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15
Determining the Similarity of Deformable Shapes
 Proc. of Workshop on Physicsbased Modeling in Computer Vision
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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.
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...
On The Anatomy Of Visual Form
 Ecological and psychophysical aspects, Perception
, 1994
"... Part based representations allow for recognition that is robust in the presence of occlusion, movement, growth, and deletion of portions of an object. We propose a general "form from function" principle arising from the interactions of objects in their environment, which, together with pro ..."
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Cited by 26 (2 self)
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Part based representations allow for recognition that is robust in the presence of occlusion, movement, growth, and deletion of portions of an object. We propose a general "form from function" principle arising from the interactions of objects in their environment, which, together with properties of visual projection, gives rise to two kinds of parts: limbbased parts arise from a pair of negative curvature minima with evidence for "good continuation" of boundaries on one side; neckbased parts arise from narrowings in shape. We then test this hypothesis by requiring subjects to partition a variety of biological and nonsense 2D shapes into perceived components. We examine: 1) whether a subject determines components consistently across different trials of the same partitioning task, 2) whether there is evidence for consistency between subjects for the same partitioning task, and 3) how the perceived parts compare with the parts proposed by the "form from function" principle. The results...
Optimal partial shape similarity
, 2005
"... Humans are able to recognize objects in the presence of significant amounts of occlusion and changes in the view angle. In human and robot vision, these conditions are normal situations and not exceptions. In digital images one more problem occurs due to unstable outcomes of the segmentation algorit ..."
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Cited by 15 (1 self)
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Humans are able to recognize objects in the presence of significant amounts of occlusion and changes in the view angle. In human and robot vision, these conditions are normal situations and not exceptions. In digital images one more problem occurs due to unstable outcomes of the segmentation algorithms. Thus, a normal case is that a given shape is only partially visible, and the visible part is distorted. To our knowledge there does not exist a shape representation and similarity approach that could work under these conditions. However, such an approach is necessary to solve the object recognition problem. The main contribution of this paper is the definition of an optimal partial shape similarity measure that works under these conditions. In particular, the presented novel approach to shapebased object recognition works
Categoryspecific object recognition and segmentation using a skeletal shape model
 BMVC
"... The success of skeletal model in object recognition from segmented images motivates the development of a skeletal model for topdown object recognition and segmentation. We propose a novel skeletonbased generative shape model which is suitable for efficient search using dynamic programming (DP). W ..."
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Cited by 5 (0 self)
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The success of skeletal model in object recognition from segmented images motivates the development of a skeletal model for topdown object recognition and segmentation. We propose a novel skeletonbased generative shape model which is suitable for efficient search using dynamic programming (DP). We have devised an exclusion principle enabling DP to discover multiple instances of an object category in one pass. Finally, we have improved an oriented chamfer distance for rankordering generated hypotheses. Improved or comparable recognition and segmentation results are reported on the ETHZ data set. 1
Partbased bayesian recognition using implicit polynomial invariants
 In IEEE International Conference on Image Processing
, 1995
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Learning descriptive and distinctive parts of objects with a partbased shape similarity measure
 in IASTED Int. Conf. on Signal and Image Processing (SIP
, 2004
"... In this paper we present a novel approach to learn visual parts of objects. The learned set of visual parts is optimized to yield an optimal performance for recognition of new objects. We divide the learning strategy into two main steps that follow our proposed, cognitively motivated principles of l ..."
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In this paper we present a novel approach to learn visual parts of objects. The learned set of visual parts is optimized to yield an optimal performance for recognition of new objects. We divide the learning strategy into two main steps that follow our proposed, cognitively motivated principles of learning descriptive and distinctive parts of objects. We first extract the most dissimilar representative parts from all possible parts of all objects in the same class. We then select the most discriminative subset of this set with respect to the classification of shapes into classes. In order to computationally evaluate our approach, we developed a shape similarity measure that is able to compare parts of objects. The obtained measure yields intuitive results for significantly distorted or occluded parts even if parts are given at different scales.
Valence Normalized Spatial Median for Skeletonization and
 Matching”, Search in 3D and Video workshop (S3DV), in conjunction with IEEE International Conference on Computer Vision (ICCV
, 2009
"... This paper describes using 3D chain expressions for encoding unitwidth curve skeletons and measuring shape dissimilarity. By integrating a robust skeletonization technique with 3D chain coding, the proposed algorithm can compare not only the skeleton topology but also the curvature of skeleton segm ..."
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Cited by 1 (1 self)
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This paper describes using 3D chain expressions for encoding unitwidth curve skeletons and measuring shape dissimilarity. By integrating a robust skeletonization technique with 3D chain coding, the proposed algorithm can compare not only the skeleton topology but also the curvature of skeleton segments. Robustness of the search and potential for retrieving similar objects is studied and shown to be better than graphbased matching. The contributions of our work include generating connected and unitwidth skeletons using valence normalization; improving the performance of 3D chain codes for similarity match; and skeleton matching through chain expressions. The advantage of our method lies in its ability to distinguish between relatively similar objects and different poses of similar objects. Experimental results demonstrating the validity of the proposed approach is described. 1.
MODELING SEGMENTATION VIA GEOMETRIC DEFORMABLE REGULARIZERS, PDE AND LEVEL SETS IN STILL AND MOTION IMAGERY: A REVISIT
"... Partial Differential Equations (PDEs) have dominated image processing research recently. The three main reasons for their success are: first, their ability to transform a segmentation modeling problem into a partial differential equation framework and their ability to embed and integrate different r ..."
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Cited by 1 (0 self)
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Partial Differential Equations (PDEs) have dominated image processing research recently. The three main reasons for their success are: first, their ability to transform a segmentation modeling problem into a partial differential equation framework and their ability to embed and integrate different regularizers into these models; second, their ability to solve PDEs in the level set framework using finite difference methods; and third, their easy extension to a higher dimensional space. This paper is an attempt to survey and understand the power of PDEs to incorporate into geometric deformable models for segmentation of objects in 2D and 3D in still and motion imagery. The paper first presents PDEs and their solutions applied to image diffusion. The main concentration of this paper is to demonstrate the usage of regularizers in PDEs and level set framework to achieve the image segmentation in still and motion imagery. Lastly, we cover miscellaneous applications such as: mathematical morphology, computation of missing boundaries for shape recovery and low pass filtering, all under the PDE framework. The paper concludes with the merits and the demerits of PDEs and level setbased framework for segmentation modeling. The paper presents a variety of examples covering both synthetic and real world images.