@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}, } @inproceedings{18347, abstract = {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.}, author = {Litany, Or and Bronstein, Alexander and Bronstein, Michael M.}, booktitle = {Computer Vision, ECCV 2012 - Workshops and Demonstrations}, isbn = {9783642338625}, issn = {1611-3349}, location = {Florence, Italy}, number = {Part 1}, pages = {1--11}, publisher = {Springer Nature}, title = {{Putting the pieces together: Regularized multi-part shape matching}}, doi = {10.1007/978-3-642-33863-2_1}, volume = {7583}, year = {2012}, } @inproceedings{18348, abstract = {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.}, author = {Rosman, Guy and Bronstein, Alexander and Bronstein, Michael M. and Tai, Xue-Cheng and Kimmel, Ron}, booktitle = {Computer Vision, ECCV 2012 - Workshops and Demonstrations}, isbn = {9783642338625}, issn = {1611-3349}, location = {Florence, Italy}, number = {Part 1}, pages = {52--62}, publisher = {Springer Nature}, title = {{Group-valued regularization for analysis of articulated motion}}, doi = {10.1007/978-3-642-33863-2_6}, volume = {7583}, year = {2012}, } @inproceedings{18349, abstract = {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.}, author = {Kovnatsky, Artiom and Bronstein, Michael M. and Bronstein, Alexander}, booktitle = {Computer Vision, ECCV 2012 - Workshops and Demonstrations}, isbn = {9783642338625}, issn = {0302-9743}, location = {Florence, Italy}, number = {Part 1}, pages = {83--91}, publisher = {Springer Nature}, title = {{Stable Spectral Mesh Filtering}}, doi = {10.1007/978-3-642-33863-2_9}, volume = {7583}, year = {2012}, } @inproceedings{18350, abstract = {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.}, author = {Raviv, Dan and Bronstein, Alexander and Bronstein, Michael M. and Kimmel, Ron and Sochen, Nir}, booktitle = {15th International Workshop on Theoretical Foundations of Computer Vision}, isbn = {9783642340901}, issn = {1611-3349}, location = {Dagstuhl, Germany}, pages = {177--190}, publisher = {Springer Nature}, title = {{Equi-affine invariant geometries of articulated objects}}, doi = {10.1007/978-3-642-34091-8_8}, volume = {7474}, year = {2012}, } @article{18364, 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.}, author = {Litman, R. and Bronstein, Alexander and Bronstein, M.M.}, issn = {0097-8493}, journal = {Computers & Graphics}, number = {5}, pages = {569--576}, publisher = {Elsevier}, title = {{Stable volumetric features in deformable shapes}}, doi = {10.1016/j.cag.2012.03.034}, volume = {36}, year = {2012}, } @inproceedings{18378, abstract = {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.}, author = {Kokkinos, I. and Bronstein, M. M. and Litman, R. and Bronstein, Alexander}, booktitle = {2012 IEEE Conference on Computer Vision and Pattern Recognition}, isbn = {9781467312264}, issn = {1063-6919}, location = {Providence, RI, United States}, publisher = {IEEE}, title = {{Intrinsic shape context descriptors for deformable shapes}}, doi = {10.1109/cvpr.2012.6247671}, year = {2012}, } @inproceedings{18379, abstract = {We consider the problem of minimum distortion intrinsic correspondence between deformable shapes, many useful formulations of which give rise to the NP-hard quadratic assignment problem (QAP). Previous attempts to use the spectral relaxation have had limited success due to the lack of sparsity of the obtained “fuzzy” solution. In this paper, we adopt the recently introduced alternative L 1 relaxation of the QAP based on the principles of game theory. We relate it to the Gromov and Lipschitz metrics between metric spaces and demonstrate on state-of-the-art benchmarks that the proposed approach is capable of finding very accurate sparse correspondences between deformable shapes.}, author = {Rodola, E. and Bronstein, Alexander and Albarelli, A. and Bergamasco, F. and Torsello, A.}, booktitle = {2012 IEEE Conference on Computer Vision and Pattern Recognition}, isbn = {978-1-4673-1226-4}, issn = {1063-6919}, location = {Providence, RI, United States}, publisher = {IEEE}, title = {{A game-theoretic approach to deformable shape matching}}, doi = {10.1109/cvpr.2012.6247674}, year = {2012}, } @article{18412, abstract = {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.}, author = {Strecha, C. and Bronstein, Alexander and Bronstein, M. M. and Fua, P.}, issn = {2160-9292}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = {1}, pages = {66--78}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{LDAHash: Improved matching with smaller descriptors}}, doi = {10.1109/tpami.2011.103}, volume = {34}, year = {2012}, } @article{22056, abstract = {We consider the mass-critical generalized Korteweg{de Vries equation (∂t + ∂xxx)u = ±∂ x(u 5) for real-valued functions u(t; x). We prove that if the global well-posedness and scattering conjecture for this equation failed, then, conditional on a positive answer to the global well-posedness and scattering conjecture for the masscritical nonlinear Schrffodinger equation (-i∂ t + ∂xx)u = ±(|u| 4u), there exists a minimal-mass blowup solution to the mass-critical generalized KdV equation which is almost periodic modulo the symmetries of the equation. Moreover, we can guarantee that this minimal-mass blowup solution is either a self-similar solution, a soliton-like solution, or a double high-to-low frequency cascade solution.