A discrete symmetric random walk is shown to be equivalent to a heat equation evolution, and an extension to nonlinear evolutions including Perona-Malik equation is shown to be of utmost importance for analysis. Upon unraveling the limitations as well as the advantages of such an equation, we are able to propose a new approach which is demonstrated to outperform existing approaches, and to lift the longstanding problem of when to stop the evolution. Substantiating and illustrating examples of image enhancement and segmentation are provided.

The problem of segmenting regions of interest from an image (or multiple images in the cases of stereo and motion) is an extremely important one in computer vision, and has been much studied. An well-known difficulty is how region information such as texture, colour and homogeneity can be combined with boundary information such as intensity gradients. In the multiple image case, there is also the question of whether computation of a dense disparity or flow should precede boundary/region identification and correspondence or follow it.
In this talk I will describe a new form of energy functional defined on closed curves in a manifold, whose minimum argument defines a segmented boundary/region. The energy functional can be used to segment regions of interest from both single images and stereo pairs and motion sequences. In the latter cases, a segmented region is found in all images along with the boundary correspondences by using the product space of the image planes. There is no need to compute a dense disparity or flow. The form of the energy functional means that whenever we are dealing with information from a single image (which includes the individual elements of a stereo pair or image sequence), arbitrary region and boundary information can be unified by transforming region information into equivalent boundary information; thus we can combine the best features of region- and boundary-based approaches. The energy is also extremely general, allowing the incorporation of large variety of image information. All choices for both single and multiple images can be globally optimised using the same, polynomial-time algorithm, by casting the problem as a minimum ratio cycle problem in the discretised plane. There is also a second polynomial-time algorithm, applicable to smaller class of energies, that is extremely parallelizable. The energy is scale-invariant in many cases, being an energy density on the boundary, thus removing the uncontrolled bias towards small or large regions present in many models.

Statistical signal and image processing have been dominated for a long time with the Gaussian assumption. This is not surprising: firstly, life is easy with the Gaussian distribution, in most cases it leads to linear equations. Secondly, for one after rigour: it is justified with the central limit theorem. However, it escaped from the vision of many in the field that the Gaussian distribution is not the only distribution satisfying the central limit theorem.
In this talk, we will challenge the "normality" of the Gaussian distribution by demonstrating its shortcomings in modelling impulsive data, and introducing an alternative distribution family namely the alpha-stable distribution.
For this model to be of any interest to us, one should also demonstrate the feasibility of developing computationally attractive new optimal signal processing algorithms for alpha-stable distributions. To this end, we present simple linear and nonlinear modelling techniques and demostrate an application in audio restoration. We also present the first numerically stable analytical representation for the alpha-stable pdf and demonstrate how it can be used to design optimal receivers for radar applications. Finally, we demonstrate preliminary results in texture modelling and mention future directions in image processing and communications which are plenty, interesting and come with a promise of good fun.

Le radar à synthèse d'ouverture (RSO) aéroporté ou spatial est un puissant outil d'observation, permettant notamment d'acquérir des images de haute résolution de la surface terrestre par tout temps, de jour comme de nuit. Le phénomène de speckle, qui se traduit par une très forte granulation dans l'image détectée, rend cependant extrêmement difficile l'interprétation automatique des données RSO. Cette présentation porte sur la segmentation d'images RSO, en particulier par l'approche contour. La segmentation consiste à diviser l'image en régions. Elle constitue un premier pas dans l'analyse de l'image, facilitant l'estimation desparamètres caractéristiques des régions.
Les détecteurs de contours déjà proposés pour l'imagerie RSO travaillent sur des données détectées et supposent que le speckle est non corrélé. En pratique, le speckle est corrélé spatialement, ce qui entraîne une certaine dégradation des performances de ces opérateurs. A partir de l'estimateur maximum de vraisemblance (MV) de la réflectivité radar, nous développons l'opérateur optimal rapport de vraisemblance généralisé, qui exploite la nature intrinsèquement complexe des données RSO monovues afin d'éviter une perte de performance due à la corrélation du speckle. Les aspects spatiaux de la détection de contours, tels que la taille et la forme de la fenêtre d'analyse, le nombre de directions à examiner, et la présence de contours multiples, sont également abordés.
Nous proposons d'utiliser des méthodes robustes basées sur l'algorithme de ligne de partage des eaux, en particulier le seuillage des dynamiques de bassin, pour extraire des contours fermés et squelettisés, définissant une segmentation de l'image. Le nombre de faux contours peut être réduit en post-traitement par la fusion de régions adjacentes ayant des propriétés similaires. L'estimateur MV de la position d'un contour dans une image RSO complexe est établi. Deux méthodes de repositionnement de contours, l'une basée sur les champs de Markov et le modèle de Potts, l'autre sur les contours actifs, sont proposées.
L'apport de la segmentation pour des traitements ultérieurs est illustré pour le filtrage adaptatif de speckle et pour la classification contextuelle supervisée.

