207 results found
Litman R, Bronstein AM, Bronstein MM, 2013, Stable semi-local features for non-rigid shapes, Mathematics and Visualization, Pages: 161-189
© Springer-Verlag Berlin Heidelberg 2013. Feature-based analysis is becoming a very popular approach for geometric shape analysis. Following the success of this approach in image analysis, there is a growing interest in finding analogous methods in the 3D world. Maximally stable component detection is a low computation cost and high repeatability method for feature detection in images.In this study, a diffusion-geometry based framework for stable component detection is presented, which can be used for geometric feature detection in deformable shapes. The vast majority of studies of deformable 3D shapes models them as the two-dimensional boundary of the volume of the shape. Recent works have shown that a volumetric shape model is advantageous in numerous ways as it better captures the natural behavior of non-rigid deformations. We show that our framework easily adapts to this volumetric approach, and even demonstrates superior performance. A quantitative evaluation of our methods on the SHREC’10 and SHREC’11 feature detection benchmarks as well as qualitative tests on the SCAPE dataset show its potential as a source of high-quality features. Examples demonstrating the drawbacks of surface stable components and the advantage of their volumetric counterparts are also presented.
Rosman G, Bronstein MM, Bronstein AM, et al., 2013, Group-valued regularization for motion segmentation of articulated shapes, Mathematics and Visualization, Pages: 263-281
© Springer-Verlag Berlin Heidelberg 2013. Motion-based segmentation is an important tool for the analysis of articulated shapes. As such, it plays an important role in mechanical engineering, computer graphics, and computer vision. In this chapter, we study motion-based segmentation of 3D articulated shapes. We formulate motion-based surface segmentation as a piecewise-smooth regularization problem for the transformations between several poses. Using Lie-group representation for the transformation at each surface point, we obtain a simple regularized fitting problem. An Ambrosio-Tortorelli scheme of a generalized Mumford-Shah model gives us the segmentation functional without assuming prior knowledge on the number of parts or even the articulated nature of the object. Experiments on several standard datasets compare the results of the proposed method to state-of-the-art algorithms.
Pokrass J, Bronstein AM, Bronstein MM, 2013, Partial shape matching without point-wise correspondence, Numerical Mathematics, Vol: 6, Pages: 223-244, ISSN: 1004-8979
Partial similarity of shapes is a challenging problem arising in many important applications in computer vision, shape analysis, and graphics, e.g. when one has to deal with partial information and acquisition artifacts. The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation. Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two, taking into account possibly different parts. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes, and present experiments demonstrating the success of the proposed method. © 2013 Global-Science Press.
Rosman G, Bronstein AM, Bronstein MM, et al., 2012, Articulated motion segmentation of point clouds by group-valued regularization, Pages: 77-84, ISSN: 1997-0463
Motion segmentation for articulated objects is an important topic of research. Yet such a segmentation should be as free as possible from underlying assumptions so as to fit general scenes and objects. In this paper we demonstrate an algorithm for articulated motion segmentation of 3D point clouds, free of any assumptions on the underlying model and yet firmly set in a well-defined variational framework. Results on scanned images show the generality of the proposed technique and its robustness to scanning artifacts and noise. © The Eurographics Association 2012.
Kovnatsky A, Bronstein MM, Bronstein AM, et al., 2012, Affine-invariant photometric heat kernel signatures, Pages: 39-46, ISSN: 1997-0463
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local shape descriptors. Our construction is based on the definition of a modified metric, which combines geometric and photometric information, and then the diffusion process on the shape manifold is simulated. Experimental results show that such data fusion is useful in coping with shape retrieval experiments, where pure geometric and pure photometric methods fail. Apart from retrieval task the proposed diffusion process may be employed in other applications. © The Eurographics Association 2012.
