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R. Litman, A. M. Bronstein, A. M. Bronstein,
"Stable volumetric features in deformable shapes", Computers and Graphics (CAG), to appear. Abstract: 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 SHREC’11 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. |
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A. Kovnatski, D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Geometric and photometric data fusion in non-rigid shape analysis", Numerical Mathematics: Theory, Methods and Applications (NM-TMA), Special issue on Scale Space and Variation Methods, submitted. Abstract: In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global 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. |
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J. Pokrass, A. M. Bronstein, M. M. Bronstein,
"Partial shape matching without point-wise correspondence", Numerical Mathematics: Theory, Methods and Applications (NM-TMA), Special issue on Scale Space and Variation Methods, submitted. Abstract: Partial similarity of shapes in 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 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 and point clouds, and present experiments demonstrating the success of the proposed method. |
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A. M. Bronstein,
"Spectral descriptors for deformable shapes", IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), submitted. Abstract: Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In the recent years, significant attention has been devoted to descriptors obtained from the spectral decomposition of the Laplace-Beltrami operator associated with the shape. Notable examples in this family are the heat kernel signature (HKS) and the wave kernel signature (WKS). Laplacian-based descriptors achieve state-of-the-art performance in numerous shape analysis tasks; they are computationally efficient, isometry-invariant by construction, and can gracefully cope with a variety of transformations. In this paper, we formulate a generic family of parametric spectral descriptors. We argue that in order to be optimal for a specific task, the descriptor should take into account the statistics of the corpus of shapes to which it is applied (the "signal") and those of the class of transformations to which it is made insensitive (the "noise"). While such statistics are hard to model axiomatically, they can be learned from examples. Following the spirit of the Wiener filter in signal processing, we show a learning scheme for the construction of optimal spectral descriptors and relate it to Mahalanobis metric learning. The superiority of the proposed approach is demonstrated on the SHREC'10 benchmark. |
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D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen,
"Affine-invariant geodesic geometry of deformable 3D shapes", Computers and Graphics (CAG), Vol. 35/3, 2011. Abstract: 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. |
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R. Litman, A. M. Bronstein, A. M. Bronstein,
"Diffusion-geometric maximally stable component detection in deformable shapes", Computers and Graphics (CAG), Vol. 35/3, 2011. Abstract: 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. |
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C. Strecha, A. M. Bronstein, M. M. Bronstein, P. Fua,
"LDAHash: improved matching with smaller descriptors", IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI), to appear. Abstract: SIFT-like local feature descriptors are ubiquitously employed in such computer vision applications as content-based retrieval, video analysis, copy detection, object recognition, photo-tourism, and 3D reconstruction from multiple views. 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. Secondly, 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 propose mapping 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. Resources: Code | Data |
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R. Kimmel, C. Zhang, A. M. Bronstein, M. M. Bronstein,
"Are MSER features really interesting?", IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), Vol. 33/11, pp. 2316-2320, 2011. Abstract: 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 (MSER) 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. |
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A. M. Bronstein, M. M. Bronstein, M. Ovsjanikov, L. J. Guibas,
"Shape Google: geometric words and expressions for invariant shape retrieval", ACM Trans. Graphics (TOG), Vol. 30/1, pp. 1-20, January 2011. Abstract: 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 paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid 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 discriminativity. 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. |
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M. M. Bronstein, A. M. Bronstein,
"Shape recognition with spectral distances", IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), to appear. Abstract: Recent works have shown the use of diffusion geometry for various pattern recognition applications, including non-rigid 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 & Sapiro are particular cases thereof. |
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G. Rosman, M. M. Bronstein, A. M. Bronstein, R. Kimmel,
"Nonlinear dimensionality reduction by topologically
constrained isometric embedding", Intl. Journal of Computer Vision (IJCV), Vol. 89/1, pp. 56-68, August 2010. Abstract: Many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space. The embedding process usually relies on distances between neighboring features, mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non-convexity. Distortions resulting from using long geodesics indiscriminately lead to a known limitation of the Isomap algorithm when used to map nonconvex manifolds. Presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries. The resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold, thus avoiding an inherent limitation of the Isomap algorithm. Since the proposed algorithm matches non-local structures, it is robust to strong noise. We show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques, both global and local in nature. |
