Section: New Results
Probabilistic models
A new birth and death algorithm for object detection
Keywords : Tree crown detection, diffusion, marked point process.
Participant : Xavier Descombes.
This study was partially supported by the EGIDE ECONET and has been conducted in collaboration with Prof. E. Zhizhina and Prof. Minlos, IIPT Moscow (Russian Academy of Sciences).
In this work, we propose a new stochastic algorithm to extract objects from images. The algorithm is based on the evolution of macro-objects in the continuum. We consider two models of the evolution of a disc. Each disc in the model is associated with a given object, a tree crown or a bird in the applications we address. The evolution is a birth-and-death equilibrium dynamics on the configuration space of discs (or the configuration space of points) with a given Gibbs measure as its stationary measure. To construct the dynamics, we must choose birth and death rates meeting the so-called detailed balance conditions. In our scheme, we take the intensity of birth to be a constant, but the intensity of death depends on the energy function and the current configuration. To reach the solution, we embed this new dynamics in a simulated annealing scheme. We thus get a non-stationary stochastic process, all of whose weak limit measures are supported by configurations giving the global minimum of the energy function under a minimal number of discs in the configuration. The final step is the discretization of this non-stationary dynamics. The discretization is a Markov chain non-homogeneous in time and in space, with transition probabilities depending on the temperature, the energy function and the discretization step. We have proved that
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the discretization process converges to the continuous time process at fixed temperature as the discretization step tends to zero;
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if we apply the discretization process to any initial measure with a continuous density w.r.t. Lebesgue-Poisson measure, then in the limit when the discretization step tends to 0, time tends to infinity, and the temperature tends to 0, we get a measure concentrated on the global minima of the energy function with a minimal number of discs.
Tests on real data in the case of tree crown extraction have proved that this new approach outperforms classical RJMCMC in terms of computation time.
A structural approach to 3D city modelling
Keywords : 3D Reconstruction, building, DEM, RJMCMC, marked point process.
Participants : Florent Lafarge, Xavier Descombes, Josiane Zerubia.
This Ph.D. is co-supervised by Marc-Pierrot Deseilligny, chief scientist of the technical direction of the IGN and is funded by a CNES/IGN grant.
3D building reconstruction is a difficult problem, mainly due to the complexity of the scenes. Urban environments are very dense and composed of many types of buildings, which makes their analysis difficult. In this work, we propose a structural approach to 3D building reconstruction. It consists in reconstructing buildings by assembling simple urban structures extracted from a grammar of 3D parametric models. The method is composed of two stages. The first one [34] , [23] consists in extracting the building footprints through configurations of connected quadrilaterals. Marked point processes are used to extract the global shape of the footprints, which are then regularized by improving both the connection of the objects and facade continuity. The second stage corresponds to 3D reconstruction from the DEMs and the building footprints obtained in the first stage [22] . An energy formulation is used within a Bayesian framework, as this is particularly well adapted to including prior knowledge concerning urban structures. A Markov Chain Monte Carlo algorithm coupled with simulated annealing allows us to find the minimum of this energy. Figure 6 shows a result on a typical French town centre.
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Target detection through texture perturbation analysis
Keywords : target detection, texture, classification, segmentation, Markov random field.
Participants : Alexandre Fournier, Xavier Descombes, Josiane Zerubia.
This Ph.D. is done with the support of the French Defense Agency (DGA).
We address the problem of target detection through the changes between two remotely sensed images of the same area. We first use the ENVI©software to process a Rotation Scaling Translation (RST) registration of the two images, and we then use a spectral transform to compensate the missing translation component of the output. We then use a recursive principal component analysis [42] in order to get a per-pixel change probability between the two images. A Markov random field segmentation based on the Potts model is applied to the change probability image to obtain a homogeneous and coherent change map.
The next step is to distinguish changes due to normal or natural circumstances (shadow orientation change, stereoscopic effects, changes in cultivated fields) from real targets (vehicles, camouflage). We address this problem by segmenting the change map with the k-means algorithm based on the intensity pairs (see figure 7 ). The result is then regularized by a second Potts model.
