• A. Bruckstein (Bell Labs, Murray Hill and Technion, Haifa),
  Invariant Recognition and Processing of Planar Shapes
  Recognition of planar shapes distorted by viewing transformations and occlusions is an issue that illustates well the difficuties encountered in image analysis. Local, semi-local and differential invariant signatures for shape/contour representation are presented, and several types of invariant smoothing processes are analyzed. Scale-space local signatures are introduced and applications of invariant signatures to shape recognition under partial occlusions and the detection of skew-symmetry are discussed.
• B. Kimia (Brown University)
  Categorization and Recognition of Form from a Graph-Based Representation of Shocks of Deformation
  Shocks, or the singularities formed in the course of deforming shape, are a complete descriptor of shape. The classification of shocks into four distinct types correlates with a perceptual organization of shape into its parts, protrusions, and bends. The detection and classification of shocks has been implemented via the curve evolution paradigm and more recently via a highly accurate and versatile wave propagation scheme. Shocks are then grouped via constraints imposed by a shock grammar as well as by geometric constraints giving rise to a hierarchical graph-based representation of shock groups. The wave propagation scheme also allows for a computation of shocks directly from unsegmented real imagery by propagation of orientation elements. However, this computation is ill-conditioned in that partial occlusion, gaps, spurious edges, etc. drastically alter the underlying symmetries. The computation can be regularized by a labeling of waves as regular or rarefaction to indicate the reliability or source orientation, resulting in three types of shocks: regular, degenerate, and semi-degenerate which identify potential parts, gaps, and spurious elements. A series of shock transforms implemented via a second generation of waves then create alternative representations for shape at these potential sites, e.g., to decompose the shape into its subparts, to group contour segments to bridge across gaps, to remove spurious elements, etc. These transforms in turn induce graph operations which generate an array of alternative graph representations for each shape which is then used to match into a database of similarly represented shapes. The matching is based on the graduated assignment graph-matching technique and takes place on the structural, parametric, and metric levels, leading to a categorization of the shape space.
• H. L. Le (University of Nottingham)
  The Representation and Measurement of Shape
  The study of shape has become increasingly important in a wide range of subjects from archaeology to astronomy, and from biology to physics and not least of course in object recognition. The basic problem which arises is that it is not possible to represent the entire variety of possible shapes by a single parameter or even by several unconstrained paremeters. In practice a number of different solutions have been developed to suit the intended applications. In this short series of talks I concentrate mainly on the work that has been done on DG Kendall's shape spaces. His space is a set, with natural metric, in which each similarity class of configurations of k vertices in m-dimensional Euclidean space is represented exactly once. The metric enables us to measure how different two shapes are and to decide for example when that difference is merely a statistically insignificant fluctuation. Kendall's spaces also admit a Riemannian structure with, in particular, geodesics giving the shortest path between two shapes, in other words, the most efficient deformation of one shape into the other. Since Kendall's spaces represent all possible shapes simultaneously they are also well-suited for testing for collinearity or other forms of degeneracy, which are implicitly excluded from other models. In addition to the above I also discuss the recent development in hyperbolic (simplex) shape spaces and the theoretical problems which arise in the statistics of shape such as what we shall mean by, and how we may estimate, an "average shape".
  The references related to my talk are
  1. Kendall, D.G. (1984) Shape manifolds, procrustean metrics, and complex projective spaces. Bull. London Math. Soc. 16, 81-121.
  2. Le, H. (1991) On geodesics in Euclidean shape spaces. J. London Math. Soc. 44, 360-372.
  3. Le, H. (1995) On consistency of procrustean mean shapes. Adv. Appl. Probab. (to appear).
  4. Le, H. & Small, C.G. (1997) Multidimensional scaling of simplex shapes.
  Request of papers by Email
  
• M. Miller (Washington University)
  Computational Anatomy: An Emerging Discipline
  Most real world scenes and shapes are characterized by high variability - they are not rigid - but yet they are strongly structured. A fundamental task in the understanding and analysis of shape is therefore the construction of models that incorporate both structure as well as variability in a mathematically precise way. The global shape models introduced in {\it Grenander's Metric Pattern} theory are intended to do this. For this, {\it templates} are introduced which for brain anatomies are {\it manifolds} in 0,1,2, and 3 dimensions. Variability is accomodated via the introduction of {\it transformations} which act on the templates, the transformations forming {\it groups}.
  In this series of talks, we will show recent results in {\it computational anatomy} applied to the geometric structures of the brain. The lectures will have several parts including (1) generating large deformations diffeomorphisms between brain anatomies, (2) characterizing anatomical variation via probabilities on brain submanifolds, and (3) applications to the study of the neocortex and subcortical areas such as the hippocampus.
  
