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32
ArticulationInvariant Representation of Nonplanar Shapes
"... Abstract. Given a set of points corresponding to a 2D projection of a nonplanar shape, we would like to obtain a representation invariant to articulations (under no selfocclusions). It is a challenging problem since we need to account for the changes in 2D shape due to 3D articulations, viewpoint ..."
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Abstract. Given a set of points corresponding to a 2D projection of a nonplanar shape, we would like to obtain a representation invariant to articulations (under no selfocclusions). It is a challenging problem since we need to account for the changes in 2D shape due to 3D articulations, viewpoint variations, as well as the varying effects of imaging process on different regions of the shape due to its nonplanarity. By modeling an articulating shape as a combination of approximate convex parts connected by nonconvex junctions, we propose to preserve distances between a pair of points by (i) estimating the parts of the shape through approximate convex decomposition, by introducing a robust measure of convexity and (ii) performing partwise affine normalization by assuming a weak perspective camera model, and then relating the points using the inner distance which is insensitive to planar articulations. We demonstrate the effectiveness of our representation on a dataset with nonplanar articulations, and on standard shape retrieval datasets like MPEG7.
Beyond Pairwise Shape Similarity Analysis
"... Abstract. This paper considers two major applications of shape matching algorithms: (a) querybyexample, i. e. retrieving the most similar shapes from a database and (b) finding clusters of shapes, each represented by a single prototype. Our approach goes beyond pairwise shape similarity analysis b ..."
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Cited by 20 (3 self)
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Abstract. This paper considers two major applications of shape matching algorithms: (a) querybyexample, i. e. retrieving the most similar shapes from a database and (b) finding clusters of shapes, each represented by a single prototype. Our approach goes beyond pairwise shape similarity analysis by considering the underlying structure of the shape manifold, which is estimated from the shape similarity scores between all the shapes within a database. We propose a modified mutual kNN graph as the underlying representation and demonstrate its performance for the task of shape retrieval. We further describe an efficient, unsupervised clustering method which uses the modified mutual kNN graph for initialization. Experimental evaluation proves the applicability of our method, e. g. by achieving the highest ever reported retrieval score of 93.40 % on the well known MPEG7 database. 1
Shape Retrieval Using Hierarchical Total Bregman Soft Clustering
"... In this paper, we consider the family of total Bregman divergences (tBDs) as an efficient and robust “distance” measure to quantify the dissimilarity between shapes. We use the tBD based ℓ1norm center as the representative of a set of shapes, and call it the tcenter. First, we briefly present and ..."
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Cited by 14 (4 self)
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In this paper, we consider the family of total Bregman divergences (tBDs) as an efficient and robust “distance” measure to quantify the dissimilarity between shapes. We use the tBD based ℓ1norm center as the representative of a set of shapes, and call it the tcenter. First, we briefly present and analyze the properties of the tBDs and tcenters following our previous work in [1]. Then, we prove that for any tBD, there exists a distribution which belongs to the lifted exponential family of statistical distributions. Further, we show that finding the maximum a posteriori estimate of the parameters of the lifted exponential family distribution is equivalent to minimizing the tBD to find the tcenters. This leads to a new clustering technique namely, the total Bregman soft clustering algorithm. We evaluate the tBD, tcenter and the soft clustering algorithm on shape retrieval applications. Our shape retrieval framework is composed of three steps: (1) extraction of the shape boundary points (2) affine alignment of the shapes and use of a Gaussian mixture model (GMM) [2], [3], [4] to represent the aligned boundaries, and (3) comparison of the GMMs using tBD to find the best matches given a query shape. To further speed up the shape retrieval algorithm, we perform hierarchical clustering of the shapes using our total Bregman soft clustering algorithm. This enables us to compare the query with a small subset of shapes which are chosen to be the cluster tcenters. We evaluate our method on various public domain 2D and 3D databases, and demonstrate comparable or better results than stateoftheart retrieval techniques.
Balancing Deformability and Discriminability for Shape Matching
"... Abstract. We propose a novel framework, aspect space, to balance deformability and discriminability, which are often two competing factors in shape and image representations. In this framework, an object is embedded as a surface in a higher dimensional space with a parameter named aspect weight, whi ..."
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Cited by 14 (3 self)
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Abstract. We propose a novel framework, aspect space, to balance deformability and discriminability, which are often two competing factors in shape and image representations. In this framework, an object is embedded as a surface in a higher dimensional space with a parameter named aspect weight, which controls the importance of intensity in the embedding. We show that this framework naturally unifies existing important shape and image representations by adjusting the aspect weight and the embedding. More importantly, we find that the aspect weight implicitly controls the degree to which a representation handles deformation. Based on this idea, we present the aspect shape context, which extends shape contextbased descriptors and adaptively selects the “best ” aspect weight for shape comparison. Another observation we have is the proposed descriptor nicely fits contextsensitive shape retrieval. The proposed methods are evaluated on two public datasets, MPEG7CEShape1 and Tari 1000, in comparison to stateoftheart solutions. In the standard shape retrieval experiment using the MPEG7 CEShape1 database, the new descriptor with context information achieves a bull’s eye score of 95.96%, which surpassed all previous results. In the Tari 1000 dataset, our methods significantly outperform previous tested methods as well. 1
Two Perceptually Motivated Strategies for Shape Classification
"... In this paper, we propose two new, perceptually motivated strategies to better measure the similarity of 2D shape instances that are in the form of closed contours. The first strategy handles shapes that can be decomposed into a base structure and a set of inward or outward pointing “strand” structu ..."
