93 μm makes direct surface scattering unlikely even at favourable geometries. Thus, neither direct nor broad specular reflections can explain the brightness of the phantom lake features in VIMS or ISS data. Clouds are also bright but have a distinct, ephemeral spectral signature [START_REF] Griffith | The evolution of Titan's mid-latitude clouds[END_REF][START_REF] Barnes | VIMS spectral mapping observations of Titan during the Cassini prime mission[END_REF][START_REF] Rodriguez | Global circulation as the main source of cloud activity on Titan[END_REF][START_REF] Rodriguez | Titan's cloud seasonal activity from winter to spring with Cassini/VIMS[END_REF] that is inconsistent with that of the phantom lakes (Supplementary Fig. 6). As the phantom lakes do not appear to drastically change between observations (October 2013-July 2017) with VIMS and ISS, clouds are unlikely to hide liquids. The adjacency effect can artificially brighten dark surfaces when photons reflected from nearby bright surfaces get scattered into the cone of acceptance of the pixel imaging the dark material. However, this effect dominates at shorter distances with increasing optical depth [START_REF] Minomura | Adjacency effect in the atmospheric correction of satellite remote sensing data: evaluation of the influence of aerosol extinction profiles[END_REF] and we observe the opposite: the phantom lakes appear brighter at the longer wavelengths. The brightness of the phantom lakes is therefore most likely due to compositional and grain size properties of the surface and not to some observational or atmospheric phenomenon.

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  ASTRoNoMy | VOL 3 | JUNE 2019 | 506-510 | www.nature.com/natureastronomy

Fig. 1 |

 1 Fig. 1 | Cassini images of Titan's north pole. a, Azimuthal stereographic projection of Titan's north pole as observed by Cassini VIMS on 13 December 2013. Titan's hydrocarbon seas (maria) lie opposite the lake district and at lower elevation 7,53 . b-e, Eastern edge of the lake district as seen by VIMS (up to 4 km pixel -1 ; b), ISS (map scale at 4 km pixel -1 ; c), non-localized denoised 21 SAR (350 m pixel -1 ; d), and a VIMS-NLDAR overlay (e). These instruments observed the eastern half of the lake district at different wavelengths (listed in the lower-right corner of each panel) and seasons (northern winter and northern spring). A, B and C labels indicate the phantom lake features on the NLDSAR image. Relevant lake names are given on the ISS map.

Fig. 2 |Fig. 3 |

 23 Fig. 2 | Sequence of observations of the phantom lakes, outlined in each dataset. SAR coverage from T16 and T19 (top), and T91 (inset) show the phantom lakes as dark. But later, the same areas appear bright in ISS (middle) and VIMS (bottom) images. Normally, lakes appear dark in all three datasets. Because our temporal coverage relies on three datasets that probe different surface properties, we consider both liquid-level change and physical phenomena as possible explanations.

Fig. 4 |

 4 Fig.4| Behaviour of phantom lakes relative to other VIMS spectral units within the atmospheric windows. a, In the T96 VIMS image (CM_1764550739_16), we identify four units (lake in purple, evaporite in pink, green and blue) as endmembers to which we compare phantom lake pixels (examples labelled in top image). b,c, Because VIMS can only see down to Titan's surface in seven windows (0.93, 1.0, 1.3, 1.6, 2.0, 2.7, 2.8 and 5.0 μm), we group surface materials into spectral units defined by the relative reflectance at these wavelengths. Phantom lakes A and B have two groups of pixels (black and grey), suggesting two spectral units within the area that RADAR sees as a dark unit. Atmospheric effects have been mitigated with a radiative transfer model. Error bars represent standard deviations from the population mean.

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Acknowledgements

This work was supported under the NASA Earth and Space Science Fellowship Program grant NNX14AO30H to S.M.M. J.W.B. acknowledges support from NASA Cassini Data Analysis Program NNX15AI77G. A.L. and S.R. acknowledge the financial support of the UnivEarthS Labex program at Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02). S.R. is also supported by the French National Research Agency (ANR-APOSTIC-11-BS56-002, ANR-12-BS05-001-3/EXO-DUNES). Part of this work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. Government sponsorship is acknowledged.

Data availability

All data presented here are available from the NASA Planetary Data System (https://pds-imaging.jpl.nasa.gov/portal/cassini_mission.html), except the NLDSAR swaths that are maintained by A.L. (http://cssnldsar.geophysx.org/). The data that support the plots within this paper are also available from the corresponding author upon reasonable request.

