190 results found
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.
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.
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.
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.
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.
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.
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.
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.
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.
Invariant shape descriptors are instrumental in numerous shape analysis tasks including deformable shape comparison, registration, classification, and retrieval. Most existing constructions model a 3D shape as a two-dimensional surface describing the shape boundary, typically represented as a triangular mesh or a point cloud. Using intrinsic properties of the surface, invariant descriptors can be designed. One such example is the recently introduced heat kernel signature, based on the Laplace-Beltrami operator of the surface. In many applications, however, a volumetric shape model is more natural and convenient. Moreover, 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 many cases. Here, we extend the idea of heat kernel signature to robust isometry-invariant volumetric descriptors, and show their utility in shape retrieval. The proposed approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.
The 3D Shape Retrieval Contest 2010 (SHREC'10) robust shape retrieval benchmark simulates a retrieval scenario, in which the queries include multiple modifications and transformations of the same shape. The benchmark allows evaluating how algorithms cope with certain classes of transformations and what is the strength of the transformations that can be dealt with. The present paper is a report of the SHREC'10 robust shape retrieval benchmark results. ©The Eurographics Association 2010.
Feature-based approaches have recently become very popular in computer vision and image analysis applications, and are becoming a promising direction in shape retrieval. The SHREC'10 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 3D Shape Retrieval Contest 2010 (SHREC'10) feature detection and description benchmark results. ©The Eurographics Association 2010.
The SHREC'10 correspondence finding benchmark simulates a one-to-one shape matching scenario, in which one of the shapes undergoes multiple modifications and transformations. The benchmark allows evaluating how correspondence algorithms cope with certain classes of transformations and what is the strength of the transformations that can be dealt with. The present paper is a report of the 3D Shape Retrieval Contest 2010 (SHREC'10) correspondence finding benchmark results. ©The Eurographics Association 2010.
Bronstein AM, Bronstein MM, Kimmel R, et al., 2010, A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching, INTERNATIONAL JOURNAL OF COMPUTER VISION, Vol: 89, Pages: 266-286, ISSN: 0920-5691
Bronstein MM, Kokkinos I, 2010, Scale-invariant heat kernel signatures for non-rigid shape recognition, Pages: 1704-1711, ISSN: 1063-6919
One of the biggest challenges in non-rigid shape retrieval and comparison is the design of a shape descriptor that would maintain invariance under a wide class of transformations the shape can undergo. Recently, heat kernel signature was introduced as an intrinsic local shape descriptor based on diffusion scale-space analysis. In this paper, we develop a scale-invariant version of the heat kernel descriptor. Our construction is based on a logarithmically sampled scale-space in which shape scaling corresponds, up to a multiplicative constant, to a translation. This translation is undone using the magnitude of the Fourier transform. The proposed scale-invariant local descriptors can be used in the bag-of-features framework for shape retrieval in the presence of transformations such as isometric deformations, missing data, topological noise, and global and local scaling. We get significant performance improvement over state-of-the-art algorithms on recently established non-rigid shape retrieval benchmarks. ©2010 IEEE.
Rosman G, Bronstein MM, Bronstein AM, et al., 2010, Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding, INTERNATIONAL JOURNAL OF COMPUTER VISION, Vol: 89, Pages: 56-68, ISSN: 0920-5691
Bronstein AM, Bronstein MM, 2010, Spatially-sensitive affine-invariant image descriptors, Pages: 197-208, ISSN: 0302-9743
Invariant image descriptors play an important role in many computer vision and pattern recognition problems such as image search and retrieval. A dominant paradigm today is that of "bags of features", a representation of images as distributions of primitive visual elements. The main disadvantage of this approach is the loss of spatial relations between features, which often carry important information about the image. In this paper, we show how to construct spatially-sensitive image descriptors in which both the features and their relation are affine-invariant. Our construction is based on a vocabulary of pairs of features coupled with a vocabulary of invariant spatial relations between the features. Experimental results show the advantage of our approach in image retrieval applications. © 2010 Springer-Verlag.