In order to give a label to each changed category, we are currently developing a region-based algorithm. In addition, in order to automate the process, the k-means algorithm is being replaced by an entropy k-means segmentation.
Damage assessment after forest fires
Keywords : forest fire, burnt area, classification, Support Vector Machines.
Participants : Olivier Zammit, Xavier Descombes, Josiane Zerubia.
This work is partly funded by a contract with Silogic. We particularly thank Commandant Poppi (Fire Brigade member and director of the cartography service, SDIS 83, Draguignan) for interesting discussions.
The main objective of this study is to evaluate and quantify the damage caused by forest fires from a single after-fire image. Our approach consists in extracting the radiometric information from the channels of SPOT 5 data [29] . The algorithm developed for mapping the burnt area uses the different spectral domains provided by such data.
The automatic discrimination of burnt and unburnt areas is achieved via a classification method based on Support Vector Machines (SVM). This supervised classification technique is well adapted to deal with data of high dimension, such as images. It enables the delineation of the affected areas with a very high degree of accuracy.
A map of the burnt areas is produced and validated. This allows the burnt areas to be referenced and placed in their geographic context, and their surface area estimated. The classification method is applied to images of areas of southern France that were heavily burnt during the summer of 2003. The results of the study show the good performance of this method by comparing its results with other traditional classifiers and with ground truth provided by SERTIT-Strasbourg and ONF-AM.
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Adaptive brushlet-based probabilistic model of texture
Keywords : Texture, brushlet, bimodal statistics, probabilistic model.
Participants : Dan Yu, Ian Jermyn.
This work is being done as part of EU project MUSCLE and is funded by an INRIA CORDI postdoctoral grant [http://www.muscle-noe.org/ ].
Texture modelling is one of the most important problems in image
processing, because texture characterizes many entities of interest in an
image. In the case of medium-resolution remote sensing images, such
entities include forests, agricultural fields, and urban areas. Texture
models must satisfy many desiderata: they should be probabilistic, to
produce principled inference algorithms; they should be translation and
rotation invariant, but direction-sensitive; and they should capture the
important structures in a texture in order best to distinguish one texture
from another. In [38] , probabilistic models of texture based
on adaptive wavelet packet bases were introduced. That work revealed the
surprising bimodal statistics of adapted wavelet packet subbands. In order
to model the varied subband statistics, a two-parameter quartic
model [15] was developed. The latter model captured the
one-point statistics of the adapted subbands well, but lacked direction
sensitivity, and did not have good translation and rotation invariance. The
current work takes the first steps in alleviating the first two drawbacks,
by extending the model in [15] to use
brushlets [40] as the adaptive basis rather than standard
wavelets. Brushlets, being complex, contain phase information. They can
thus distinguish more directions than standard wavelets, and behave better
under translations. Translation invariance requires that the probability
distribution be a function only of the amplitude of the coefficients. The
generalization of the subband model of [15] is P(b|f, g)
exp {-(f|b|2 + g|b|4)} , where changes in f and
g enable the various types of subband statistics to be modelled. The
optimal basis and optimal per-subband parameters are found by combining a
depth-first tree search with maximum likelihood. An example of an optimal
decomposition is shown in the top row of figure 9 , where
black, grey, and white correspond to Gaussian (g = 0 ), platykurtic (f>0 , g>0 ) and bimodal (f<0 , g>0 ) subbands respectively. Corresponding scatter plots of the complex
brushlet coefficients from these three types of subband are shown in the
bottom row of figure 9 . The structure of the bimodal subband
shows how the model captures the texture structure. There are very few
near-zero coefficients; the most probable coefficient values are grouped
around a finite amplitude with uniformly distributed phase arising from
translation invariance. Texture classification experiments using the model
are underway. The extension to rotation-invariant models, and the modelling
of the strong and structured inter-subband dependencies revealed by these
models remains for future work.
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