Part structure and articulation are of fundamental importance in computer and human vision. We propose using the inner-distance to build shape descriptors that are robust to articulation and capture part structure. The inner-distance 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 inner-distance 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 inner-distance. The first method combines the inner-distance and multidimensional scaling (MDS) to build articulation invariant signatures for articulated shapes. The second method uses the inner-distance 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 dataset, MPEG7 CE-Shape-1, Kimia silhouettes, the ETH-80 data set, two leaf data sets, and a human motion silhouette dataset. In all the experiments, our methods demonstrate effective performance compared with other algorithms.

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We propose using the inner-distance between landmark points to build shape descriptors. The inner-distance 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 CE-Shape-1, 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

The recognition community has long avoided bridging the representational gap between traditional, low-level image features and generic models. Instead, the gap has been artificially eliminated by either bringing the image closer to the models, using simple scenes containing idealized, textureless objects, or by bringing the models closer to the images, using 3-D CAD model templates or 2-D appearance model templates. In this paper, we attempt to bridge the representational gap for the domain of model acquisition. Specifically, we address the problem of automatically acquiring a generic 2-D view-based class model from a set of images, each containing an exemplar object belonging to that class. We introduce a novel graph-theoretical formulation of the problem, and demonstrate the approach on real imagery.

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 non-terminal 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 Or-node points to alternative sub-configurations and an And-node is decomposed into a number of components. This representation supports recursive top-down/bottom-up procedures for image parsing under the Bayesian framework and make it convenient to scale

We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuous-valued attributes, and can be equally applied to ordered and unordered, rooted and unrooted trees. We prove that our measures satisfy the metric constraints and provide a polynomial-time algorithm to compute them. This is a remarkable and attractive property, since the computation of tra-ditional edit-distance-based metrics is NP-complete, except for ordered structures. We experimentally validate the usefulness of our metrics on shape matching tasks, and compare them with edit-distance measures. ∗ Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence 1

We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this representation for 3-D object model retrieval. Our formulation uses the geometric information

Object recognition can be formulated as matching image features to model features. When recognition is exemplar-based, feature correspondence is one-to-one. However, segmentation errors, articulation, scale difference, and within-class deformation can yield image and model features which don't match one-to-one but rather many-to-many. Adopting a graph-based representation of a set of features, we present a matching algorithm that establishes many-to-many correspondences between the nodes of two noisy, vertex-labeled weighted graphs. Our approach reduces the problem of many-to-many matching of weighted graphs to that of many-to-many matching of weighted point sets in a normed vector space. This is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure. Many-to-many vector correspondences established by the Earth Mover's Distance framework are mapped back into many-to-many correspondences between graph nodes. Empirical evaluation of the algorithm on an extensive set of recognition trials, including a comparison with two competing graph matching approaches, demonstrates both the robustness and efficacy of the overall approach.

Abstract—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. Index Terms—Skeleton, skeleton pruning, contour partition, discrete curve evolution. 1

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.