Author contributions

S.M.M. led the procuring and analysis of the data and wrote the manuscript. J.W.B. assisted in all aspects of the analysis and writing. J.D.H. and S.P.D.B. contributed to the analysis of RADAR data. M.M.H. helped develop scattering models. A.L. wrote the code to produce NLDSAR and provided these data. All authors contributed to the discussion of these results. S.R. provided the radiative transfer model and contributed to their analysis. E.P.T. assisted in the calibration of ISS data and planned the ISS observations. C.S. planned the VIMS Titan observations.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information is available for this paper at https://doi.org/10.1038/ s41550-018-0687-6.


Wassim Swaileh
email: wassim.swaileh@irisa.fr

Michel Jordan
email: michel.jordan@cyu.fr

Dimitris Kotzinos
email: dimitrios.kotzinos@cyu.fr

3D Modelling Approach for Ancient Floor Plans' Quick Browsing ⋆

Keywords: 3D modelling, Convolutional neural network, Ancient architectural archives

Although 2D architectural floor plans are a commonly used way to express the design of a building, 3D models provide precious insight into modern building usability and safety. In addition, for a historical monument like the Palace of Versailles, the 3D models of its ancient floor plans help us to reconstruct the evolution of its buildings over the years. Such old floor plans are hand made and thus present some problems in automatic creation of a 3D model due to the drawing style variability. In this paper, we introduce a fully automatic and fast method to compute 3D building models from a set of architectural floor plans of the Palace of Versailles dated to the 17 th and 18 th century. First, we detect and localise walls in an input floor plan image using a statistical image segmentation model based on the U-net convolutional neural network architecture and a binary wall mask image is obtained. Secondly, using the generated wall mask image, the 3D model is built upon the linear edge segments representing the detected wall sides in the mask image. In order to cope with the lack of accurate ground truth information for the 3D models of ancient floor plans, we use a dedicated semi-automatic software to build a set of reference 3D models that describe plans' wall projections from three sides of view. We evaluate the performance of our approach on an input floor plan image by measuring the overlapping between the 3D reference model and our 3D model. Our fast and fully automatic approach performs efficiently and produces quite accurate 3D models with 84.2% of IoU score in average. Furthermore, its performance surpasses the performance of the state of the art approach in the wall detection task.

Introduction

Since the ancient architectural plans of a historical monument, such as the Palace of Versailles, reflect the evolution of the monument's buildings over the years, ⋆ First and second authors contributed equally to this research the conversion of these 2D plans into 3D models automatically, allows the visualisation of certain disappeared or unrealised places of the monument. Such old plans present several difficulties and challenges regarding drawing styles and paper format variabilities, in addition to foreground and background variable colour contrast. Due to these variabilities, building a 3D model from such floor plan images is not trivial. Actually, even creating the 3D model manually is not trivial either, and requires skill and time [START_REF] Yin | Generating 3d building models from architectural drawings: A survey[END_REF] In the literature, most of the related works detect walls in modern architectural drawings for building representative 3D models. Such drawings respect a set of standard protocols and symbols. However, architectural drawings in ancient floor plans show sometimes shapeless walls of variable drawing style [START_REF] Swaileh | Versailles-FP Dataset: Wall Detection in Ancient Floor Plans[END_REF]. The navigation through a virtual 3D environment becomes a common practice in order to to access the past of the historical monuments and is nowadays commonly used in various domains and applications such as cultural heritage, archaeology, virtual tourism, etc. (see for instance [START_REF] Fiorucci | Machine learning for cultural heritage: A survey[END_REF][START_REF] Grilli | A review of point clouds segmentation and classification algorithms[END_REF]). Virtual reality and augmented reality, combined with semantic analysis, allow professionals, as well as the general audience, to visualise any kind of data including cultural heritage and historic data [START_REF] Lampropoulos | Enhancing the functionality of augmented reality using deep learning, semantic web and knowledge graphs: A review[END_REF].

In this article, we present a 3D modelling approach that provides access to historical architectural archives by building 3D models in a fast and fully automated way. The paper is organised as follows: related works are presented in the following section. The proposed approach is then introduced in section 3. Finally, we present the evaluation protocol and system performance evaluation results in section 4 before introducing the conclusion and future works.