Glashoff K, Bronstein MM, 2012, Structure from motion using augmented Lagrangian robust factorization, Pages: 379-386
The classical Tomasi-Kanade method for Structure from Motion (SfM) based on measurement matrix factorization using SVD is known to perform poorly in the presence of occlusions and outliers. In this paper, we present an efficient approach by which we are able to deal with both problems at the same time. We use the Augmented Lagrangian alternative minimization method to solve iteratively a robust version of the matrix factorization approach. Experiments on synthetic and real data show the computational efficiency and good convergence of the method, which make it favorably compare to other approaches used in the SfM problem. © 2012 IEEE.
Raviv D, Bronstein AM, Bronstein MM, et al., 2012, Equi-affine invariant geometries of articulated objects, Pages: 177-190, ISSN: 0302-9743
We introduce an (equi-)affine invariant geometric structure by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to evaluate a new form of geodesic distances and to construct an invariant Laplacian from which local and global diffusion geometry is constructed. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis. © 2012 Springer-Verlag.
Kokkinos I, Bronstein MM, Litman R, et al., 2012, Intrinsic shape context descriptors for deformable shapes, Pages: 159-166, ISSN: 1063-6919
In this work, we present intrinsic shape context (ISC) descriptors for 3D shapes. We generalize to surfaces the polar sampling of the image domain used in shape contexts: for this purpose, we chart the surface by shooting geodesic outwards from the point being analyzed; angle is treated as tantamount to geodesic shooting direction, and radius as geodesic distance. To deal with orientation ambiguity, we exploit properties of the Fourier transform. Our charting method is intrinsic, i.e., invariant to isometric shape transformations. The resulting descriptor is a meta-descriptor that can be applied to any photometric or geometric property field defined on the shape, in particular, we can leverage recent developments in intrinsic shape analysis and construct ISC based on state-of-the-art dense shape descriptors such as heat kernel signatures. Our experiments demonstrate a notable improvement in shape matching on standard benchmarks. © 2012 IEEE.
Marras S, Bronstein MM, Hormann K, et al., 2012, Motion-based mesh segmentation using augmented silhouettes, Pages: 164-172, ISSN: 1524-0703
Motion-based segmentation, the problem of detecting rigid parts of an articulated three-dimensional shape, is an open challenge that has several applications in mesh animation, compression, and interpolation. We present a novel approach that uses the visual perception of the shape and its motion to distinguish the rigid from the deformable parts of the object. Using two-dimensional projections of the different shape poses with respect to a number of different view points, we derive a set of one-dimensional curves, which form a superset of the mesh silhouettes. Analysing these augmented silhouettes, we identify the vertices of the mesh that correspond to the deformable parts, and a subsequent clustering approach, which is based on the diffusion distance, yields a motion-based segmentation of the shape. © 2012 Elsevier Inc. All rights reserved.
Wang C, Bronstein MM, Bronstein AM, et al., 2012, Discrete minimum distortion correspondence problems for non-rigid shape matching, Pages: 580-591, ISSN: 0302-9743
Similarity and correspondence are two fundamental archetype problems in shape analysis, encountered in numerous application in computer vision and pattern recognition. Many methods for shape similarity and correspondence boil down to the minimum-distortion correspondence problem, in which two shapes are endowed with certain structure, and one attempts to find the matching with smallest structure distortion between them. Defining structures invariant to some class of shape transformations results in an invariant minimum-distortion correspondence or similarity. In this paper, we model shapes using local and global structures, formulate the invariant correspondence problem as binary graph labeling, and show how different choice of structure results in invariance under various classes of deformations. © 2012 Springer-Verlag.
Rosman G, Bronstein MM, Bronstein AM, et al., 2012, Group-valued regularization framework for motion segmentation of dynamic non-rigid shapes, Pages: 725-736, ISSN: 0302-9743
Understanding of articulated shape motion plays an important role in many applications in the mechanical engineering, movie industry, graphics, and vision communities. In this paper, we study motion-based segmentation of articulated 3D shapes into rigid parts. We pose the problem as finding a group-valued map between the shapes describing the motion, forcing it to favor piecewise rigid motions. Our computation follows the spirit of the Ambrosio-Tortorelli scheme for Mumford-Shah segmentation, with a diffusion component suited for the group nature of the motion model. Experimental results demonstrate the effectiveness of the proposed method in non-rigid motion segmentation. © 2012 Springer-Verlag.
