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17
Minimum near-convex decomposition for robust shape representation
- in Proc. IEEE Int. Conf. Computer Vision
"... Shape decomposition is a fundamental problem for part-based shape representation. We propose a novel shape decomposition method called Minimum Near-Convex De-composition (MNCD), which decomposes 2D and 3D arbi-trary shapes into minimum number of “near-convex ” parts. With the degree of near-convexit ..."
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Cited by 18 (4 self)
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Shape decomposition is a fundamental problem for part-based shape representation. We propose a novel shape decomposition method called Minimum Near-Convex De-composition (MNCD), which decomposes 2D and 3D arbi-trary shapes into minimum number of “near-convex ” parts. With the degree of near-convexity a user specified param-eter, our decomposition is robust to large local distortions and shape deformation. The shape decomposition is formu-lated as a combinatorial optimization problem by minimiz-ing the number of non-intersection cuts. Two major percep-tion 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 subgradient-based branch-and-bound search. Both theoretical analysis and experiment re-sults show that our approach outperforms the state-of-the-art results without introducing redundant parts. Finally we also show the superiority of our method in the application of hand gesture recognition. 1.
Computing large convex regions of obstacle-free space through semi-definite programming
- in Workshop on the Algorithmic Foundations of Robotics (WAFR
, 2014
"... Abstract. This paper presents iris (Iterative Regional Inflation by Semi-definite programming), a new method for quickly computing large poly-topic and ellipsoidal regions of obstacle-free space through a series of convex optimizations. These regions can be used, for example, to effi-ciently optimiz ..."
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Cited by 8 (6 self)
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Abstract. This paper presents iris (Iterative Regional Inflation by Semi-definite programming), a new method for quickly computing large poly-topic and ellipsoidal regions of obstacle-free space through a series of convex optimizations. These regions can be used, for example, to effi-ciently optimize an objective over collision-free positions in space for a robot manipulator. The algorithm alternates between two convex opti-mizations: (1) a quadratic program that generates a set of hyperplanes to separate a convex region of space from the set of obstacles and (2) a semidefinite program that finds a maximum-volume ellipsoid inside the polytope intersection of the obstacle-free half-spaces defined by those hyperplanes. Both the hyperplanes and the ellipsoid are refined over several iterations to monotonically increase the volume of the inscribed ellipsoid, resulting in a large polytope and ellipsoid of obstacle-free space. Practical applications of the algorithm are presented in 2D and 3D, and extensions to N-dimensional configuration spaces are discussed. Experi-ments demonstrate that the algorithm has a computation time which is linear in the number of obstacles, and our matlab [18] implementation converges in seconds for environments with millions of obstacles. 1
Fast approximate convex decomposition using relative concavity
, 2012
"... Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. I ..."
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Cited by 7 (1 self)
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Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of nc non-crossing (independent) cuts that can be simultaneously applied to decompose the component into nc +1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparitive results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark [5]. 1.
Minimum Near-Convex Shape Decomposition
- IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2013
"... Shape decomposition is a fundamental problem for part-based shape representation. We propose the Minimum Near-Convex Decomposition (MNCD) to decompose arbitrary shapes into minimum number of “near-convex ” parts. The near-convex shape decomposition is formulated as a discrete optimization problem by ..."
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Cited by 2 (1 self)
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Shape decomposition is a fundamental problem for part-based shape representation. We propose the Minimum Near-Convex Decomposition (MNCD) to decompose arbitrary shapes into minimum number of “near-convex ” parts. The near-convex shape decomposition is formulated as a discrete optimization problem by minimizing the number of non-intersecting cuts. Two perception rules are imposed as constraints into our objective function to improve the visual naturalness of the decomposition. With the degree of near-convexity a user specified parameter, our decomposition is robust to local distortions and shape deformation. The optimization can be efficiently solved via Binary Integer Linear Programming. Both theoretical analysis and experiment results show that our approach outperforms the state-of-the-art results without introducing redundant parts, and thus leads to robust shape representation.
Support Vector Shape: A Classifier Based Shape . . .
, 2012
"... We introduce a novel implicit representation for 2D and 3D shapes based on Support Vector Machine (SVM) theory. Each shape is represented by an analytic decision function obtained by training SVM, with a Radial Basis Function (RBF) kernel, so that the interior shape points are given higher values. T ..."
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Cited by 1 (0 self)
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We introduce a novel implicit representation for 2D and 3D shapes based on Support Vector Machine (SVM) theory. Each shape is represented by an analytic decision function obtained by training SVM, with a Radial Basis Function (RBF) kernel, so that the interior shape points are given higher values. This empowers support vector shape (SVS) with multifold advantages. First, the representation uses a sparse subset of feature points determined by the support vectors, which significantly improves the discriminative power against noise, fragmentation and other artifacts that often come with the data. Second, the use of the RBF kernel provides scale, rotation, and translation invariant features, and allows any shape to be represented accurately regardless of its complexity. Finally, the decision function can be used to select reliable feature points. These features are described using gradients computed from from highly consistent decision functions instead from conventional edges. Our experiments demonstrates promising results.
Modelling composite shapes by gibbs random fields
- In Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on
, 2011
"... We analyse the potential of Gibbs Random Fields for shape prior modelling. We show that the expressive power of second order GRFs is already sufficient to express spatial relations between shape parts and simple shapes simultane-ously. This allows to model and recognise complex shapes as spatial com ..."
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We analyse the potential of Gibbs Random Fields for shape prior modelling. We show that the expressive power of second order GRFs is already sufficient to express spatial relations between shape parts and simple shapes simultane-ously. This allows to model and recognise complex shapes as spatial compositions of simpler parts. 1.
A Computational Model of the Short-Cut Rule for 2D Shape Decomposition
, 2014
"... We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible cuts. We propose and implement a computational model for t ..."
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Cited by 1 (0 self)
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We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible cuts. We propose and implement a computational model for the short-cut rule and apply it to the problem of shape decomposition. The model we proposed generates a set of cut hypotheses passing through the points on the silhouette which represent the negative minima of curvature. We then show that most part-cut hypotheses can be eliminated by analysis of local properties of each. Finally, the remaining hypotheses are evaluated in ascending length order, which guarantees that of any pair of conflicting cuts only the shortest will be accepted. We demonstrate that, compared with state-of-the-art shape decomposition methods, the proposed approach achieves decomposition results which better correspond to human intuition as revealed in psychological experiments.
A Shape Reconstructability Measure of Object Part Importance with Applications to Object Detection and Localization
, 2013
"... Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media New York. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript ve ..."
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Cited by 1 (0 self)
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Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media New York. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com”.
Planar shape decomposition made simple
, 2015
"... We present a very simple computational model for planar shape decomposition that naturally captures most of the rules and salience measures suggested by psychophysical studies, including the minima and short-cut rules, convexity, and symmetry. It is based on a medial axis representation in ways that ..."
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We present a very simple computational model for planar shape decomposition that naturally captures most of the rules and salience measures suggested by psychophysical studies, including the minima and short-cut rules, convexity, and symmetry. It is based on a medial axis representation in ways that have not been explored before and sheds more light into the connection between existing rules like minima and convexity. In particular, vertices of the exterior medial axis directly provide the position and extent of negative minima of curvature, while a traversal of the interior medial axis directly provides a small set of candidate endpoints for part-cuts. The final selection follows a simple local con-vexity rule that can incorporate arbitrary salience measures. Neither global optimization nor differentiation is involved. We provide qualitative and quantitative evaluation and comparisons on ground-truth data from psychophysical experiments.