Related work

In the literature we observe that the 3D modelling process of scanned floor plans consists of two main steps: the wall detection process and the 3D model generation process. Indeed, while the wall detection is not the main task but can be a sub-task, there are some works which are only focused on wall detection and we discuss those works in the following section.

Wall detection

Traditionally, the wall detection task consists of several low-level image processing techniques including floor plan image noise reduction, graphics/text splitting, and drawing vectorisation. For detecting walls in ancient floor plan images, [START_REF] Tabia | Automatic reconstruction of heritage monuments from old architecture documents[END_REF] used mathematical morphology operators in order to detect the main walls' drawings in a given input floor plan image, then built the corresponding 3D model. The proposed method requires human intervention to tune a threshold parameter in order to accurately detect thick walls and thin ones. In the same context, [START_REF] Swaileh | Versailles-FP Dataset: Wall Detection in Ancient Floor Plans[END_REF] introduced a U-Net convolutional neural network model for wall segmentation in ancient floor plan images. The model is trained to produce main wall mask images from grayscale floor plan images with no need for human intervention. We are using this work in our fully automatic 3D modelling processing chain.

In modern architectural drawings, many works are reported on wall detection and/or room segmentation. [START_REF] Macé | A system to detect rooms in architectural floor plan images[END_REF] used Hough transform to detect walls and doors. Subsequently wall polygons are created by the Hough lines and are partitioned iteratively into rooms, assuming convex room shapes. [START_REF] Ahmed | Automatic room detection and room labeling from architectural floor plans[END_REF] first segment wall footprints in high-resolution images according to their line thickness. Then, they used geometrical reasoning to find room segments. SURF descriptors are used to detect doors. Convolutional neural networks were recently adopted to achieve the wall detection task. [START_REF] Dodge | Parsing Floor Plan Images[END_REF] used a simple neural network for denoising the plan image then used a fully convolutional neural network (FCN) for detecting walls. This approach is one of the state-of-the-art methods and performs well on multi-color contemporary floor plan images. [START_REF] Liu | Raster-to-vector: Revisiting floorplan transformation[END_REF] used a combination of deep neural networks and integer programming, where they first identify junction points in a given floor plan image and then join the junctions to locate walls in the floor plan. The method can only handle walls aligned with the two major axes of the floor plan image. Therefore, it can recognise layouts with only rectangular rooms and walls of uniform thickness, this is a critical limitation in the context of historical layouts where the shapes of the rooms are not always rectangular and often round shaped rooms are used. [START_REF] Yang | Dula-net: A dual-projection network for estimating room layouts from a single rgb panorama[END_REF] also trained an FCN to label pixels in a floor plan image with multiple classes. The classified pixels formed a graphic model and were used to recover houses of similar structures.

As stated earlier all these works use different methods ranging from low level image processing to heuristics and furthermore to deep learning. However, the success of these methods in modern architectural documents cannot be replicated in the case of ancient architectural documents.

3D modelling

Nowadays, 3D representations are a useful tool for architects because they provide an intuitive view on the architects' work and help them to present their projects to their clients. Thus, the research about 3D model computation from architectural drawings is an active research field since more than 20 years [START_REF] Yin | Generating 3d building models from architectural drawings: A survey[END_REF]. Contemporary architectural floor plans are composed of geometric shapes (straight lines, curves) representing the building structure (external and inner walls), while various symbols represent openings, stairs, heating and furniture elements, etc. A lot of textual annotations provide information about the building's use, its rooms, dimensions, etc. This standard drawings give a strong basis for a lot of research works that succeeded in the floor plan analysis and automatic 3D modelling tasks. In [START_REF] Dosch | A complete system for the analysis of architectural drawings[END_REF], authors from the Loria lab present a system for the analysis of architectural drawings, with the aim of reconstructing in 3D the represented buildings. Authors follow a set of graphics recognition steps including image processing and feature extraction. This system demonstrates some robustness though it requires moderate human assistance. Siu-Hang Or et al. [START_REF] Or | Highly Automatic Approach to Architectural Floorplan Image Understanding & Model Generation[END_REF] developed a system to solve a slightly simplified problem that considers only walls, doors, and windows. The system distinguishes walls as inner structures from building outlines and uses it to match neighbouring floors; during vectorisation, the system extracts outlines of black pixels in the raster image and matches them with walls of various shapes. An improved example-driven symbol recognition algorithm is proposed for CAD engineering drawings in [START_REF] Guo | An improved example-driven symbol recognition approach in engineering drawings[END_REF]. Firstly, in order to represent the structure of symbols, Guo et al. involve the text entity as one of the basic elements and redefine the relation representation mechanism. Then, the structure graph and a constrained tree is established for the target symbol, using the knowledge acquisition algorithm. In the recognition process, the nodes with the same type as the key features are located first in the drawing. The authors of [START_REF] De Las Heras | CVC-FP and SGT: a new database for structural floor plan analysis and its groundtruthing tool[END_REF] propose a database for structural floor plan analysis and the associated ground truth tool. The ground truth tool especially focuses on wall segmentation using the Hough line transform combined with an alignment heuristic fitting, and room detection.

