[{"status":"public","publication_status":"published","abstract":[{"lang":"eng","text":"Fiber tractography is an important tool of computational neuroscience that enables reconstructing the spatial connectivity and organization of white matter of the brain. Fiber tractography takes advantage of diffusion Magnetic Resonance Imaging (dMRI) which allows measuring the apparent diffusivity of cerebral water along different spatial directions. Unfortunately, collecting such data comes at the price of reduced spatial resolution and substantially elevated acquisition times, which limits the clinical applicability of dMRI. This problem has been thus far addressed using two principal strategies. Most of the efforts have been extended towards improving the quality of signal estimation for any, yet fixed sampling scheme (defined through the choice of diffusion-encoding gradients). On the other hand, optimization over the sampling scheme has also proven to be effective. Inspired by the previous results, the present work consolidates the above strategies into a unified estimation framework, in which the optimization is carried out with respect to both estimation model and sampling design concurrently. The proposed solution offers substantial improvements in the quality of signal estimation as well as the accuracy of ensuing analysis by means of fiber tractography. While proving the optimality of the learned estimation models would probably need more extensive evaluation, we nevertheless claim that the learned sampling schemes can be of immediate use, offering a way to improve the dMRI analysis without the necessity of deploying the neural network used for their estimation. We present a comprehensive comparative analysis based on the Human Connectome Project data. Code and learned sampling designs available at https://github.com/tomer196/Learned_dMRI."}],"article_processing_charge":"No","page":"13-28","title":"Towards learned optimal q-space sampling in diffusion MRI","year":"2021","scopus_import":"1","publication":"Computational Diffusion MRI","day":"30","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2009.03008"}],"arxiv":1,"OA_type":"green","alternative_title":["Mathematics and Visualization"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","date_updated":"2024-10-16T09:51:45Z","oa":1,"citation":{"ista":"Weiss T, Vedula S, Senouf O, Michailovich O, Bronstein AM. 2021.Towards learned optimal q-space sampling in diffusion MRI. In: Computational Diffusion MRI. Mathematics and Visualization, , 13–28.","ama":"Weiss T, Vedula S, Senouf O, Michailovich O, Bronstein AM. Towards learned optimal q-space sampling in diffusion MRI. In: Gyori N, Hutter J, Nath V, Palombo M, Pizzolato M, Zhang F, eds. <i>Computational Diffusion MRI</i>. Cham: Springer Nature; 2021:13-28. doi:<a href=\"https://doi.org/10.1007/978-3-030-73018-5_2\">10.1007/978-3-030-73018-5_2</a>","chicago":"Weiss, Tomer, Sanketh Vedula, Ortal Senouf, Oleg Michailovich, and Alex M. Bronstein. “Towards Learned Optimal Q-Space Sampling in Diffusion MRI.” In <i>Computational Diffusion MRI</i>, edited by Noemi Gyori, Jana Hutter, Vishwesh Nath, Marco Palombo, Marco Pizzolato, and Fan Zhang, 13–28. Cham: Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-73018-5_2\">https://doi.org/10.1007/978-3-030-73018-5_2</a>.","mla":"Weiss, Tomer, et al. “Towards Learned Optimal Q-Space Sampling in Diffusion MRI.” <i>Computational Diffusion MRI</i>, edited by Noemi Gyori et al., Springer Nature, 2021, pp. 13–28, doi:<a href=\"https://doi.org/10.1007/978-3-030-73018-5_2\">10.1007/978-3-030-73018-5_2</a>.","apa":"Weiss, T., Vedula, S., Senouf, O., Michailovich, O., &#38; Bronstein, A. M. (2021). Towards learned optimal q-space sampling in diffusion MRI. In N. Gyori, J. Hutter, V. Nath, M. Palombo, M. Pizzolato, &#38; F. Zhang (Eds.), <i>Computational Diffusion MRI</i> (pp. 13–28). