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A spectral approach to shapebased retrieval of articulated 3D models
 CAD
, 2007
"... We present an approach to robust shape retrieval from databases containing articulated 3D models. Each shape is represented by the eigenvectors of an appropriately defined affinity matrix, forming a spectral embedding which achieves normalization against rigidbody transformations, uniform scaling, ..."
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Cited by 53 (1 self)
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We present an approach to robust shape retrieval from databases containing articulated 3D models. Each shape is represented by the eigenvectors of an appropriately defined affinity matrix, forming a spectral embedding which achieves normalization against rigidbody transformations, uniform scaling, and shape articulation (bending). Retrieval is performed in the spectral domain using global shape descriptors. On the McGill database of articulated 3D shapes, the spectral approach leads to absolute improvement in retrieval performance for both the spherical harmonic and the light field shape descriptors. The best retrieval results are obtained using a simple and novel eigenvaluebased descriptor we propose.
Efficient 3D shape matching and retrieval using a concrete radialized spherical . . .
, 2007
"... ..."
Minimum nearconvex decomposition for robust shape representation
 in Proc. IEEE Int. Conf. Computer Vision
"... Shape decomposition is a fundamental problem for partbased shape representation. We propose a novel shape decomposition method called Minimum NearConvex Decomposition (MNCD), which decomposes 2D and 3D arbitrary shapes into minimum number of “nearconvex ” parts. With the degree of nearconvexit ..."
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Cited by 18 (4 self)
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Shape decomposition is a fundamental problem for partbased shape representation. We propose a novel shape decomposition method called Minimum NearConvex Decomposition (MNCD), which decomposes 2D and 3D arbitrary shapes into minimum number of “nearconvex ” parts. With the degree of nearconvexity a user specified parameter, our decomposition is robust to large local distortions and shape deformation. The shape decomposition is formulated as a combinatorial optimization problem by minimizing the number of nonintersection cuts. Two major perception rules are also imposed into our scheme to improve the visual naturalness of the decomposition. The global optimal solution of this challenging discrete optimization problem is obtained by a dynamic subgradientbased branchandbound search. Both theoretical analysis and experiment results show that our approach outperforms the stateoftheart results without introducing redundant parts. Finally we also show the superiority of our method in the application of hand gesture recognition. 1.
GMAT: The Groupwise Medial Axis Transform for Fuzzy Skeletonization and Intelligent Pruning
"... Abstract. There is a frequent need to compute medial shape representations of each of a group of structures, e.g. for use in a medical study of anatomical shapes. We present a novel approach to skeletonization that leverages information provided from such a group. We augment the traditional medial a ..."
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Cited by 17 (2 self)
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Abstract. There is a frequent need to compute medial shape representations of each of a group of structures, e.g. for use in a medical study of anatomical shapes. We present a novel approach to skeletonization that leverages information provided from such a group. We augment the traditional medial axis transform with an additional coordinate stored at each medial locus, indicating the confidence that the branch on which that locus lies represents signal and not noise. This confidence is calculated based on the support given to that branch by corresponding branches in other skeletons in the group. We establish the aforementioned correspondence by a set of bipartite graph matchings using the Hungarian algorithm, and compute branch support based on similarity of computed geometric and topological features at each branch. This groupwise skeletonization approach supports an intelligent pruning algorithm, which we show to operate quickly and provide pruning in an intuitive manner. We show that the method is amenable to automatic detection of skeletal configurations with one, or more than one, topological class of skeletons. This is useful to medical studies which often involve patient groups whose structures may differ topologically. 1
Multiscale Symmetric Part Detection and Grouping
"... Skeletonization algorithms typically decompose an object’s silhouette into a set of symmetric parts, offering a powerful representation for shape categorization. However, having access to an object’s silhouette assumes correct figureground segmentation, leading to a disconnect with the mainstream c ..."
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Cited by 14 (5 self)
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Skeletonization algorithms typically decompose an object’s silhouette into a set of symmetric parts, offering a powerful representation for shape categorization. However, having access to an object’s silhouette assumes correct figureground segmentation, leading to a disconnect with the mainstream categorization community, which attempts to recognize objects from cluttered images. In this paper, we present a novel approach to recovering and grouping the symmetric parts of an object from a cluttered scene. We begin by using a multiresolution superpixel segmentation to generate medial point hypotheses, and use a learned affinity function to perceptually group nearby medial points likely to belong to the same medial branch. In the next stage, we learn higher granularity affinity functions to group the resulting medial branches likely to belong to the same object. The resulting framework yields a skeletal approximation that’s free of many of the instabilities plaguing traditional skeletons. More importantly, it doesn’t require a closed contour, enabling the application of skeletonbased categorization systems to more realistic imagery. 1.