  See references in http://cis.wustl.edu/research.html
  
  
• Rolf P. Würtz and Jan C. Vorbrüggen (Institut fùr Neuroinformatik, Ruhr-Universitat Bochum, Germany)
  JV's talk:
  Overview early visual processing
  The correspondence problem
  Recognition from correspondences
  Elastic graph matching (examples: faces, gestures, object shapes)
  Integrating segmentation and object recognition
  
  RW's talk:
  Object representations and flexible matching methods
  
  Hierarchical matching
  Corner detection
  Color processing
  Matching of symbolic edge graphs
  Papers on the web
  Other papers on the web
  Email: Rolf.Wuertz@neuroinformatik.ruhr-uni-bochum.de
  Web site
  Long abstract LaTeX file (includes bibliography)
  
  

• Olivier CATONI (ENS Ulm)
  A mixture approach to statistical model selection
  The mixture approach has proved in the past years to be a very efficient and general way to build universal codes. In this talk, we will show how to apply it to statistical model selection with respect to the Kullback risk function, in the case of the adaptive estimation of a density.
• Stephane CHAUVIN (ITC-UCM, Campus de Somosaguas, 28223 Madrid)
  Tracking Knowledge Data Bases : Fusion of data Software
  The aim of Track European Esprit project is to extract the customer behaviour in the temporal view for the financial sector. Data mining applications are now providing remarkably successful for identifying patterns in banking, insurance, retail and telecommunications. There is a significant number of differents approaches taken by commercial tools with the aim of identifying customer behaviour clusters. Most of these tools use specific technologies (e.g. neural nets, genetic algorithms, induction, statistical, see http://www.kdnuggets.com) to resolve the problem of the optimum characteristic choice of customer according to a product set information or the set of the product according to the characteristic of customers. More specifically, financial institution wish to broaden their relationship with customers to include multiple accounts (to control the general cost and optimized bank's strategy), and to target customer behaviour in temporal handling view with stability and reliable results. To improve user decision making through the help of a more active and powerful decision system is the general objective, building an Active Decision Support Toolkit called Track. Objectives are based in two main challenges : a) taking into account the temporal variable and b), coping with the ability of working with several decision toolkit technologies, not in an independent way, but looking for synergy through fusion technology. Effectively, the individual software calculation rarely gives a consensus of the solution. Whenever, banks are need of an estimation of each potential results (risk, reliability, stability) and a global solution. Track toolkit integrates the System Optimized by Fusion Information (S.O.F.I.) which fuses three sub-optimal temporal handling solutions which are given by commercial data mining tools. S.O.F.I. uses the whole of information without taking a partial decision and proposes a consensus or severable of individual results with its accurate evaluation. Technically speaking, S.O.F.I. model uses spring mechanic energy allowing to slide along the space of the solution and merges all software results. The fusion process can be shown like a process initialized by software results and developes a general shape which moves in order to refine the result and to have a realistic solution.
  References
  
• Francoise DIBOS (CEREMADE, Universite Paris Dauphine )
  Projective Analysis of 2D images
  
