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185
Shape Matching and Object Recognition Using Shape Contexts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform ..."
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Cited by 1809 (21 self)
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We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape con texts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; reg ularized thin plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning trans form. We treat recognition in a nearestneighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits and the COIL dataset.
Recognition of Shapes by Editing Their Shock Graphs
, 2004
"... 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, thr ..."
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Cited by 204 (8 self)
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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.
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 174 (7 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.
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 170 (37 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 Similarity Measure Based on Correspondence of Visual Parts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2000
"... AbstractÐA cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2D objects. To reduce influence of digitization noise, as well as segmentation errors, the shapes are simplified by a nov ..."
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Cited by 155 (31 self)
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AbstractÐA cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2D objects. To reduce influence of digitization noise, as well as segmentation errors, the shapes are simplified by a novel process of digital curve evolution. To compute our similarity measure, we first establish the best possible correspondence of visual parts (without explicitly computing the visual parts). Then, the similarity between corresponding parts is computed and aggregated. We applied our similarity measure to shape matching of object contours in various image databases and compared it to wellknown approaches in the literature. The experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions. Index TermsÐShape representation, shape similarity measure, visual parts, discrete curve evolution. 1
Recognition of Shapes by Editing Shock Graphs
 In IEEE International Conference on Computer Vision
, 2001
"... This paper presents a novel recognition framework which is based on matching shock graphs of 2D shape outlines, where the distance between two shapes is defined to be the cost of the least action path deforming one shape to another. Three key ideas render the implementation of this framework practic ..."
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Cited by 125 (7 self)
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This paper presents a novel recognition framework which is based on matching shock graphs of 2D shape outlines, where the distance between two shapes is defined to be the cost of the least action path deforming one shape to another. Three key ideas render the implementation of this framework practical. First, the shape space is partitioned by defining an equivalence class on shapes, where two shapes with the same shock graph topology are considered to be equivalent. Second, the space of deformations is discretized by defining all deformations with the same sequence of shock graph transitions as equivalent. Shock transitions are points along the deformation where the shock graph topology changes. Third, we employ a graph edit distance algorithm that searches in the space of all possible transition sequences and finds the globally optimal sequence in polynomial time. The effectiveness of the proposed technique in the presence of a variety of visual transformations including occlusion, articulation and deformation of parts, shadow and highlights, viewpoint variation, and boundary perturbations is demonstrated. Indexing into two separate databases of roughly 100 shapes results in 100% accuracy for top three matches and 99:5% for the next three matches. 1
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 112 (1 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.
An efficient earth mover’s distance algorithm for robust histogram comparison
 PAMI
, 2007
"... DRAFT We propose EMDL1: a fast and exact algorithm for computing the Earth Mover’s Distance (EMD) between a pair of histograms. The efficiency of the new algorithm enables its application to problems that were previously prohibitive due to high time complexities. The proposed EMDL1 significantly s ..."
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Cited by 96 (5 self)
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DRAFT We propose EMDL1: a fast and exact algorithm for computing the Earth Mover’s Distance (EMD) between a pair of histograms. The efficiency of the new algorithm enables its application to problems that were previously prohibitive due to high time complexities. The proposed EMDL1 significantly simplifies the original linear programming formulation of EMD. Exploiting the L1 metric structure, the number of unknown variables in EMDL1 is reduced to O(N) from O(N 2) of the original EMD for a histogram with N bins. In addition, the number of constraints is reduced by half and the objective function of the linear program is simplified. Formally without any approximation, we prove that the EMDL1 formulation is equivalent to the original EMD with a L1 ground distance. To perform the EMDL1 computation, we propose an efficient treebased algorithm, TreeEMD. TreeEMD exploits the fact that a basic feasible solution of the simplex algorithmbased solver forms a spanning tree when we interpret EMDL1 as a network flow optimization problem. We empirically show that this new algorithm has average time complexity of O(N 2), which significantly improves the best reported supercubic complexity of the original EMD. The accuracy of the proposed methods is evaluated by
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.
Using the InnerDistance for Classification of Articulated Shapes
 In Proc. CVPR
, 2005
"... We propose using the innerdistance between landmark points to build shape descriptors. The innerdistance is defined as the length of the shortest path between landmark points within the shape silhouette. We show that the innerdistance is articulation insensitive and more effective at capturing com ..."
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Cited by 71 (10 self)
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We propose using the innerdistance between landmark points to build shape descriptors. The innerdistance is defined as the length of the shortest path between landmark points within the shape silhouette. We show that the innerdistance is articulation insensitive and more effective at capturing complex shapes with part structures than Euclidean distance. To demonstrate this idea, it is used to build a new shape descriptor based on shape contexts. After that, we design a dynamic programming based method for shape matching and comparison. We have tested our approach on a variety of shape databases including an articulated shape dataset, MPEG7 CEShape1, Kimia silhouettes, a Swedish leaf database and a human motion silhouette dataset. In all the experiments, our method demonstrates effective performance compared with other algorithms. 1