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75
Recognition of Shapes by Editing Their Shock Graphs
 Proc. Int’l Conf. Computer Vision
, 2001
"... Abstract—This paper presents a novel framework for the recognition of objects based on their silhouettes. The main idea is to measure the distance between two shapes as the minimum extent of deformation necessary for one shape to match the other. Since the space of deformations is very highdimensio ..."
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Cited by 151 (7 self)
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Abstract—This paper presents a novel framework for the recognition of objects based on their silhouettes. The main idea is to measure the distance between two shapes as the minimum extent of deformation necessary for one shape to match the other. Since the space of deformations is very highdimensional, three steps are taken to make the search practical: 1) define an equivalence class for shapes based on shockgraph topology, 2) define an equivalence class for deformation paths based on shockgraph transitions, and 3) avoid complexityincreasing deformation paths by moving toward shockgraph degeneracy. Despite these steps, which tremendously reduce the search requirement, there still remain numerous deformation paths to consider. To that end, we employ an editdistance algorithm for shock graphs that finds the optimal deformation path in polynomial time. The proposed approach gives intuitive correspondences for a variety of shapes and is robust in the presence of a wide range of visual transformations. The recognition rates on two distinct databases of 99 and 216 shapes each indicate highly successful within category matches (100 percent in top three matches), which render the framework potentially usable in a range of shapebased recognition applications. Index Terms—Shape deformation, shock graphs, graph matching, edit distance, shape matching, object recognition, dynamic programming. æ 1
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinitedimensional spaces and their pairwise di#erences are quantified using the lengths of ge ..."
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Cited by 112 (17 self)
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For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinitedimensional spaces and their pairwise di#erences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradientbased shooting method to solve for the tangent that connects any two shapes via a geodesic.
Shape classification using the innerdistance
 PATTERN ANALYSIS AND MACHINE INTELLIGENCE, IEEE TRANSACTIONS ON
, 2007
"... Part structure and articulation are of fundamental importance in computer and human vision. We propose using the innerdistance to build shape descriptors that are robust to articulation and capture part structure. The innerdistance is defined as the length of the shortest path between landmark poin ..."
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Cited by 99 (6 self)
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Part structure and articulation are of fundamental importance in computer and human vision. We propose using the innerdistance to build shape descriptors that are robust to articulation and capture part structure. The innerdistance is defined as the length of the shortest path between landmark points within the shape silhouette. We show that it is articulation insensitive and more effective at capturing part structures than the Euclidean distance. This suggests that the innerdistance can be used as a replacement for the Euclidean distance to build more accurate descriptors for complex shapes, especially for those with articulated parts. In addition, texture information along the shortest path can be used to further improve shape classification. With this idea, we propose three approaches to using the innerdistance. The first method combines the innerdistance and multidimensional scaling (MDS) to build articulation invariant signatures for articulated shapes. The second method uses the innerdistance to build a new shape descriptor based on shape contexts. The third one extends the second one by considering the texture information along shortest paths. The proposed approaches have been tested on a variety of shape databases, including an articulated shape data set, MPEG7 CEShape1, Kimia silhouettes, the ETH80 data set, two leaf data sets, and a human motion silhouette data set. In all the experiments, our methods demonstrate effective performance compared with other algorithms.
Hierarchical matching of deformable shapes
 In CVPR
, 2007
"... We describe a new hierarchical representation for twodimensional objects that captures shape information at multiple levels of resolution. The representation is based on a hierarchical description of an object’s boundary, and can be used in an elastic matching framework, both for comparing pairs of ..."
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Cited by 74 (0 self)
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We describe a new hierarchical representation for twodimensional objects that captures shape information at multiple levels of resolution. The representation is based on a hierarchical description of an object’s boundary, and can be used in an elastic matching framework, both for comparing pairs of objects and for detecting objects in cluttered images. In contrast to classical elastic models, our representation explicitly captures global shape information. This leads to richer geometric models and more accurate recognition results. Our experiments demonstrate classification results that are significantly better than the current stateoftheart in several shape datasets. We also show initial experiments in matching shapes to cluttered images. 1 1.