Beside the 3D model computation, another field of interest concerning floor plan analysis is the need to refer to reference drawings when designing new buildings and to find solutions for similar architectural problems. In [START_REF] Ahmed | Automatic analysis and sketch-based retrieval of architectural floor plans[END_REF], authors present a system for semantic search from an architect's sketch: the semantic information of reference floor plans is extracted thanks to a "divide and conquer" strategy that separates text from graphics, and then graphics between thick lines (mainly walls) and thin lines (symbols). A further structural analysis allows us to perform the room detection and labelling. The DANIEL architecture presented in [START_REF] Sharma | Daniel: A deep architecture for automatic analysis and retrieval of building floor plans[END_REF] is a deep learning model that learns the representative floor plan features using a convolutional neural network (CNN); the existing datasets provide the examples for the learning step. The authors of this paper proposed the ROBIN dataset that they used for evaluation.

The historical floor plans such as the ones we are working with have some drawing and digitizing specific features that do not allow their processing by one of the system described in previous section: the symbols for openings, doors, stairs, furniture, etc., are different depending of the epochs and architects, and the digitization retains marks of the document state (for instance creases, since these documents have been kept in folders during long periods) or stamps that are on the drawing's reverse side. For these reasons, some of us developed in a previous project a system which copes with these particularities and help to build an accurate 3D model from the floor plans, thanks to a limited number of user interactions [START_REF] Tabia | Automatic reconstruction of heritage monuments from old architecture documents[END_REF]. This system demonstrates a good ability to perform this task, but is not appropriate when processing a lot of drawings.

In the field of cultural heritage and architecture, some projects deal with text and image extraction from archived documents [START_REF] Oliveira | dhsegment: A generic deep-learning approach for document segmentation[END_REF], other projects intend to build 3D models from various data sources such as photographs, laser scanning or point clouds [START_REF] Grilli | Application of machine and deep learning strategies for the classification of heritage point clouds[END_REF]. The European Time Machine project intends to build 3D models of historical European cities across the centuries and analyses for this purpose various types of data including texts and graphics such as cadastral data; this allows to build city 3D models but not to enter the building interiors. In fact, it seems that the architectural drawing collection describing the palace of Versailles between 17 th and 18 th centuries is exceptional and lead to particular problems and particular algorithmic solutions.

Proposed approach

Our approach relies on three main steps: the floor plan digitization step, the wall mask generation step and the 3D modelling step. There is no need for human intervention during the whole processing chain and the result is obtained in a few seconds. Such fast and automatic 3D model construction system allow fast access to disappeared or non-realised architectural projects that interest specialists as well as the general public (sections 3.1-3.2-3.3). Figure 1 illustrates our processing pipeline from the floor plan image as input to the resulting 3D model.

Floor plan digitization

The ancient floor plans of the Palace of Versailles have various sizes and drawing styles. This is due to the lack of standards for the drawing styles and paper formats at that age, and to the long period (about 120 years) covered by these plans. The images of these floor plans, including those of Versaille-FP dataset, were captured in a very high resolution. Our approach receives a multi-colour floor plan image as input. Then, it converts it into grayscale in order to reduce the colour noise and increase the intensity between the foreground and background colours at the input image. After that, it scales the grayscale image down to images of 512 × 512 pixels. To maintain the aspect ratio of the original input image, we square padded the input image to its largest dimension before applying the scaling process. Once the scaled image is obtained, we apply the wall segmentation model based on the U-net convolutional neural network to obtain the wall mask image. The wall mask image is a binary image where the foreground colour represents the wall regions detected by the segmentation model in the scaled input image.