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D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Full and partial symmetries of non-rigid shapes", Intl. Journal of Computer Vision (IJCV), Vol. 89/1, pp. 18-39, August 2010. Abstract: Symmetry and self-similarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones: extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we present a generalization of symmetries for non-rigid shapes and a numerical framework for their analysis, addressing the problems of full and partial exact and approximate symmetry detection and classification. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel, M. Mahmoudi, G. Sapiro,
"A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching", Intl. Journal of Computer Vision (IJCV), Vol. 89/2-3, pp. 266-286, September 2010. Abstract: In this paper, the problem of non-rigid shape recognition is viewed from the perspective of metric geometry, and the applicability of diffusion distances within the Gromov-Hausdorff framework is explored. While the commonly used geodesic distance exploits the shortest path between points on the surface, the diffusion distance averages all paths connecting between the points. The diffusion distance provides an intrinsic distance measure which is robust, in particular to topological changes. Such changes may be a result of natural non-rigid deformations, as well as acquisition noise, in the form of holes or missing data, and representation noise due to inaccurate mesh construction. The presentation of the proposed framework is complemented with numerous examples demonstrating that in addition to the relatively low complexity involved in the computation of the diffusion distances between surface points, its recognition and matching performances favorably compare to the classical geodesic distances in the presence of topological changes between the non-rigid shapes. |
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A. M. Bronstein, M. M. Bronstein, Y. Carmon, R. Kimmel,
"Partial similarity of shapes using a statistical
significance measure", IPSJ Trans. Computer Vision and Application, Vol. 1, pp. 105-114, 2009. Abstract: 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 (tfidf) 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. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Topology-invariant similarity of nonrigid shapes", Intl. Journal of Computer Vision (IJCV), Vol. 81/3, pp. 281-301, March 2009. Abstract: This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their advantages and disadvantages: extrinsic similarity is sensitive to nonrigid deformations, while intrinsic similarity is sensitive to topological noise. In this paper, we approach the problem from the perspective of metric geometry. We show that by unifying the extrinsic and intrinsic similarity criteria, it is possible to obtain a stronger topology-invariant similarity, suitable for comparing deformed shapes with different topology. We construct this new joint criterion as a tradeoff between the extrinsic and intrinsic similarity and use it as a set-valued distance. Numerical results demonstrate the efficiency of our approach in cases where using either extrinsic or intrinsic criteria alone would fail. |
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A. M. Bronstein, M. M. Bronstein, A. M. Bruckstein, R. Kimmel,
"Partial similarity of objects, or how to compare a centaur to a horse", Intl. Journal of Computer Vision (IJCV), Vol. 84/2, pp. 163-183, 2009. Abstract: Similarity is one of the most important abstract concepts in human perception of the world. In computer vision, numerous applications deal with comparing objects observed in a scene with some a priori known patterns. Often, it happens that while two objects are not similar, they have large similar parts, that is, they are partially similar. Here, we present a novel approach to quantify partial similarity using the notion of Pareto optimality. We exemplify our approach on the problems of recognizing non-rigid geometric objects, images, and analyzing text sequences. Resources: 3D non-rigid shapes dataset |
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O. Weber, Y. Devir, A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Parallel algorithms for approximation of distance maps on parametric surfaces", ACM Transactions on Graphics, Vol. 27/4, October 2008. Abstract: We present an efficient O(n) numerical algorithm for first-order approximation of geodesic distances on geometry images, where n is the number of points on the surface. The structure of our algorithm allows efficient implementation on parallel architectures. Two implementations on a SIMD processor and on a GPU are discussed. Numerical results demonstrate up to four orders of magnitude improvement in execution time compared to the state-of-the-art algorithms. Resources: SSE2 code | GPU code (by Ofir Weber) | SIGGRAPH'08 trailer |
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A. M. Bronstein, M. M. Bronstein, A. M. Bruckstein, R. Kimmel,
