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Hausdorff distance is a deformation tolerant measure between two sets of points. The main advantage of this measure is that it does not need an explicit correspondence between the points of the two sets. This paper presents the application to automatic face recognition of a novel supervised Hausdorff-based measure. This measure is designed to minimize the distance between sets of the same class (subject) and at the same time maximize the distance of sets between different classes.

Most of the traditional methods for shape classification are based on contour. They often encounter difficulties when dealing with classes that have large nonlinear variability, especially when the variability is structural or due to articulation. It is well-known that shape representation based on skeletons is superior to contour based representation in such situations. However, approaches to shape similarity based on skeletons suffer from the instability of skeletons, and matching of skeleton graphs is still an open problem.

Using a new skeleton pruning method, we are able to obtain stable pruned skeletons even in the presence of significant contour distortions. We also propose a new method for matching of skeleton graphs. In contrast to most existing methods, it does not require converting of skeleton graphs to trees and it does not require any graph editing. Shape classification is done with Bayesian classifier. We present excellent classification results for complete shapes.

Image cosegmentation is a newly emerging research area in image processing. It refers to the problem of segmenting the common objects simultaneously in multiple images by utilizing the similarity of foreground regions among these images. In this paper, a new active contour model is proposed by using shape-similarity and foreground discovery scheme. The foreground discovery scheme is used to obtain the rough contours of the common objects which are used as initial evolution curves. The energy function of the proposed model includes two parts: an intra-image energy and an inter-image energy. The intra-image energy explores the differences between foreground regions and background regions in each image. And the inter-image energy is used to explore the similarities of the common objects among target images, which composes of a region color feature energy term and a shape constraint energy term. The region color feature term indicates the foreground consistency and the background consistency among the images; and the shape constraint energy term allows the global changes of shapes and truncates the local variation caused by misleading features. Experimental results show that the proposed model can improve the accuracy of the image cosegmentation significantly through regularizing the changes of shapes.

This article presents a 3D shape matching method for 3D mesh models applied to content-based search in database of 3D objects. The approach is based on the multiresolution Reeb graph (MRG) proposed by Hilaga et al.¹ MRG provides a rich representation of shapes able in particular to embed the object topology. In our framework, we consider 3D mesh models of various geometrical complexity, of different resolution, and when available with color texture map. The original approach, mainly based on the 3D object topology, is not accurate enough to obtain satisfying matching. Therefore we propose to reinforce the topological consistency conditions of the matching and to merge within the graph geometrical and visual information to improve matching and calculation of shape similarity between models. Besides, all these new attributes can be freely weighted to fit the user requirements for object retrieval. We obtain a flexible multiresolutional and multicriteria representation that we called augmented multiresolution Reeb graph (aMRG). The approach has been tested and compared with other methods. It reveals very performant for the retrieval and the classification of similar 3D shapes.

In this paper we prove a well known contour evolution technique can result in inconsistent non-simple or self-intersecting polygons. This technique is used as a pre-processing step to a number of shape matching and part-decomposition strategies which are only well-defined for simple polygons. We analyze one such class of shape matching strategies, which use a highly cited method based on turning-functions to determine similarity. We prove that due to the possibility of self-intersecting polygons these methods are not well-defined. A simple alteration to the original contour evolution technique, which ensures the evolution of a consistent simple polygon, is proposed. This technique only alters the result slightly relative to the original evolution technique and therefore maintains the property of suitable shape evolution.