Wall mask generation

At the second step of our proposed approach we used a U-Net architecture of convolutional neural network (CNN) to generate the wall mask image from the input image. We used the same CNN model architecture introduced by [START_REF] Swaileh | Versailles-FP Dataset: Wall Detection in Ancient Floor Plans[END_REF] and illustrated in figure 2. We choose this architecture due to its precious proprieties of high speed and performance with small amount of data, according to [START_REF] Gao | Pixel deconvolutional networks[END_REF]. The CNN model consists of two symmetric paths connected at a bottle neck layer. The first path namely called contracted path extracts contextual and semantic information from the input image. The second path (expanding path) achieves the accurate localization, by copying, cropping and concatenating information that are observed by the contracting path toward the expanding path. The model The loss function L D of Dice [START_REF] Milletari | Fully convolutional neural networks for volumetric medical image segmentation[END_REF] is used to train the model. The Dice Coefficient is an overlapping measure between two samples. It ranges from 0 to 1 where a Dice coefficient of 1 denotes perfect and complete overlap. The Dice loss is simply equals to 1-Dice coefficient. The L D loss value is calculated as in equation 1.

L D = 1 - 2 × |A ∩ B| + 1 |A| + |B| + 1 ( 1
)
where A is the neural network prediction about the segmentation and B is the ground truth value. We compared the performance of the U-net model using different loss functions including the Dice loss with which we obtained the best results. Similarly, we selected the Rmsprop optimisation algorithm for learning our model. We used a learning rate that start with 10e -4 with batch size of 25 and we selected the best model during the learning process. We applied learning rate decay whenever validation accuracy does not improve. Although our model training is guided by the validation datasets, learning rate adjustment based on validation accuracy still works well according to our experience. It is worthy to mention that our model differs from the state art model [START_REF] Swaileh | Versailles-FP Dataset: Wall Detection in Ancient Floor Plans[END_REF] by the models' hyper-parameters fine tuning strategies, specially with regards to the batch size and the learning rate decay. The model training is achieved in 4 days using 2

x GPU Nvidia GTX 1080 11Go. We used early stopping with patience of fifty epochs.

To produce wall mask image for an input floor plan image, we applied the final CNN model on the scaled grayscale image at the input. The generated wall mask image is then feed to the next process of the pipeline in order to produce the corresponding 3D model. In the next section, we describe in detail the 3D model construction process and its related sub-processes.

3D model generation

We develop in this section an algorithm for a fast computation of 3D models from a wall mask image such as the one provided by the deep learning architecture in section 3.2. This algorithm includes the following steps:

pruning of the residual small structures in the wall mask image; computation of edges; polygonalization of the edges; computation of the 3D model based on the wall polygons.

These steps consist of an arrangement of well-known image processing algorithms, whose parameters are fixed.

Small structures pruning Though the wall image computation is an accurate and carefully designed process, it may persist some pixels either isolated or in thin structures. The first step of our algorithm is a morphological opening with a rectangular 3 × 3 structuring element. We heuristically fixed the morphological opening number of iterations according to the wall image size. This operation allows not only to discard noisy pixels in the wall image, but also to remove thin structures such as dividing walls (cf. figure 3).

Edge detection and polygonalization

The center image of Figure 3 represents the basis for the 3D model extrusion. The walls in the 3D model have inner and outer sides, since in future steps they could be covered with more or less realistic textures. We compute wall contours by means of the Canny edge detector [START_REF] Canny | A computational approach to edge detection[END_REF] with σ parameter 0.1, and then perform edge polygonalization using a probabilistic Hough line detector [START_REF] Galambos | Progressive probabilistic hough transform for line detection[END_REF] (cf. figure 4). 3D model building The 3D model is computed as an extrusion upon the straight lines of figure 4, at an arbitrary height that we fixed as 0.15 of max(H, W ) where H and W are the initial image dimensions, in order to get a clearly visible 3D model. This height will be easily modified in further processes, depending on the final objective of the 3D modelling. Each line resulting from the polygonalization step gives an edge and two vertices for the 3D model, two other vertices are positioned vertically upon the first two, and these four vertices finally shape a vertical face (cf. figure 8).