Aligning experimental data into a standard coordinate system (SCS) is of great interest to neuroimaging science, and a necessary tool in support of genomics efforts for gene expression. Multimodality imaging, noisy data and transformations are frequent difficulties. Geometric based alignments carry across-multimodalities, yet have to be well structured to handle the noisy/occluded data.
In this work, we introduce a non-iterative geometric-based method to align 3D brain surfaces into standard coordinate system (SCS), which is based on a novel set of surface landmarks (e.g., planar embilical points, zero torsion points, etc..), which are intrinsic and are computed from the differential geometry of the surface. This is in contrast to existing methods that depend on anatomical landmarks that require expert intervention to locate - a very hard task.
The landmarks are local, and are preserved under affine transformations. To reduce the sensitivity of the landmarks to noise, we use a B-Spline surface representation that smoothed out the surface prior to the computation of the landmarks. The alignment is driven by establishing correspondences between the landmarks after a conformal sorting based on derived absolute invariants (volumes confined between parallelepipeds spanned by sets of the landmark point quadruplets). The method is tested for intra- and inter-brain alignments while entertaining cubic nonlinear transformations.

The overall aim of this work is to provide a hierarchical framework of methodologies for recognising objects represented as line patterns from large structural libraries.
One of the novel aspects of our work is a new shape representation for rapidly indexing and recognising line-patterns from large databases. The basic idea is to exploit both geometric attributes and structural information to compute a two-dimensional relational pairwise geometric histogram. Shapes are indexed by searching for the line-pattern that maximises the cross-correlation of the normalised histogram bin-contents. This technique provides the first level of the hierarchy, which is used to prune the database of many unwanted candidates.
The intermediate level of our hierarchical framework is based on a novel similarity measure for object recognition from large libraries of line-patterns. This operates at a more local image level than the histogram based indexing layer. The measure is derived from a Bayesian consistency criterion and resembles the Hausdorff distance. This consistency criterion has been developed for locating correspondence matches between attributed relational graphs using iterative relaxation operations. Our aim here, is to simplify the consistency measure so that it may be used in a non-iterative manner without the need to compute explicit correspondence matches. This considerably reduces the computational overheads and renders the consistency measure suitable for large-scale object recognition.
A Bayesian graph matching algorithm for data-mining from large structural databases operates as final level of the hierarchy. The matching algorithm uses both edge-consistency and node attribute similarity to determine the a posteriori probability of a query graph for each of the candidate matches in the reduced database generated by the lower levels of the hierarchy. The node feature-vectors are constructed by computing normalised histograms of pairwise geometric attributes. Attribute similarity is assessed by computing the Bhattacharyya distance between the histograms. Recognition is realised by selecting the candidate with the largest a posteriori probability.
For each of the above methodologies a thorough sensitivity study is undertaken for a library of over 2500 lines-patterns containing radar aerial images and a number of other images types. The analysis reveals the robustness of each method on its own as well as within the hierarchical framework. This suggests that there is a degree of complementarity between the approaches.

Nous décrivons une nouvelle approche pour la calibration des paramètres des fonctionnelles d'énergie utilisées en analyse d'images. Sans s'appuyer sur un modèle statistique a priori, comme dans un cadre bayésienne, le principe est générer une quantité arbitraire de mauvais exemples à partir d'une base d'apprentissage, et d'affiner les paramètres de manière à ce que les bons exemples forment des minima locaux de l'énergie.
Nous montrerons également comment cette approche peut être étendue pour apprendre une forme fonctionnelle des paramètres relativement aux données observées, qui peut être mis en place, par exemple, dans un cadre de restauration ou de segmentation d'images.

Référence : Calibrating parameters of cost functionals (à paraître, actes ECCV 2000).

We consider the weak plate functional, proposed by Blake and Zisserman for visual reconstruction, which depends on free discontinuities, free gradient discontinuities and second order derivatives. It is shown how this functional can be approximated by elliptic functionals defined on Sobolev spaces. The approximation takes place in a variational sense, the De Giorgi Gamma-convergence, and extends to this second order model an approximation theorem of the Mumford-Shah functional obtained by Ambrosio and Tortorelli. For the purpose of the illustration of the Gamma-convergent approximation some numerical examples on simple synthetic images are presented. This is a joint work with Luigi Ambrosio and Loris Faina.

Markov random fields are used extensively in image segmentation. In this talk I describe a class of models, the double Markov random field, for images composed of several textures, and how to use the model class for image segmentation. I show that many approaches to Bayesian image segmentation are special cases of this model. From a simulation study, a comparison between these models is made.
If time permits, I will also discuss how to extend these approaches to the case where the number of texture classes is not known.

One of the most challenging problems in automatic target recognition (ATR) for remote sensing is reliable detection of poorly illuminated objects buried in high clutter backgrounds. When the clutter statistics are unknown or highly variable, the false alarm rate of classical linear or quadratic detection algorithms, e.g. the adaptive matched filter/detector, cannot be controlled and target detection becomes unreliable. In this talk we will present methods for improving detection performance using the generalized likelihood ratio (GLR) test and the maximal invariant (MI) test for cases where clutter uncertainty can be described by an orbit induced by group actions on parameter space. Our focus application will be the difficult "deep hide" problem where the target straddles a boundary between two unknown clutter types.