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local heat kernel signature shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail. © 2012 Springer-Verlag.
Bruckstein AM, Romeny BTH, Bronstein AM, et al., 2012, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface, ISBN: 9783642247842
Hooda A, Bronstein MM, Bronstein AM, et al., 2012, Shape palindromes: Analysis of intrinsic symmetries in 2D articulated shapes, Pages: 665-676, ISSN: 0302-9743
Analysis of intrinsic symmetries of non-rigid and articulated shapes is an important problem in pattern recognition with numerous applications ranging from medicine to computational aesthetics. Considering articulated planar shapes as closed curves, we show how to represent their extrinsic and intrinsic symmetries as self-similarities of local descriptor sequences, which in turn have simple interpretation in the frequency domain. The problem of symmetry detection and analysis thus boils down to analysis of descriptor sequence patterns. For that purpose, we show two efficient computational methods: one based on Fourier analysis, and another on dynamic programming. © 2012 Springer-Verlag.
Pokrass J, Bronstein AM, Bronstein MM, 2012, A correspondence-less approach to matching of deformable shapes, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol: 6667 LNCS, Pages: 592-603, ISSN: 0302-9743
Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise correspondence between the two. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use diffusion geometric descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular meshes. Experiments demonstrating the success of the proposed method are presented. © 2012 Springer-Verlag.
Aflalo Y, Bronstein AM, Bronstein MM, et al., 2012, Deformable shape retrieval by learning diffusion kernels, Pages: 689-700, ISSN: 0302-9743
In classical signal processing, it is common to analyze and process signals in the frequency domain, by representing the signal in the Fourier basis, and filtering it by applying a transfer function on the Fourier coefficients. In some applications, it is possible to design an optimal filter. A classical example is the Wiener filter that achieves a minimum mean squared error estimate for signal denoising. Here, we adopt similar concepts to construct optimal diffusion geometric shape descriptors. The analogy of Fourier basis are the eigenfunctions of the Laplace-Beltrami operator, in which many geometric constructions such as diffusion metrics, can be represented. By designing a filter of the Laplace-Beltrami eigenvalues, it is theoretically possible to achieve invariance to different shape transformations, like scaling. Given a set of shape classes with different transformations, we learn the optimal filter by minimizing the ratio between knowingly similar and knowingly dissimilar diffusion distances it induces. The output of the proposed framework is a filter that is optimally tuned to handle transformations that characterize the training set. © 2012 Springer-Verlag.
Litman R, Bronstein AM, Bronstein MM, 2012, Stable volumetric features in deformable shapes, Pages: 569-576, ISSN: 0097-8493
Region feature detectors and descriptors have become a successful and popular alternative to point descriptors in image analysis due to their high robustness and repeatability, leading to a significant interest in the shape analysis community in finding analogous approaches in the 3D world. Recent works have successfully extended the maximally stable extremal region (MSER) detection algorithm to surfaces. In many applications, however, a volumetric shape model is more appropriate, and modeling shape deformations as approximate isometries of the volume of an object, rather than its boundary, better captures natural behavior of non-rigid deformations. In this paper, we formulate a diffusion-geometric framework for volumetric stable component detection and description in deformable shapes. An evaluation of our method on the SHREC11 feature detection benchmark and SCAPE human body scans shows its potential as a source of high-quality features. Examples demonstrating the drawbacks of surface stable components and the advantage of their volumetric counterparts are also presented. © 2012 Elsevier Ltd. All rights reserved.
Litany O, Bronstein AM, Bronstein MM, 2012, Putting the pieces together: Regularized multi-part shape matching, Pages: 1-11, ISSN: 0302-9743
Multi-part shape matching is an important class of problems, arising in many fields such as computational archaeology, biology, geometry processing, computer graphics and vision. In this paper, we address the problem of simultaneous matching and segmentation of multiple shapes. We assume to be given a reference shape and multiple parts partially matching the reference. Each of these parts can have additional clutter, have overlap with other parts, or there might be missing parts. We show experimental results of efficient and accurate assembly of fractured synthetic and real objects. © 2012 Springer-Verlag.