Results and Evaluation

In this section, we present the experimental framework we followed to evaluate the performance of our fast and automatic 3D modelling approach. First, we introduce the ancient floor plan dataset that we used. Then, we present the evaluation protocol and results for a set of 15 3D models obtained by our approach and evaluated against reference 3D models that were produced using the VERSPERA semi-automatic 3D modelling tool [START_REF] Tabia | Automatic reconstruction of heritage monuments from old architecture documents[END_REF].

Dataset

In this study, we used the ancient floor plan "Versailles-FP" dataset which is based on the french VERSPERA research project2 . The dataset consists in 500 annotated images collected from scanned floor plans that belongs to the Palace of Versailles constructions dated of 17 th and 18 th century. The VERSPERA research project was started in 2013 with the aim of digitizing a large amount of graphical documents related to the construction of the Palace of Versailles during the 17 th and 18 th centuries. There is a large corpus of floor plans including elevations and sketches present in the collection of French National Archives. The total number of documents in this archive is around 6,500 among which about 1,500 are floor plans. An ambitious project to digitize this varied corpus started in 2014, extraordinary technical capability is needed to achieve this task due to fragile and varied nature of the paper documents (for example some document can be as big as 3m × 4m). The digitized plans of the Palace of Versailles consist of graphics that illustrate the building architecture such as walls, stairs, halls, king rooms, royal apartments, etc. in addition to texts and decorations. Since the palace of Versailles digitized floor plans cover 120 years (1670-1790) of architectural design, different drawing styles clearly appear in the corpus.

Evaluation protocol

Since most of the used ancient floor plans do not refer to real buildings of the Palace of Versailles of today, a straightforward numerical evaluation of the produced 3D models is not applicable. In fact, there is no absolute 3D ground truth for these data: 3D measurements in real rooms is not ever possible, since these floor plans represent parts of the monument that have been rebuilt or destroyed; even in the case of the current state of the monument is the same as the plan drawings, we can not infer that a floor plan of the 18 th century is a perfectly scaled representation of the monument. In fact, the only absolute reference would be an entirely manual processing of the floor plan images by computer graphics professionals, which is a time consuming and expensive task. We tried thus to compare some of these 3D models with the ones generated from the same floor plan images by means of the VERSPERA software [START_REF] Tabia | Automatic reconstruction of heritage monuments from old architecture documents[END_REF]. This software is an interactive semi-automatic application that we developed in a previous research project; for a rather experienced user, building a 3D model with this application requires between 5 and 10 minutes. The VERSPERA software involves the following steps: (i) image denoising and preprossessing, including downsizing to a roughly similar size for all plans; (ii) image binarization; (iii) wall detection through mathematical morphology tools and manual thresholding; (iv) wall footprint extrusion for 3D modelling. The VERSPERA software allows some other processings such as staircase detection and wall decoration, that we do not consider in this study. In the following sections, we compare our method and the VERSPERA software method by means of two criteria: computation time and 3D model accuracy. For the wall detection task, we used the same 5 fold cross validation protocol introduced in the Versailles-FP dataset paper [START_REF] Swaileh | Versailles-FP Dataset: Wall Detection in Ancient Floor Plans[END_REF]. We provide in figure 6 a set of good and bad wall detection images (images with black background). Bad results (lower row of the figure) occur when sketch scale differs too much from the learning set (lower left example) or sketch technique is different (pencil -lower right example -against ink in the learning set).

Results

Wall detection evaluation

We applied our software to floor plans of other monuments, freely available in the Gallica database from the French national Library (fig. 7); results appear to be not so good for these low resolution images, it will be interesting to add some of these examples in a transfer learning set to add more versatility to our models.

Figure 8 presents a comparison of the wall detection task evaluations using the accuracy, IoU and Dice coefficient scores for both cases of "learning from scratch" (blue lines, with best Dice score of 93%), and the "sequential learning" (red lines with best Dice score of 94%). From this two learning tasks, we observe that the sequential learning of the pre-trained model is better than learning from scratch. In addition, our model outperforms the state of the art model. The slit performance enhancement is obtained thanks to the applied training parameter settings that are different of the state of the art ones. We think that the pretrained model is learning better when using fine tuned learning rate with bigger batch size, recalling that the state of the art batch size is 16 since we used batch size of 25.