Bronstein MM, Bronstein AM, Michel F, et al., 2010, Data fusion through cross-modality metric learning using similarity-sensitive hashing, Pages: 3594-3601, ISSN: 1063-6919
Visual understanding is often based on measuring similarity between observations. Learning similarities specific to a certain perception task from a set of examples has been shown advantageous in various computer vision and pattern recognition problems. In many important applications, the data that one needs to compare come from different representations or modalities, and the similarity between such data operates on objects that may have different and often incommensurable structure and dimensionality. In this paper, we propose a framework for supervised similarity learning based on embedding the input data from two arbitrary spaces into the Hamming space. The mapping is expressed as a binary classification problem with positive and negative examples, and can be efficiently learned using boosting algorithms. The utility and efficiency of such a generic approach is demonstrated on several challenging applications including cross-representation shape retrieval and alignment of multi-modal medical images. ©2010 IEEE.
Mitra NJ, Bronstein A, Bronstein M, 2010, Intrinsic regularity detection in 3D geometry, Pages: 398-410, ISSN: 0302-9743
Automatic detection of symmetries, regularity, and repetitive structures in 3D geometry is a fundamental problem in shape analysis and pattern recognition with applications in computer vision and graphics. Especially challenging is to detect intrinsic regularity, where the repetitions are on an intrinsic grid, without any apparent Euclidean pattern to describe the shape, but rising out of (near) isometric deformation of the underlying surface. In this paper, we employ multidimensional scaling to reduce the problem of intrinsic structure detection to a simpler problem of 2D grid detection. Potential 2D grids are then identified using an autocorrelation analysis, refined using local fitting, validated, and finally projected back to the spatial domain. We test the detection algorithm on a variety of scanned plaster models in presence of imperfections like missing data, noise and outliers. We also present a range of applications including scan completion, shape editing, super-resolution, and structural correspondence. © 2010 Springer-Verlag.
Bronstein AM, Bronstein MM, Carmon Y, et al., 2009, Partial similarity of shapes using a statistical significance measure, Pages: 105-114
Partial matching of geometric structures is important in computer vision, pattern recognition and shape analysis applications. The problem consists of matching similar parts of shapes that may be dissimilar as a whole. Recently, it was proposed to consider partial similarity as a multi-criterion optimization problem trying to simultaneously maximize the similarity and the significance of the matching parts. A major challenge in that framework is providing a quantitative measure of the significance of a part of an object. Here, we define the significance of a part of a shape by its discriminative power with respect do a given shape database - that is, the uniqueness of the part. We define a point-wise significance density using a statistical weighting approach similar to the term frequency-inverse document frequency (tf-idf) weighting employed in search engines. The significance measure of a given part is obtained by integrating over this density. Numerical experiments show that the proposed approach produces intuitive significant parts, and demonstrate an improvement in the performance of partial matching between shapes. © 2009 Information Processing Society of Japan.
We introduce a design of a coded light-based 3D color video camera optimized for build up cost as well as accuracy in depth reconstruction and acquisition speed. The components of the system include a monochromatic camera and an off-the-shelf LED projector synchronized by a miniature circuit. The projected patterns are captured and processed at a rate of 200 fps and allow for real-time reconstruction of both depth and color at video rates. The reconstruction and display are performed at around 30 depth profiles and color texture per second using a graphics processing unit (GPU). ©2009 IEEE.
Ovsjanikov M, Bronstein AM, Bronstein MM, et al., 2009, Shape Google: A computer vision approach to isometry invariant shape retrieval, Pages: 320-327
Feature-based methods have recently gained popularity in computer vision and pattern recognition communities, in applications such as object recognition and image retrieval. In this paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid shape search and retrieval in large databases. ©2009 IEEE.
Devir YS, Rosman G, Bronstein AM, et al., 2009, On reconstruction of non-rigid shapes with intrinsic regularization, Pages: 272-279
Shape-from-X is a generic type of inverse problems in computer vision, in which a shape is reconstructed from some measurements. A specially challenging setting of this problem is the case in which the reconstructed shapes are non-rigid. In this paper, we propose a framework for intrinsic regularization of such problems. The assumption is that we have the geometric structure of a shape which is intrinsically (up to bending) similar to the one we would like to reconstruct. For that goal, we formulate a variation with respect to vertex coordinates of a triangulated mesh approximating the continuous shape. The numerical core of the proposed method is based on differentiating the fast marching update step for geodesic distance computation. ©2009 IEEE.
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