"Analysis of two-dimensional non-rigid shapes", Intl. Journal of Computer Vision (IJCV), Vol. 78/1, pp. 67-88, June 2008. Abstract: Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence.We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper. Resources: 2D mythological creatures dataset |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Weighted distance maps computation on parametric three-dimensional manifolds", Journal of Computational Physics, Vol. 255/1, pp. 771-784, July 2007. Abstract: We propose an effcient computational solver for the eikonal equations on parametric three-dimensional manifolds. Our approach is based on the fast marching method for solving the eikonal equation in O(n log n) steps by numerically simulating wavefront propagation. The obtuse angle splitting problem is reformulated as a set of small integer linear programs, that can be solved in O(n). Numerical simulations demonstrate the accuracy of the proposed algorithm. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Calculus of non-rigid surfaces for geometry and texture manipulation", IEEE Trans. Visualization and Computer Graphics, Vol 13/5, pp. 902-913, September-October 2007. Abstract: We present a geometric framework for automatically finding intrinsic correspondence between three-dimensional nonrigid objects. We model object deformation as near isometries and find the correspondence as the minimum-distortion mapping. A generalization of multidimensional scaling is used as the numerical core of our approach. As a result, we obtain the possibility to manipulate the extrinsic geometry and the texture of the objects as vectors in a linear space. We demonstrate our method on the problems of expression-invariant texture mapping onto an animated three-dimensional face, expression exaggeration, morphing between faces, and virtual body painting. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Expression-invariant representation of faces", IEEE Trans. Image Processing, Vol. 16/1, pp. 188-197, January 2007. Abstract: Addressed here is the problem of constructing and analyzing expression-invariant representations of human faces. We demonstrate and justify experimentally a simple geometric model that allows to describe facial expressions as isometric deformations of the facial surface. The main step in the construction of expression-invariant representation of a face involves embedding of the facial intrinsic geometric structure into some convenient low-dimensional space. We study the influence of the embedding space geometry and dimensionality choice on the representation accuracy and argue that compared to its Euclidean counterpart, spherical embedding leads to notably smaller metric distortions. We experimentally support our claim showing that a smaller embedding error leads to better recognition. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Efficient computation of isometry-invariant distances between surfaces", SIAM J. Scientific Computing, Vol. 28/5, pp. 1812-1836, 2006. Abstract: We present an efficient computational framework for isometry-invariant comparison of smooth surfaces. We formulate the Gromov-Hausdorff distance as a multidimensional scaling (MDS)-like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples. For isometry-invariant comparison of surfaces in the case of partially missing data, we present the partial embedding distance, which is computed using a similar scheme. The main idea is finding a minimum-distortion mapping from one surface to another, while considering only relevant geodesic distances. We discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency. |
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M. M. Bronstein, A. M. Bronstein, R. Kimmel, I. Yavneh, "Multigrid multidimensional scaling",
Numerical Linear Algebra with Applications (NLAA), Special issue on multigrid methods, Vol. 13/2-3, pp. 149-171, March-April 2006. Abstract: Multidimensional scaling (MDS) is a generic name for a family of algorithms that construct a configuration of points in a target metric space from information about inter-point distances measured in some other metric space. Large-scale MDS problems often occur in data analysis, representation and visualization. Solving such problems efficiently is of key importance in many applications. In this paper we present a multigrid framework for MDS problems. We demonstrate the performance of our algorithm on dimensionality reduction and isometric embedding problems, two classical problems requiring efficient large-scale MDS. Simulation results show that the proposed approach significantly outperforms conventional MDS algorithms. Resources: Multigrid MDS code (MATLAB) | Tutorial (MATLAB) |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching", Proc. National Academy of Sciences (PNAS), Vol. 103/5, pp. 1168-1172, January 2006. Abstract: An efficient algorithm for isometry-invariant matching of surfaces is presented. The key idea is computing the minimum-distortion mapping between two surfaces. For this purpose, we introduce the generalized multidimensional scaling, a computationally efficient continuous optimization algorithm for finding the least distortion embedding of one surface into another. The generalized multidimensional scaling algorithm allows for both full and partial surface matching. As an example, it is applied to the problem of expression- invariant three-dimensional face recognition. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Three-dimensional face recognition",
Intl. Journal of Computer Vision (IJCV), Vol. 64/1, pp. 5-30, August 2005. Abstract: An expression-invariant 3D face recognition approach is presented. Our basic assumption is that facial expressions can be modelled as isometries of the facial surface. This allows to construct expression-invariant representations of faces using the canonical forms approach. The result is an efficient and accurate face recognition algorithm, robust to facial expressions that can distinguish between identical twins (the first two authors). We demonstrate a prototype system based on the proposed algorithm and compare its performance to classical face recognition methods. The numerical methods employed by our approach do not require the facial surface explicitly. The surface gradients field, or the surface metric, are sufficient for constructing the expression-invariant representation of any given face. It allows us to perform the 3D face recognition task while avoiding the surface reconstruction stage. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Sparse ICA for blind separation of transmitted and reflected images",