• Alexandre Guimond (EPIDAURE, INRIA Sophia Antipolis)
  Average representation of anatomical brain structures.
  The design of representative models of the human body is of great interest to medical doctors. Qualitative information about the characteristics of the brain is widely available, but due to the volume of information that needs to be analyzed and the complexity of its structure, rarely is there quantification according to a standard model. To address this problem, we propose an automatic method to retrieve corresponding structures from a database of medical images. This procedure being local and fast, will permit navigation through large databases in a practical amount of time. We present as examples of applications the building of an average volume of interest and preliminary results of classification according to morphology.
  See references in http://zenon.inria.fr/epidaure/personnel/guimond/publications/
• Stephane HERBIN (CMLA/DIAM, ENS de Cachan)
  Reconnaissance active d'objets 3D: concilier geometrie et probabilites
  Active 3D object recognition: conciliating geometry and probability
  The usual model of the recognition skill consists in a ``matching'' between a sensory signal and an object model stored in memory. It distinguishes implicitly between a perceptual level, whose goal is to generate representations that subsitute for the input signal, and a cognitive level, able to produce inferences from the representations. However, direct perception is generally not able to provide at the same time all the useful information needed for object recognition. The perceptual context is often ambiguous and sensory systems have a limited capacity. Object recognition necessitates an exploratory phase to be able to deal with complex situations. In this talk, I will present a general model accounting for a genuine recognition "activity" and apply it to a problem of tri-dimensional object recognition. The typical context consists of an agent able to acquire new images either by moving its viewpoint or by modifying the parameters of its sensors. The external contour of the object and the structure of its corner points will be considered as the discriminative feature. The theory of aspect graphs, based on the theory of differentiable mappings, ensures that the sequence of feature point structures will be characteristic of the observed object. When fitted with a probabilistic model in the form of a markovian dependance, the aspect graph gains a quantitative predictive power. The asymptotic theory of hypothesis testing, in its relation to the theory of large deviations, gives then a global evaluation of the statistical complexity of the recognition problem.
  Reference:
  These disponible sur le web
• Eric LHOMER (Paris 13 et ENS Cachan)
  Modélisation stochastique et reconnaissance de lettres manuscrites.
  Parmi les très nombreuses méthodes de reconnaissance de lettres manuscrites proposées ces dernières années, un nombre très restreint d'entre elles utilisent ou proposent une modélisation de l'écriture. Cette rareté est due à la difficulté d'estimer, à partir d'une image de lettre, du fait de nombreux croisements et chevauchements, le tracé des courbes qui la compose, à partir desquelles une modélisation efficace peut etre proposée. Dans la méthode que nous présentons, une modélisation des traits est décrit, ainsi qu'un algorithme d'estimation des trajectoires de traits, plus particulièrement adaptés aux problèmes de croisements de traits. Chaque lettre est alors décrit par un petit nombre de courbes; une modélisation de celles-ci, à l'aide d'un mélange de lois gaussiennes, est estimée par un algorithme de type EM. Les simulations d'images de lettres obtenues permettent d'estimer une regression des courbes sur la silhouette de chaque lettre, obtenant ainsi une identification rapide des classes de lettre.
• Isabelle MAGNIN et Patrick CLARYSSE (Creatis Lyon)
  The active pyramid: a new tool for modelling and matching deformable objects
  The concept of active pyramids is introduced. It is used to model a non rigid object and track its deformation throughout a temporal image sequence.
  In a first step, a pyramidal model is built on each frame of the image sequence. Each level of the pyramid is recursively built on a low-pass version of the original picture. Each image is subdivided into elementary regions using a regular mesh. The mesh, considered as a graph, is given elastic properties. It deforms iteratively (while minimizing a functional) to model the local image content. A features vector, is attached to each cell of the graph: it contains both information extracted from the image and prior geometrical knowledge about the object.
  In a second step, a coarse-to-fine strategy is proposed to match two pyramids. The matching operator is based on a self-organizing map introduced by Kohonen. The result of the matching is a vector field of local non-rigid transform. Softness and multiresolution properties of the active pyramidal model lead to accurate and robust practical results.
  Results will be presented on the matching of cardiac Magnetic Resonance Images in 2D and 3D image sequences.
  
  References:
  * Reissman P.J., Magnin I.E., Modeling 3D Deformable Object with the Active Pyramid, Int. Jour. of Pattern Recognition and Artificial Intelligence, 1997, 11(7)1129-1139.
  * Reissman P.J., Clarysse P., Magnin I.E., Modelisation et mise en correspondance avec la pyramide neuractive, Traitement du Signal , 1997,14(4):1-9.
  * Reissman P.J., Modelisation et mise en correspondance par pyramides actives: application a l'imagerie cardiaque par resonance magnetique,these INSA-Lyon, 11 juillet 1997.
  