The Evolution of Object Categorization and the Challenge of Image Abstraction
"... Technical University. During my visit, a graduate student was kind enough to show me around Prague, including a visit to the Museum of Modern and Contemporary Art (Veletr˘zní Palác). It was there that I saw the sculpture ..."
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Cited by 13 (1 self)
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Technical University. During my visit, a graduate student was kind enough to show me around Prague, including a visit to the Museum of Modern and Contemporary Art (Veletr˘zní Palác). It was there that I saw the sculpture
PANORAMA: A 3D Shape Descriptor based on Panoramic Views for Unsupervised 3D Object Retrieval
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2010
"... We present a novel 3D shape descriptor that uses a set of panoramic views of a 3D object which describe the position and orientation of the object’s surface in 3D space. We obtain a panoramic view of a 3D object by projecting it to the lateral surface of a cylinder parallel to one of its three prin ..."
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Cited by 12 (2 self)
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We present a novel 3D shape descriptor that uses a set of panoramic views of a 3D object which describe the position and orientation of the object’s surface in 3D space. We obtain a panoramic view of a 3D object by projecting it to the lateral surface of a cylinder parallel to one of its three principal axes and centered at the centroid of the object. The object is projected to three perpendicular cylinders, each one aligned with one of its principal axes in order to capture the global shape of the object. For each projection we compute the corresponding 2D Discrete Fourier Transform as well as 2D Discrete Wavelet Transform. We further increase the retrieval performance by employing a local (unsupervised) relevance feedback technique that shifts the descriptor of an object closer to its cluster centroid in feature space. The effectiveness of the proposed 3D object retrieval methodology is demonstrated via an extensive evaluation in standard benchmarks that clearly shows better performance against stateoftheart 3D object retrieval methods.
A Study of Graph Spectra for Comparing Graphs and Trees
, 2008
"... The spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure. It has also been employed as a graph representation for pattern matching since it is invariant to the labelling of the graph. There are however a number ..."
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Cited by 9 (1 self)
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The spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure. It has also been employed as a graph representation for pattern matching since it is invariant to the labelling of the graph. There are however a number of potential drawbacks in using the spectrum as a representation of a graph; Firstly, more than one graph may share the same spectrum. It is well known, for example, that very few trees can be uniquely specified by their spectrum. Secondly, the spectrum may change dramatically with a small change structure. There are a wide variety of graph matrix representations from which the spectrum can be extracted. Among these are the adjacency matrix, combinatorial Laplacian, normalised Laplacian and unsigned Laplacian. Spectra can also be derived from the heat kernel matrix and path length distribution matrix. The choice of matrix representation clearly has a large effect on the suitability of spectrum in a number of pattern recognition tasks. In this paper we investigate the performance of the spectra as a graph representation in a variety of situations. Firstly, we investigate the cospectrality of the various matrix representations over large graph and tree sets, extending the work of previous authors. We then show that the Euclidean distance between spectra tracks the edit distance between graphs over a wide range of edit costs, and we analyse the accuracy of this relationship. We then use the spectra to both cluster and classify the graphs and demonstrate the effect of the graph matrix formulation on error rates. These results are produced using both synthetic graphs and trees and graphs derived from shape and image data.
3D Shape Matching by Geodesic Eccentricity
, 2008
"... This paper makes use of the continuous eccentricity transform to perform 3D shape matching. The eccentricity transform has already been proved useful in a discrete graphtheoretic setting and has been applied to 2D shape matching. We show how these ideas extend to higher dimensions. The eccentricity ..."
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Cited by 7 (2 self)
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This paper makes use of the continuous eccentricity transform to perform 3D shape matching. The eccentricity transform has already been proved useful in a discrete graphtheoretic setting and has been applied to 2D shape matching. We show how these ideas extend to higher dimensions. The eccentricity transform is used to compute descriptors for 3D shapes. These descriptors are defined as histograms of the eccentricity transform and are naturally invariant to euclidean motion and articulation. They show promising results for shape discrimination.
Posture Invariant Correspondence Of Triangular Meshes In Shape Space
"... We find dense pointtopoint correspondences between two surfaces corresponding to different postures of the same articulated object in a fully automatic way. The approach requires no prior knowledge about the shapes being registered. Furthermore, the approach does not require any userspecified par ..."
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Cited by 7 (1 self)
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We find dense pointtopoint correspondences between two surfaces corresponding to different postures of the same articulated object in a fully automatic way. The approach requires no prior knowledge about the shapes being registered. Furthermore, the approach does not require any userspecified parameters. We register possibly incomplete triangular meshes. We model the deformations of an object as isometries and solve the correspondence problem by aligning the intrinsic geometries of the manifolds in a suitable space. We apply the technique to segment the surface into nearrigid components. 1.