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In this paper, we propose two new, perceptually motivated strategies to better measure the similarity of 2D shape instances that are in the form of closed contours. The first strategy handles shapes that can be decomposed into a base structure and a set of inward or outward pointing “strand” structures, where a strand structure represents a very thin, elongated shape part attached to the base structure. The similarity of two such shape contours can be better described by measuring the similarity of their base structures and strand structures in different ways. The second strategy handles shapes that exhibit good bilateral symmetry. In many cases, such shapes are invariant to a certain level of scaling transformation along their symmetry axis. In our experiments, we show that these two strategies can be integrated into available shape matching methods to improve the performance of shape classification on several widelyused shape data sets. Shape matching through nonrigid shape deformation is a typical approach to measure shape similarity [6, 14, 10, 21, 13, 16]. In general, this approach measures the amount of energy required to deform one shape contour into another based on some physical or mathematical model. The model is then optimized using methods such as dynamic programming to obtain a set of corresponded points on the two shape contours that minimize the deformation cost of this model. However, this approach is often very sensitive to strong, local shape variations that human vision may handle very well. For example, the two shape contours shown in Figs. 1(a) and (b) are similar in general, but their outward parts, represented by the dashed curves, are quite different from each other. A large deformation cost may be required to match these two shape contours. 1.
Affinity Learning on a Tensor Product Graph with Applications to Shape and Image Retrieval
"... As observed in several recent publications, improved retrieval performance is achieved when pairwise similarities between the query and the database objects are replaced with more global affinities that also consider the relation among the database objects. This is commonly achieved by propagating t ..."
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Cited by 8 (3 self)
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As observed in several recent publications, improved retrieval performance is achieved when pairwise similarities between the query and the database objects are replaced with more global affinities that also consider the relation among the database objects. This is commonly achieved by propagating the similarity information in a weighted graph representing the database and query objects. Instead of propagating the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. By virtue of this construction, not only local but also long range similarities among graph nodes are explicitly represented as higher order relations, making it possible to better reveal the intrinsic structure of the data manifold. In addition, we improve the local neighborhood structure of the original graph in a preprocessing stage. We illustrate the benefits of the proposed approach on shape and image ranking and retrieval tasks. We are able to achieve the bull’s eye retrieval score of 99.99 % on MPEG7 shape dataset, which is much higher than the stateoftheart algorithms. 1.
H.: Diffusion processes for retrieval revisited
 In: Proceedings of IEEEE Conference on Computer Vision and Pattern Recognition (CVPR). (2013) 1320–1327
"... In this paper we revisit diffusion processes on affinity graphs for capturing the intrinsic manifold structure defined by pairwise affinity matrices. Such diffusion processes have already proved the ability to significantly improve subsequent applications like retrieval. We give a thorough overvie ..."
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Cited by 5 (1 self)
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In this paper we revisit diffusion processes on affinity graphs for capturing the intrinsic manifold structure defined by pairwise affinity matrices. Such diffusion processes have already proved the ability to significantly improve subsequent applications like retrieval. We give a thorough overview of the stateoftheart in this field and discuss obvious similarities and differences. Based on our observations, we are then able to derive a generic framework for diffusion processes in the scope of retrieval applications, where the related work represents specific instances of our generic formulation. We evaluate our framework on several retrieval tasks and are able to derive algorithms that e. g. achieve a 100 % bullseye score on the popular MPEG7 shape retrieval data set. 1.
Affinity Learning with Diffusion on Tensor Product Graph
"... Abstract—In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due ..."
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Abstract—In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples. As observed in several recent approaches, more reliable similarities can be obtained if the original similarities are diffused in the context of other data points, where the context of each point is a set of points most similar to it. Compared to the existing methods, our approach differs in two main aspects. First, instead of diffusing the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. Since TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities. However, it comes at the price of higher order computational complexity and storage requirement. The key contribution of the proposed approach is that the information propagation on TPG can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph. We prove that a graph diffusion process on TPG is equivalent to a novel iterative algorithm on the original graph, which is guaranteed to converge. After its convergence we obtain new edge weights that can be interpreted as new, learned affinities. We stress that the affinities are learned in an unsupervised setting. We illustrate the benefits of the proposed approach for data manifolds composed of shapes, images, and image patches on two very different tasks of image retrieval and image segmentation. With learned affinities, we achieve the bull’s eye retrieval score of 99.99 percent on the MPEG7 shape dataset, which is much higher than the stateoftheart algorithms. When the
Consensus of kNNs for Robust Neighborhood Selection on GraphBased Manifolds
"... Propagating similarity information along the data manifold requires careful selection of local neighborhood. Selecting a “good ” neighborhood in an unsupervised setting, given an affinity graph, has been a difficult task. The most common way to select a local neighborhood has been to use the knea ..."
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Propagating similarity information along the data manifold requires careful selection of local neighborhood. Selecting a “good ” neighborhood in an unsupervised setting, given an affinity graph, has been a difficult task. The most common way to select a local neighborhood has been to use the knearest neighborhood (kNN) selection criterion. However, it has the tendency to include noisy edges. In this paper, we propose a way to select a robust neighborhood using the consensus of multiple rounds of kNNs. We explain how using consensus information can give better control over neighborhood selection. We also explain in detail the problems with another recently proposed neighborhood selection criteria, i.e., Dominant Neighbors, and show that our method is immune to those problems. Finally, we show the results from experiments in which we compare our method to other neighborhood selection approaches. The results corroborate our claims that consensus of kNNs does indeed help in selecting more robust and stable localities. 1.