• J.-F. MANGIN (service hospitalier F. Joliot, Dep. de recherche medicale, CEA)
  A Markovian random field based random graph modelling the human cortical topography
  This lecture would present a project aiming at the automatic detection and recognition of the human cortical sulci in a 3-D magnetic resonance image. The two first steps of this project (automatic extraction of an attributed relational graph (ARG) representing individual cortical shapes, constitution of a database of labelled ARGs) would be briefly described. Then we would address a way of inferring a probabilistic structural model of the cortical topography from this database. This model relies on several original interpretations of the inter-individual structural variability of the cortical topography. The model is a structural prototype whose nodes can split into pieces according to syntactic constraints. This prototype is endowed with a random graph structure taking into account the anatomical variability. The recognition process is formalized as a consistent labelling problem and the solution is obtained from the maximum a posteriori (MAP) estimator using simulated annealing.
  Mangin, J.-F., Frouin, V., Bloch, I., Regis, J., and Lopez-Krahe, J. From 3D magnetic resonance images to structural representations of the cortex topography using topology preserving deformations. Journal of Mathematical Imaging and Vision, 5(4):297--318, 1995.
  Mangin, J.-F., Regis, J., Bloch, I., Frouin, V., Samson, Y., and Lopez-Krahe, J. A Markovian random field based random graph modelling the human cortical topography. In CVRMED, Nice, France, volume 905 of LNCS, Springer-Verlag, pages 177--183., 1995.
  Manceaux-Demiau, A., Mangin, J.-F., Regis, J., Pizzato, O., and Frouin, V. Differential features of cortical folds. In CVRMED/MRCAS, Grenoble, vol 1205 in LNCS, Springer-Verlag, pages 439--448,
• Gérard SUBSOL (EPIDAURE, INRIA Sophia Antipolis)
  Construction automatique d'atlas anatomiques morphometriques a partir d'images medicales tridimensionnelles.
  Nous présenterons nos travaux sur la construction automatique d'un atlas anatomique morphométrique à partir d'une base de données d'images médicales tridimensionnelles (scanographiques ou obtenues par Imagerie par Résonance Magnétique).
  La méthode s'appuie sur une représentation simplifiée de la structure anatomique étudiée à l'aide des <>. Nous détectons automatiquement les lignes qui sont communes à tous les éléments de la base de données. Nous calculons alors la moyenne de leurs positions afin de trouver la forme moyenne de l'atlas. Enfin, le calcul d'un nombre nombre très réduit de paramètres statistiques permet de quantifier la variabilité de la forme.
  La même méthode nous a permis de construire un atlas des lignes de crête du crâne et du cerveau.
  Les paramètres statistiques sur la variabilité de la forme permettent d'envisager diverses applications médicales : base de données de référence avec étiquetage automatique, mise en correspondance normalisée, assistance passive pour la thérapie, analyse des formes et des déformations à des fins diagnostiques ou aide à la planification de la thérapie. Nous avons étudié, en particulier, une difformité maxillo-faciale et des déformations des ventricules cérébraux latéraux.
  
  In this talk, we address the new problem of automated building of morphometric anatomical atlases from volumetric medical images (X-ray CT or Magnetic Resonance Imaging). We describe a method composed of four steps. First, we automatically extract feature lines from the volumetric images. We use "crest lines" which are a simplified representation of the studied structure and which are anatomically significant. Then, we have developed a non-rigid matching algorithm to register sets of lines extracted from different patients in order to find the common lines which form the atlas. We then compute their average positions and a very reduced set of statistical parameters describing their variation. This method has allowed us to build an atlas of crest lines of the skull from 6 CT-Scans and of the brain from 10 MRI images. The statistical parameters can be used for several medical applications: reference database with automatic labeling, normalized registration, computer assisted therapy planning, morphometric analysis, computer aided diagnosis and therapy planning. We study, in particular, a maxillary disease and the deformations of cerebral lateral ventricles.
  BibTeX References
  Web page

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