Computation time Figure 9 presents some 3D model examples of floor plans we computed using the approach described in section 3.3. Computing 3D models for the 500 wall mask images of the Versailles-FP dataset took around 20 minutes on a laptop with a Intel Xeon CPU E3-1505M processor, which gives an average of 2.4 seconds for each image. In comparison with the computation time of the reference 3D models constructed using the interactive VERSPERA software, we observe that our approach is 25 time faster than the interactive one. We give on table 1 a comparison of computation times for both methods.

3D model accuracy We compare first our models by a visual examination and comparison of the resulting 3D models for both automatic and interactive methods (see figure 10). Then, in order to get a more accurate and quantitative evaluation, we overlap the polygonalized wall mask image resulting of our approach with the vertical ground projection of the 3D model resulting from the VERSPERA software (fig. 10, right column); in fact, these two images are the basis of the 3D model extrusion, and comparing them gives a rather good approximation of fidelity between both 3D models since, as we discussed, a real reference 3D model is missing when dealing with the ancient floor plans. The right column images show small differences (non-white pixels) between the two masks that do not lead to drastic 3D model differences. For a numeric evaluation, we computed the min, max and average values and standard deviation of the IoU scores for the overlapping masks on a set of 15 models; table 2 sums up these values and shows a 84.2% average value, which is a rather good value depending on the final objective of the 3D modelling.

Min Max Average Std dev. 0.780 0.906 0.842 0.041 Table 2. IoU scores computed on 15 models. Fig. 9. Some 3D models (wireframe or solid screen capture on right) computed from the floor plan (left) and wall mask images (middle).

Perspectives and conclusion

We presented in this paper a fast 3D model computation approach for historical floor plan quick browsing. The proposed approach uses the U-net architecture of the convolutional neural neworks for detecting the wall regions in an input floor plan image, resulting in a binary wall mask image. The resulting image is filtered in a way that only the main walls remain, corresponding to the main structures of the monument. Finally, a 3D model is computed by extruding 3D faces upon linear segments corresponding to the wall edges. We applied this method to build 3D models from the 500 floor plan images of the Versailles-FP dataset (floor plans representing the palace of Versailles between 17 th and 18 th centuries), and were able to build 3D models very fast . This tool gives historians and archivists a mean to have a fast and quick but complete 3D perspective at the floor plans, and thus to get an easy perception and understanding of the volumes of the monument represented on the plan. Further work includes the integration in 3D models of other architectural details such as staircases, by means of a dedicated machine learning approach. We will also apply our algorithms to other historical datasets of architectural plans, if available.

Fig. 1 .

 1 Fig. 1. Summary scheme of the processing pipeline

Fig. 2 .

 2 Fig. 2. U-net architecture for detecting walls in ancient floor plans

Fig. 3 .

 3 Fig. 3. Discarding thin structures: original wall image (left), after processing (center), difference image (right).

Fig. 4 .

 4 Fig. 4. Edge (left) and straight line (right) images computed from center image in fig. 3.

Fig. 5 .

 5 Fig. 5. A 3D face is computed upon a polygonal line.

  To evaluate the performance of the wall detection model we distinguish between two training schemes; 1) training from scratch where the model weights are initialised arbitrary for training the model on the Versailles-FP dataset samples directly, 2) sequential training in two phases; I) training from scratch the model on the CVC modern floor plan dataset, and II) continue the training of the model on the Versailles-FP training set.

Fig. 6 .

 6 Fig. 6. Illustration of wall detection good and bad results.

Fig. 7 .

 7 Fig. 7. Some examples of wall mask computation for other monuments.

Fig. 8 .

 8 Fig. 8. Wall detection evaluation using pre-trained / trained from scratch model and comparison with the state-of-the-art.

Fig. 10 .

 10 Fig. 10. Comparison of 3D models: VERSPERA semi-manual software (left), our automatic and fast approach (center), and wall mask difference images (right).

Table 1 .

 1 Comparison of computation times.

	Method	VERSPERA software Our method
		(interactive)	(fully automatic)
	Nb of images	15	500
	Overall time	120 min	20 min
	Time per image	8 min	2.4 sec

https://www.etis-lab.fr/versailles-fp/

https://verspera.hypotheses.org/

Acknowledgements

We thank our colleagues of the VERSPERA research project in the Research Center of Château de Versailles, French national Archives and French national Library, and the Fondation des sciences du patrimoine which supports VERSPERA.