Strecha C, Bronstein AM, Bronstein MM, et al., 2012, LDAHash: Improved matching with smaller descriptors, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol: 34, Pages: 66-78, ISSN: 0162-8828
SIFT-like local feature descriptors are ubiquitously employed in computer vision applications such as content-based retrieval, video analysis, copy detection, object recognition, photo tourism, and 3D reconstruction. Feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations, in particular, affine and intensity scale transformations. However, real transformations that an image can undergo can only be approximately modeled in this way, and thus most descriptors are only approximately invariant in practice. Second, descriptors are usually high dimensional (e.g., SIFT is represented as a 128-dimensional vector). In large-scale retrieval and matching problems, this can pose challenges in storing and retrieving descriptor data. We map the descriptor vectors into the Hamming space in which the Hamming metric is used to compare the resulting representations. This way, we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples. We show extensive experimental validation, demonstrating the advantage of the proposed approach. © 2012 IEEE.
Rosman G, Bronstein AM, Bronstein MM, et al., 2012, Group-valued regularization for analysis of articulated motion, Pages: 52-62, ISSN: 0302-9743
We present a novel method for estimation of articulated motion in depth scans. The method is based on a framework for regularization of vector- and matrix- valued functions on parametric surfaces. We extend augmented-Lagrangian total variation regularization to smooth rigid motion cues on the scanned 3D surface obtained from a range scanner. We demonstrate the resulting smoothed motion maps to be a powerful tool in articulated scene understanding, providing a basis for rigid parts segmentation, with little prior assumptions on the scene, despite the noisy depth measurements that often appear in commodity depth scanners. © 2012 Springer-Verlag.
Kovnatsky A, Bronstein MM, Bronstein AM, 2012, Stable spectral mesh filtering, Pages: 83-91, ISSN: 0302-9743
The rapid development of 3D acquisition technology has brought with itself the need to perform standard signal processing operations such as filters on 3D data. It has been shown that the eigenfunctions of the Laplace-Beltrami operator (manifold harmonics) of a surface play the role of the Fourier basis in the Euclidean space; it is thus possible to formulate signal analysis and synthesis in the manifold harmonics basis. In particular, geometry filtering can be carried out in the manifold harmonics domain by decomposing the embedding coordinates of the shape in this basis. However, since the basis functions depend on the shape itself, such filtering is valid only for weak (near all-pass) filters, and produces severe artifacts otherwise. In this paper, we analyze this problem and propose the fractional filtering approach, wherein we apply iteratively weak fractional powers of the filter, followed by the update of the basis functions. Experimental results show that such a process produces more plausible and meaningful results. © 2012 Springer-Verlag.
Michel F, Bronstein M, Bronstein A, et al., 2011, Boosted metric learning for 3D multi-modal deformable registration, Pages: 1209-1214, ISSN: 1945-7928
Defining a suitable metric is one of the biggest challenges in deformable image fusion from different modalities. In this paper, we propose a novel approach for multi-modal metric learning in the deformable registration framework that consists of embedding data from both modalities into a common metric space whose metric is used to parametrize the similarity. Specifically, we use image representation in the Fourier/Gabor space which introduces invariance to the local pose parameters, and the Hamming metric as the target embedding space, which allows constructing the embedding using boosted learning algorithms. The resulting metric is incorporated into a discrete optimization framework. Very promising results demonstrate the potential of the proposed method. © 2011 IEEE.
Detection and description of affine-invariant features is a cornerstone component in numerous computer vision applications. In this note, we analyze the notion of maximally stable extremal regions (MSERs) through the prism of the curvature scale space, and conclude that in its original definition, MSER prefers regular (round) regions. Arguing that interesting features in natural images usually have irregular shapes, we propose alternative definitions of MSER which are free of this bias, yet maintain their invariance properties. © 2011 IEEE.