}, author = {Killip, Rowan and Kwon, Soonsik and Shao, Shuanglin and Visan, Monica}, issn = {1553-5231}, journal = {Discrete and Continuous Dynamical Systems}, number = {1}, pages = {191--221}, publisher = {American Institute of Mathematical Sciences}, title = {{On the mass-critical generalized KdV equation}}, doi = {10.3934/dcds.2012.32.191}, volume = {32}, year = {2012}, } @article{22075, abstract = {In this short note, we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical nonlinear Schrödinger equation (NLS) in four space dimensions obtained previously by Ryckman and Visan [“Global well-posedness and scattering for the defocusing energycritical nonlinear Schrödinger equation in R^1+4⁠.” American Journal of Mathematics 129 (2007): 1–60. MR2288737]. The argument is inspired by the recent work of Dodson [“Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d≥3.” (2009): preprint arXiv:0912.2467.] on the mass-critical NLS.}, author = {Visan, Monica}, issn = {1687-0247}, journal = {International Mathematics Research Notices}, number = {5}, pages = {1037--1067}, publisher = {Oxford University Press}, title = {{Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions}}, doi = {10.1093/imrn/rnr051}, volume = {2012}, year = {2012}, } @article{2318, abstract = {We show that bosons interacting via pair potentials with negative scattering length form bound states for a suitable number of particles. In other words, the absence of many-particle bound states of any kind implies the non-negativity of the scattering length of the interaction potential. }, author = {Seiringer, Robert}, journal = {Journal of Spectral Theory}, number = {3}, pages = {321--328}, publisher = {EMS Press}, title = {{Absence of bound states implies non-negativity of the scattering length}}, doi = {10.4171/JST/31}, volume = {2}, year = {2012}, } @article{2954, abstract = {Spontaneous postsynaptic currents (PSCs) provide key information about the mechanisms of synaptic transmission and the activity modes of neuronal networks. However, detecting spontaneous PSCs in vitro and in vivo has been challenging, because of the small amplitude, the variable kinetics, and the undefined time of generation of these events. Here, we describe a, to our knowledge, new method for detecting spontaneous synaptic events by deconvolution, using a template that approximates the average time course of spontaneous PSCs. A recorded PSC trace is deconvolved from the template, resulting in a series of delta-like functions. The maxima of these delta-like events are reliably detected, revealing the precise onset times of the spontaneous PSCs. Among all detection methods, the deconvolution-based method has a unique temporal resolution, allowing the detection of individual events in high-frequency bursts. Furthermore, the deconvolution-based method has a high amplitude resolution, because deconvolution can substantially increase the signal/noise ratio. When tested against previously published methods using experimental data, the deconvolution-based method was superior for spontaneous PSCs recorded in vivo. Using the high-resolution deconvolution-based detection algorithm, we show that the frequency of spontaneous excitatory postsynaptic currents in dentate gyrus granule cells is 4.5 times higher in vivo than in vitro.}, author = {Pernia-Andrade, Alejandro and Goswami, Sarit and Stickler, Yvonne and Fröbe, Ulrich and Schlögl, Alois and Jonas, Peter M}, journal = {Biophysical Journal}, number = {7}, pages = {1429 -- 1439}, publisher = {Biophysical Society}, title = {{A deconvolution based method with high sensitivity and temporal resolution for detection of spontaneous synaptic currents in vitro and in vivo}}, doi = {10.1016/j.bpj.2012.08.039}, volume = {103}, year = {2012}, } @article{3160, abstract = {There is a long-running controversy about how early cell fate decisions are made in the developing mammalian embryo. 1,2 In particular, it is controversial when the first events that can predict the establishment of the pluripotent and extra-embryonic lineages in the blastocyst of the pre-implantation embryo occur. It has long been proposed that the position and polarity of cells at the 16- to 32-cell stage embryo influence their decision to either give rise to the pluripotent cell lineage that eventually contributes to the inner cell mass (ICM), comprising the primitive endoderm (PE) and the epiblast (EPI), or the extra-embryonic trophectoderm (TE) surrounding the blastocoel. The positioning of cells in the embryo at this developmental stage could largely be the result of random events, making this a stochastic model of cell lineage allocation. Contrary to such a stochastic model, some studies have detected putative differences in the lineage potential of individual blastomeres before compaction, indicating that the first cell fate decisions may occur as early as at the 4-cell stage. Using a non-invasive, quantitative in vivo imaging assay to study the kinetic behavior of Oct4 (also known as POU5F1), a key transcription factor (TF) controlling pre-implantation development in the mouse embryo, 3-5 a recent study identifies Oct4 kinetics as a predictive measure of cell lineage patterning in the early mouse embryo. 6 Here, we discuss the implications of such molecular heterogeneities in early development and offer potential avenues toward a mechanistic understanding of these observations, contributing to the resolution of the controversy of developmental cell lineage allocation.}, author = {Pantazis, Periklis and Bollenbach, Tobias}, journal = {Cell Cycle}, number = {11}, pages = {2055 -- 2058}, publisher = {Taylor & Francis}, title = {{Transcription factor kinetics and the emerging asymmetry in the early mammalian embryo}}, doi = {10.4161/cc.20118}, volume = {11}, year = {2012}, }