Intl. Journal of Imaging Science and Technology (IJIST), Vol. 15/1, pp. 84-91, 2005. Abstract: We address the problem of recovering a scene recorded through a semireflecting medium (i.e. planar lens), with a virtual reflected image being superimposed on the image of the scene transmitted through the semirefelecting lens. Recent studies propose imaging through a linear polarizer at several orientations to estimate the reflected and the transmitted components in the scene. In this study we extend the sparse ICA (SPICA) technique and apply it to the problem of separating the image of the scene without having any a priori knowledge about its structure or statistics. Recent novel advances in the SPICA approach are discussed. Simulation and experimental results demonstrate the efficacy of the proposed methods. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky,
"Quasi maximum likelihood blind deconvolution: super- an sub-Gaussianity versus consistency",
IEEE Trans. Signal Processing, Vol. 53/7, pp. 2576-2579, July 2005. Abstract: In this note we consider the problem of MIMO quasi maximum likelihood (QML) blind deconvolution. We examine two classes of estimators, which are commonly believed to be suitable for super- and sub-Gaussian sources. We state the consistency conditions and demonstrate a distribution, for which the studied estimators are unsuitable, in the sense that they are asymptotically unstable. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky,
"Relative optimization for blind deconvolution", IEEE Trans. Signal Processing, Vol. 53/6, pp. 2018-2026, June 2005. Abstract: We propose a relative optimization framework for quasi maximum likelihood (QML) blind deconvolution and the relative Newton method as its particular instance. Special Hessian structure allows fast Newton system construction and solution, resulting in a fast-convergent algorithm with iteration complexity comparable to that of gradient methods. We also propose the use of rational IIR restoration kernels, which constitute a richer family of filters than the traditionally used FIR kernels. We discuss different choices of non-linear functions suitable for deconvolution of super- and sub-Gaussian sources, and formulate the conditions, under which the QML estimation is stable. Simulation results demonstrate the efficiency of the proposed methods. |
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M. M. Bronstein, A. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Blind deconvolution of images using optimal sparse representations",
IEEE Trans. Image Processing, Vol. 14/6, pp. 726-736, June 2005. Abstract: We propose a relative optimization framework for quasi maximum likelihood (QML) blind deconvolution and the relative Newton method as its particular instance. Special Hessian structure allows fast Newton system construction and solution, resulting in a fast-convergent algorithm with iteration complexity comparable to that of gradient methods. We also propose the use of rational IIR restoration kernels, which constitute a richer family of filters than the traditionally used FIR kernels. We discuss different choices of non-linear functions suitable for deconvolution of super- and sub-Gaussian sources, and formulate the conditions, under which the QML estimation is stable. Simulation results demonstrate the efficiency of the proposed methods. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky,
"Blind source separation using block-coordinate relative Newton method",
Signal Processing, Vol. 84/8, pp. 1447-1459, August 2004. Abstract: Presented here is a generalization of the relative Newton method, recently proposed for quasi maximum likelihood blind source separation. Special structure of the Hessian matrix allows performing block-coordinate Newton descent, which significantly reduces the algorithm computational complexity and boosts its performance. Simulations based on artificial and real data showed that the separation quality using the proposed algorithm is superior compared to other accepted blind source separation methods. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Optimal nonlinear line-of-flight estimation in positron emission tomography",
IEEE Trans. Nuclear Science, Vol. 50/3, pp. 421-426, June 2003. Abstract: We consider detection of high-energy photons in PET using thick scintillation crystals. Parallax effect and multiple Compton interactions such crystals significantly reduce the accuracy of conventional detection methods. In order to estimate the photon line of flight based on photomultiplier responses, we use asymptotically optimal nonlinear techniques, implemented by feedforward and radial basis function (RBF) neural networks. Incorporation of information about angles of incidence of photons, significantly improves accuracy of estimation. The proposed estimators are fast enough to perform detection, using conventional computers. Monte-Carlo simulation results show that our approach significantly outperforms the conventional Anger algorithm. |
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M. M. Bronstein, A. M. Bronstein, M. Zibulevsky, H. Azhari,
"Reconstruction in ultrasound diffraction tomography using non-uniform FFT",
IEEE Trans. Medical Imaging, Vol. 21/11, pp. 1395-1401, November 2002. Abstract: We show an iterative reconstruction framework for diffraction ultrasound tomography. The use of broad-band illumination allows significant reduction of the number of projections compared to straight ray tomography. The proposed algorithm makes use of forward nonuniform fast Fourier transform (NUFFT) for iterative Fourier inversion. Incorporation of total variation regularization allows the reduction of noise and Gibbs phenomena while preserving the edges. The complexity of the NUFFT-based reconstruction is comparable to the frequency domain interpolation (gridding) algorithm, whereas the reconstruction accuracy (in sense of the L2 and the Linf norm) is better. |
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