This lecture will address the problem how to interpret image structure when it is evaluated through massively parallel computation, considering a finite neighborhood in each iteration.

Applications may include MRF segmentation, motion tracking, image compression and visualization by painting rendering. Some solutions will be demonstrated for

• painting by stochastic paintbrush generation: It is based on a random search to insert brush-strokes into a generated image at decreasing scale of brush-sizes, without predefined models or interaction. One of the goals of the method is to transform the image into a representation that is very similar to the human sensation of artistic images.
• pre-processing images by anisotropic diffusion to get better quality of compressed images: The proposed method preserves well the main structure of the decompressed image and it does not change the perceptible image quality of the decompressed image considering all details, while removes most of the compression artifacts.
• motion tracking and segmentation: A split and merge segmentation algorithm is demonstrated, where the process starts from an oversegmented image, then the segments are merged by applying the information coming from the spatial and temporal auxiliary data: motion fields and motion history, calculated from consecutive image frames.

These processes are controlled in parallel and are themselves organized by the structure which they are evolving through an iterative process. Several results show that most of image processing tasks and a broad class of image analysis problems can be solved in parallel structures by self-organizing methods. Here parallel structure means that different processors run on the same task at the same time. It is found that "parallelism" and "self-organization" usually are coupled: if a process is implemented in a parallel structure, it can be described by using some type of self-organizing in the evolution of the solution.

In this talk, an introduction to numerical Bayesian methods will be given and new methods for sequential applications will be introduced.
Some results for audio and image restoration will be presented.

It is well known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a (derived) association graph. However, it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized, i.e., are trees, since maximal cliques are not constrained to preserve the partial order. Here we provide a solution to the problem of matching two attributed trees by constructing a (weighted) association graph using the graph-theoretic concept of connectivity. We prove that in the new formulation there is a one-to-one correspondence between maximal weight cliques and maximal similarity subtree isomorphisms. This allows us to cast the tree matching problem as an indefinite quadratic program using a recent extension of the so-called Motzkin-Straus theorem. We then use "replicator" equations, a class of dynamical systems developed in evolutionary game theory, to solve it. Such continuous solutions to discrete problems are attractive because they can motivate analog and biological implementations. We illustrate the power of the approach by matching articulated and deformed shapes described by shock trees. An extension of this framework to deal with many-to-one matchings will also be presented.

[joint work with K. Siddiq (McGill) and S. W. Zucker (Yale)]

La séparation aveugle de sources est un problème essentiel en traitement du signal. Plusieurs sources physiques émettent simultanément des signaux qui sont reçus par des capteurs. Les techniques de séparation aveugle de sources consistent à retrouver les signaux émis par chacune des sources. Elles s'appliquent dans des situations où la connaissance sur le processus de mélange et sur les sources est très faible. Leur vaste domaine d?application s'étend de l'ingénierie : traitement de la parole, des signaux radar, au domaine médical : électroencéphalographie, électrocardiographie,....et pourquoi pas en télédétection.
Je présenterai d'abord le modèle de mélange et ses hypothèses, puis le principe des méthodes de "démélange" et leurs limitations. Le regain d'intérêt (1990) pour ce sujet a permis la modernisation de l'analyse en composantes principales, sous la forme de l'analyse en composantes indépendantes. J'exposerai ces méthodes et en particulier différents algorithmes basés sur les corrélations locales ou sur les statistiques d'ordres élevés. Je montrerai quelques résultats obtenus par leur mise en oeuvre en analyse spectrale par résonance magnétique nucléaire. Puis je montrerai l'apport de cet outil statistique exploratoire à la description physique de la radiosource 3C120.

D. Nuzillard, S. Bourg, J.-M. Nuzillard : Model-free analysis of mixtures by NMR using blind source separation, Journal of magnetic resonance 133, 358-363, 1998
D.Nuzillard & A.Bijaoui : Blind source separation and analysis of multispectral astronomical images. Astronomy and Astrophysics supplement series, 147, novembre 2000 sous presse.

Les modèles de circulation générale (GCMs), qui sont utilisés pour étudier l'évolution du climat terrestre, nécessitent des données permettant de calculer les caractéristiques optiques des nuages (rayon effectif des gouttelettes nuageuses et épaisseur optique) à l'échelle globale. Les imageurs qui équipent les satellites météorologiques permettent la détermination de ces paramètres. Néanmoins, les algorithmes utilisés pour cette détermination sont souvent de nature intuitive et/ou empirique, ce qui réduit leur domaine d'applicabilité. On présentera une méthode de détermination des caractéristiques optiques des nuages qui s'appuie sur une analyse fondée théoriquement et qui utilise simultanément les images transmises dans l'IR par le satellite GOES et celles transmises dans le domaines des micro-ondes par le satellite de la série DMSP. La validation de la méthode est effectué par comparaison avec les résultats des observations collectées durant le " International Satellite Cloud Climatology Project.