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92
Shape Descriptors for Nonrigid Shapes with a Single Closed Contour
 Proc. IEEE Conf. Computer Vision and Pattern Recognition
, 2000
"... The Core Experiment CEShape1 for shape descriptors performed for the MPEG7 standard gave a unique opportunity to compare various shape descriptors for nonrigid shapes with a single closed contour. There are two main differences with respect to other comparison results reported in the literature: ..."
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Cited by 185 (19 self)
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The Core Experiment CEShape1 for shape descriptors performed for the MPEG7 standard gave a unique opportunity to compare various shape descriptors for nonrigid shapes with a single closed contour. There are two main differences with respect to other comparison results reported in the literature: (1) For each shape descriptor, the experiments were carried out by an institute that is in favor of this descriptor. This implies that the parameters for each system were optimally determined and the implementations were throughly tested. (2) It was possible to compare the performance of shape descriptors based on totally different mathematical approaches. A more theoretical comparison of these descriptors seems to be extremely hard. In this paper we report on the MPEG7 Core Experiment CEShape1. 1.
A Stochastic Grammar of Images
 Foundations and Trends in Computer Graphics and Vision
, 2006
"... This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents bot ..."
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Cited by 121 (26 self)
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This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents both the hierarchical decompositions from scenes, to objects, parts, primitives and pixels by terminal and nonterminal nodes and the contexts for spatial and functional relations by horizontal links between the nodes. It formulates each object category as the set of all possible valid configurations produced by the grammar. (ii) The grammar is embodied in a simple And–Or graph representation where each Ornode points to alternative subconfigurations and an Andnode is decomposed into a number of components. This representation supports recursive topdown/bottomup procedures for image parsing under the Bayesian framework and make it convenient to scale
Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution
 Computer Vision and Image Understanding
, 1999
"... We concentrate here on decomposition of 2D objects into meaningful parts of visual form,orvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. ..."
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Cited by 110 (19 self)
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We concentrate here on decomposition of 2D objects into meaningful parts of visual form,orvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. We solve this problem by identifying convex parts at different stages of a proposed contour evolution method in which significant visual parts will become convex object parts at higher stages of the evolution. We obtain a novel rule for decomposition of 2D objects into visual parts, called the hierarchical convexity rule, which states that visual parts are enclosed by maximal convex (with respect to the object) boundary arcs at different stages of the contour evolution. This rule determines not only parts of boundary curves but directly the visual parts of objects. Moreover, the stages of the evolution hierarchy induce a hierarchical structure of the visual parts. The more advanced the stage of contour evolution, the more significant is the shape contribution of the obtained visual parts. c ○ 1999 Academic Press Key Words: visual parts; discrete curve evolution; digital curves; digital straight line segments; total curvature; shape hierarchy; digital geometry. 1.
Representation and Detection of Deformable Shapes
 PAMI
, 2004
"... We describe some techniques that can be used to represent and detect deformable shapes in images. The main di#culty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates. This makes the problem of finding an optimal match of a ..."
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Cited by 95 (3 self)
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We describe some techniques that can be used to represent and detect deformable shapes in images. The main di#culty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates. This makes the problem of finding an optimal match of a deformable template to an image incredibly hard. Using a new representation for deformable shapes we show how to e#ciently find a global optimal solution to the nonrigid matching problem. The representation is based on the description of objects using triangulated polygons. Our matching algorithm can minimize a large class of energy functions, making it applicable to a wide range of problems. We present experimental results of detecting shapes in medical images and images of natural scenes. Our method does not depend on initialization and is very robust, yielding good matches even in images with high clutter.
Shapes, Shocks, and Deformations I: The Components of TwoDimensional Shape and the ReactionDiffusion Space
 International Journal of Computer Vision
, 1994
"... We undertake to develop a general theory of twodimensional shape by elucidating several principles which any such theory should meet. The principles are organized around two basic intuitions: first, if a boundary were changed only slightly, then, in general, its shape would change only slightly. Th ..."
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Cited by 83 (5 self)
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We undertake to develop a general theory of twodimensional shape by elucidating several principles which any such theory should meet. The principles are organized around two basic intuitions: first, if a boundary were changed only slightly, then, in general, its shape would change only slightly. This leads us to propose an operational theory of shape based on incremental contour deformations. The second intuition is that not all contours are shapes, but rather only those that can enclose "physical" material. A theory of contour deformation is derived from these principles, based on abstract conservation principles and HamiltonJacobi theory. These principles are based on the work of Sethian [82, 86], the OsherSethian level set formulation [65], the classical shock theory of Lax [53, 54], as well as curve evolution theory for a curve evolving as a function of the curvature and the relation to geometric smoothing of GageHamiltonGrayson [32, 37]. The result is a characterization of th...
Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution
 IEEE TRANS. PATTERN ANAL. MACH. INTELL
, 2007
"... In this paper, we introduce a new skeleton pruning method based on contour partitioning. Any contour partition can be used, but the partitions obtained by Discrete Curve Evolution (DCE) yield excellent results. The theoretical properties and the experiments presented demonstrate that obtained skele ..."
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Cited by 76 (14 self)
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In this paper, we introduce a new skeleton pruning method based on contour partitioning. Any contour partition can be used, but the partitions obtained by Discrete Curve Evolution (DCE) yield excellent results. The theoretical properties and the experiments presented demonstrate that obtained skeletons are in accord with human visual perception and stable, even in the presence of significant noise and shape variations, and have the same topology as the original skeletons. In particular, we have proven that the proposed approach never produces spurious branches, which are common when using the known skeleton pruning methods. Moreover, the proposed pruning method does not displace the skeleton points. Consequently, all skeleton points are centers of maximal disks. Again, many existing methods displace skeleton points in order to produces pruned skeletons.
Approximate tree matching and shape similarity
 In Proceedings, 7th International Conference on Computer Vision
, 1999
"... We present a framework for 2D shape contour (silhouette) comparison that can account for stretchings, occlusions and region information. Topological changes due to the original 3D scenarios and articulations are also addressed. To compare the degree of similarity between any two shapes, our approach ..."
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Cited by 68 (1 self)
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We present a framework for 2D shape contour (silhouette) comparison that can account for stretchings, occlusions and region information. Topological changes due to the original 3D scenarios and articulations are also addressed. To compare the degree of similarity between any two shapes, our approach is to represent each shape contour with a free tree structure derived from a shape axis (SA) model, which we have recently proposed. We then use a tree matching scheme to find the best approximate match and the matching cost. To deal with articulations, stretchings and occlusions, three local tree matching operations, merge, cut, and mergeandcut, are introduced to yield optimally approximate matches, which can accommodate not only onetoone but manytomany mappings. The optimization process gives guaranteed globally optimal match efficiently. Experimental results on a variety of shape contours are provided. 1
Ligature Instabilities in the Perceptual Organization of Shape
 Computer Vision and Image Understanding
, 1999
"... Although the classical Blum skeleton has long been considered unstable, many have attempted to alleviate this defect through pruning. Unfortunately, these methods have an arbitrary basis, and, more importantly, they do not prevent internal structural alterations due to slight changes in an object&ap ..."
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Cited by 52 (8 self)
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Although the classical Blum skeleton has long been considered unstable, many have attempted to alleviate this defect through pruning. Unfortunately, these methods have an arbitrary basis, and, more importantly, they do not prevent internal structural alterations due to slight changes in an object's boundary. The result is a relative lack of development of skeleton representations for indexing object databases, despite a long history. Here we revisit a subset of the skeletoncalled ligature by Blumto demonstrate how the topological sensitivity of the skeleton can be alleviated. In particular, we show how the deletion of ligature regions leads to stable hierarchical descriptions, illustrating this point with several computational examples. We then relate ligature to a natural growth principle to provide an account of the perceptual parts of shape. Finally, we discuss the duality between the problems of shape partitioning and contour fragment grouping. 1
Practical Reliable Bayesian Recognition of 2D and 3D Objects Using Implicit Polynomials and Algebraic Invariants
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... Patches of quadric curves and surfaces such as spheres, planes and cylinders have found widespread use in modeling and recognition of objects of interest in computer vision. In this paper, we treat use of more complex higher degree polynomial curves and surfaces of degree higher than two, which have ..."
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Cited by 52 (12 self)
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Patches of quadric curves and surfaces such as spheres, planes and cylinders have found widespread use in modeling and recognition of objects of interest in computer vision. In this paper, we treat use of more complex higher degree polynomial curves and surfaces of degree higher than two, which have many desirable properties for object recognition and position estimation, and attack the instability problem arising in their use with partial and noisy data. The scenario discussed in this paper is one where we have a set of objects that are modeled as implicit polynomial functions, or a set of representations of classes of objects with each object in a class modeled as an implicit polynomial function, stored in the database. Then, given partial data from one of the objects, we want to recognize the object (or the object class) or collect more data in order to get better parameter estimates for more reliable recognition. Two problems arising in this scenario are discussed in this paper : (...