@book{18340, abstract = {This book constitutes the thoroughly refereed post-conference proceedings of the Third International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2011, held in Ein-Gedi, Israel in May/June 2011. The 24 revised full papers presented together with 44 poster papers were carefully reviewed and selected from 78 submissions. The papers are organized in topical sections on denoising and enhancement, segmentation, image representation and invariants, shape analysis, and optical flow. }, editor = {Bruckstein, Alfred M. and ter Haar Romeny, Bart M. and Bronstein, Alexander and Bronstein, Michael M.}, isbn = {9783642247842}, issn = {1611-3349}, pages = {XIV, 798}, publisher = {Springer Nature}, title = {{Scale Space and Variational Methods in Computer Vision}}, doi = {10.1007/978-3-642-24785-9}, volume = {6667}, year = {2012}, } @inproceedings{18341, abstract = {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.}, author = {Wang, Chaohui and Bronstein, Michael M. and Bronstein, Alexander and Paragios, Nikos}, booktitle = {3rd International Conference on Scale Space and Variational Methods in Computer Vision}, isbn = {9783642247842}, issn = {1611-3349}, location = {Ein-Gedi, Israel}, pages = {580 -- 591}, publisher = {Springer Nature}, title = {{Discrete minimum distortion correspondence problems for non-rigid shape matching}}, doi = {10.1007/978-3-642-24785-9_49}, volume = {6667}, year = {2012}, } @inproceedings{18342, abstract = {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.}, author = {Pokrass, Jonathan and Bronstein, Alexander and Bronstein, Michael M.}, booktitle = {3rd International Conference on Scale Space and Variational Methods in Computer Vision}, isbn = {9783642247842}, issn = {1611-3349}, location = {Ein-Gedi, Israel}, pages = {592 -- 603}, publisher = {Springer Nature}, title = {{A correspondence-less approach to matching of deformable shapes}}, doi = {10.1007/978-3-642-24785-9_50}, volume = {6667}, year = {2012}, } @inproceedings{18343, abstract = {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.}, author = {Kovnatsky, Artiom and Bronstein, Michael M. and Bronstein, Alexander and Kimmel, Ron}, booktitle = {3rd International Conference on Scale Space and Variational Methods in Computer Vision}, isbn = {9783642247842}, issn = {1611-3349}, location = {Ein-Gedi, Israel}, pages = {616--627}, publisher = {Springer Nature}, title = {{Photometric heat kernel signatures}}, doi = {10.1007/978-3-642-24785-9_52}, volume = {6667}, year = {2012}, } @inproceedings{18344, abstract = {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.}, author = {Hooda, Amit and Bronstein, Michael M. and Bronstein, Alexander and Horaud, Radu P.}, booktitle = {Scale Space and Variational Methods in Computer Vision}, isbn = {9783642247842}, issn = {1611-3349}, location = {Ein-Gedi, Israel}, pages = {665–676}, publisher = {Springer Nature}, title = {{Shape palindromes: Analysis of intrinsic symmetries in 2D articulated shapes}}, doi = {10.1007/978-3-642-24785-9_56}, volume = {6667}, year = {2012}, } @inproceedings{18345, abstract = {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.}, author = {Aflalo, Yonathan and Bronstein, Alexander and Bronstein, Michael M. and Kimmel, Ron}, booktitle = {3rd International Conference on Scale Space and Variational Methods in Computer Vision}, isbn = {9783642247842}, issn = {1611-3349}, location = {Ein-Gedi, Israel}, pages = {689--700}, publisher = {Springer Nature}, title = {{Deformable shape retrieval by learning diffusion kernels}}, doi = {10.1007/978-3-642-24785-9_58}, volume = {6667}, year = {2012}, } @inproceedings{18346, abstract = {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.}, author = {Rosman, Guy and Bronstein, Michael M. and Bronstein, Alexander and Wolf, Alon and Kimmel, Ron}, booktitle = {3rd International Conference on Scale Space and Variational Methods in Computer Vision}, isbn = {9783642247842}, issn = {1611-3349}, location = {Ein-Gedi, Israel}, pages = {725--736}, publisher = {Springer Nature}, title = {{Group-valued regularization framework for motion segmentation of dynamic non-rigid shapes}}, doi = {10.1007/978-3-642-24785-9_61}, volume = {6667}, year = {2012}, }