Bronstein MM, 2011, Lazy sliding window implementation of the bilateral filter on parallel architectures., IEEE Trans Image Process, Vol: 20, Pages: 1751-1756
Bilateral filter is one of the state-of-the-art methods for noise reduction in images. The plausible visual result the filter produces makes it a common choice for image and video processing applications, yet, its high computational complexity makes a real-time implementation a challenging task. Presented here is a parallel version of the bilateral filter using a lazy sliding window, suitable for SIMD-type architectures.
Bronstein MM, Bronstein AM, 2011, Shape recognition with spectral distances, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol: 33, Pages: 1065-1071, ISSN: 0162-8828
Recent works have shown the use of diffusion geometry for various pattern recognition applications, including nonrigid shape analysis. In this paper, we introduce spectral shape distance as a general framework for distribution-based shape similarity and show that two recent methods for shape similarity due to Rustamov and Mahmoudi and Sapiro are particular cases thereof. © 2006 IEEE.
Boyer E, Bronstein AM, Bronstein MM, et al., 2011, SHREC 2011: Robust feature detection and description benchmark, Eurographics Workshop on 3D Object Retrieval, EG 3DOR, Pages: 71-78, ISSN: 1997-0463
© The Eurographics Association 2011. Feature-based approaches have recently become very popular in computer vision and image analysis applications, and are becoming a promising direction in shape retrieval. SHREC'11 robust feature detection and description benchmark simulates the feature detection and description stages of feature-based shape retrieval algorithms. The benchmark tests the performance of shape feature detectors and descriptors under a wide variety of transformations. The benchmark allows evaluating how algorithms cope with certain classes of transformations and strength of the transformations that can be dealt with. The present paper is a report of the SHREC'11 robust feature detection and description benchmark results.
Raviv D, Bronstein MM, Bronstein AM, et al., 2011, Affine-invariant diffusion geometry for the analysis of deformable 3D shapes, Pages: 2361-2367, ISSN: 1063-6919
We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant Laplacian from which local and global geometric structures are extracted. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis. © 2011 IEEE.
Litman R, Bronstein AM, Bronstein MM, 2011, Diffusion-geometric maximally stable component detection in deformable shapes, Computers and Graphics (Pergamon), Vol: 35, Pages: 549-560, ISSN: 0097-8493
Maximally stable component detection is a very popular method for feature analysis in images, mainly due to its low computation cost and high repeatability. With the recent advance of feature-based methods in geometric shape analysis, there is significant interest in finding analogous approaches in the 3D world. In this paper, we formulate a diffusion-geometric framework for stable component detection in non-rigid 3D shapes, which can be used for geometric feature detection and description. A quantitative evaluation of our method on the SHREC'10 feature detection benchmark shows its potential as a source of high-quality features. © 2011 Elsevier Ltd. All rights reserved.
Bronstein AM, Bronstein MM, Guibas LJ, et al., 2011, Shape google: Geometric words and expressions for invariant shape retrieval, ACM Transactions on Graphics, Vol: 30, ISSN: 0730-0301
The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in object recognition and image retrieval applications. These methods allow representing images as collections of "visual words" and treat them using text search approaches following the "bag of features" paradigm. In this article, we explore analogous approaches in the 3D world applied to the problem of nonrigid shape retrieval in large databases. Using multiscale diffusion heat kernels as "geometric words," we construct compact and informative shape descriptors by means of the "bag of features" approach. We also show that considering pairs of "geometric words" ("geometric expressions") allows creating spatially sensitive bags of features with better discriminative power. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark. © 2011 ACM.
Raviv D, Bronstein AM, Bronstein MM, et al., 2011, Affine-invariant geodesic geometry of deformable 3D shapes, Pages: 692-697, ISSN: 0097-8493
Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R3 in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis. © 2011 Elsevier Ltd. All rights reserved.
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