Shape representation and classification using the poisson equation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Silhouettes contain rich information about the shape of objects that can be used for recognition and classification. We present a novel approach that allows us to reliably compute many useful properties of a silhouette. Our approach assigns for every internal point of the silhouette a value reflecti ..."
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Cited by 58 (8 self)
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Silhouettes contain rich information about the shape of objects that can be used for recognition and classification. We present a novel approach that allows us to reliably compute many useful properties of a silhouette. Our approach assigns for every internal point of the silhouette a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries. This function can be computed by solving Poisson’s equation, with the silhouette contours providing boundary conditions. We show how this function can be used to reliably extract various shape properties including part structure and rough skeleton, local orientation and aspect ratio of different parts, and convex and concave sections of the boundaries. In addition to this we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms. We demonstrate the utility of the extracted properties by using them for shape classification. 1.
Distance sets for shape filters and shape recognition
 IEEE TRANS. IMAGE PROCESSING
, 2003
"... We introduce a novel rich local descriptor of an image point, we call the (labeled) distance set, which is determined by the spatial arrangement of image features around that point. We describe a twodimensional (2D) visual object by the set of (labeled) distance sets associated with the feature p ..."
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Cited by 46 (7 self)
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We introduce a novel rich local descriptor of an image point, we call the (labeled) distance set, which is determined by the spatial arrangement of image features around that point. We describe a twodimensional (2D) visual object by the set of (labeled) distance sets associated with the feature points of that object. Based on a dissimilarity measure between (labeled) distance sets and a dissimilarity measure between sets of (labeled) distance sets, we address two problems that are often encountered in object recognition: object segmentation, for which we formulate a distance sets shape filter, and shape matching. The use of the shape filter is illustrated on printed and handwritten character recognition and detection of traffic signs in complex scenes. The shape comparison procedure is illustrated on handwritten character classification, COIL20 database object recognition and MPEG7 silhouette database retrieval.
On the Shape of Plane Elastic Curves
 International Journal of Computer Vision
, 2005
"... We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments nonuniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shapepreservi ..."
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Cited by 35 (5 self)
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We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments nonuniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shapepreserving transformations. The elastic properties of the curves are encoded in Riemannian metrics on these spaces. Geodesics in shape spaces are used to quantify shape divergence and to develop morphing techniques. The shape spaces and metrics constructed are novel and offer an environment for the study of shape statistics. Elasticity leads to shape correspondences and deformations that are more natural and intuitive than those obtained in several existing models. Applications of shape geodesics to the definition and calculation of mean shapes and to the development of shape clustering techniques are also investigated.
Path similarity skeleton graph matching
 IEEE TRANS. PAMI
, 2008
"... This paper proposes a novel graph matching algorithm and applies it to shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the geodesic paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we do not consider the to ..."
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Cited by 31 (9 self)
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This paper proposes a novel graph matching algorithm and applies it to shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the geodesic paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we do not consider the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of geodesic paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with Discrete Curve Evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and contour deformations.
Hierarchical Procrustes matching for shape retrival
 in CVPR
, 2006
"... We introduce Hierarchical Procrustes Matching (HPM), a segmentbased shape matching algorithm which avoids problems associated with purely global or local methods and performs well on benchmark shape retrieval tests. The simplicity of the shape representation leads to a powerful matching algorithm w ..."
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Cited by 30 (2 self)
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We introduce Hierarchical Procrustes Matching (HPM), a segmentbased shape matching algorithm which avoids problems associated with purely global or local methods and performs well on benchmark shape retrieval tests. The simplicity of the shape representation leads to a powerful matching algorithm which incorporates intuitive ideas about the perceptual nature of shape while being computationally efficient. This includes the ability to match similar parts even when they occur at different scales or positions. While comparison of multiscale shape representations is typically based on specific features, HPM avoids the need to extract such features. The hierarchical structure of the algorithm captures the appealing notion that matching should proceed in a global to local direction. 1.
Integral invariants for shape matching
 PAMI
, 2006
"... Abstract—For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential ..."
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Cited by 29 (2 self)
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Abstract—For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database. Index Terms—Integral invariants, shape, shape matching, shape distance, shape retrieval. Ç 1