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-73018-5_2\">https://doi.org/10.1007/978-3-030-73018-5_2</a>","short":"T. Weiss, S. Vedula, O. Senouf, O. Michailovich, A.M. Bronstein, in:, N. Gyori, J. Hutter, V. Nath, M. Palombo, M. Pizzolato, F. Zhang (Eds.), Computational Diffusion MRI, Springer Nature, Cham, 2021, pp. 13–28.","ieee":"T. Weiss, S. Vedula, O. Senouf, O. Michailovich, and A. M. Bronstein, “Towards learned optimal q-space sampling in diffusion MRI,” in <i>Computational Diffusion MRI</i>, N. Gyori, J. Hutter, V. Nath, M. Palombo, M. Pizzolato, and F. Zhang, Eds. Cham: Springer Nature, 2021, pp. 13–28."},"author":[{"last_name":"Weiss","first_name":"Tomer","full_name":"Weiss, Tomer"},{"full_name":"Vedula, Sanketh","first_name":"Sanketh","last_name":"Vedula"},{"last_name":"Senouf","first_name":"Ortal","full_name":"Senouf, Ortal"},{"first_name":"Oleg","full_name":"Michailovich, Oleg","last_name":"Michailovich"},{"id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","orcid":"0000-0001-9699-8730","full_name":"Bronstein, Alexander","first_name":"Alexander","last_name":"Bronstein"}],"OA_place":"repository","place":"Cham","_id":"18242","oa_version":"Preprint","date_created":"2024-10-08T13:03:26Z","month":"09","publication_identifier":{"issn":["1612-3786"],"eisbn":["9783030730185"],"isbn":["9783030730178"]},"editor":[{"last_name":"Gyori","full_name":"Gyori, Noemi","first_name":"Noemi"},{"last_name":"Hutter","full_name":"Hutter, Jana","first_name":"Jana"},{"last_name":"Nath","first_name":"Vishwesh","full_name":"Nath, Vishwesh"},{"full_name":"Palombo, Marco","first_name":"Marco","last_name":"Palombo"},{"last_name":"Pizzolato","full_name":"Pizzolato, Marco","first_name":"Marco"},{"first_name":"Fan","full_name":"Zhang, Fan","last_name":"Zhang"}],"extern":"1","external_id":{"arxiv":["2009.03008"]},"type":"book_chapter","doi":"10.1007/978-3-030-73018-5_2","conference":{"name":"MICCAI: Conference on Medical Image Computing and Computer-Assisted Intervention","start_date":"2020-10-08","location":"Lima, Peru/Virtual","end_date":"2020-10-08"},"related_material":{"link":[{"url":"https://github.com/tomer196/Learned_dMRI","relation":"software"}]},"language":[{"iso":"eng"}],"date_published":"2021-09-30T00:00:00Z","publisher":"Springer Nature"},{"author":[{"full_name":"Pokrass, Jonathan","first_name":"Jonathan","last_name":"Pokrass"},{"orcid":"0000-0001-9699-8730","full_name":"Bronstein, Alexander","first_name":"Alexander","last_name":"Bronstein","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6"},{"last_name":"Bronstein","full_name":"Bronstein, Michael M.","first_name":"Michael M."},{"last_name":"Sprechmann","full_name":"Sprechmann, Pablo","first_name":"Pablo"},{"first_name":"Guillermo","full_name":"Sapiro, Guillermo","last_name":"Sapiro"}],"citation":{"apa":"Pokrass, J., Bronstein, A. M., Bronstein, M. M., Sprechmann, P., &#38; Sapiro, G. (2016). Sparse Models for Intrinsic Shape Correspondence. In M. Breuß, A. Bruckstein, P. Maragos, &#38; S. Wuhrer (Eds.), <i>Perspectives in Shape Analysis</i> (1st ed., pp. 211–230). Cham: Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-319-24726-7_10\">https://doi.org/10.1007/978-3-319-24726-7_10</a>","mla":"Pokrass, Jonathan, et al. “Sparse Models for Intrinsic Shape Correspondence.” <i>Perspectives in Shape Analysis</i>, edited by Michael Breuß et al., 1st ed., Springer International Publishing, 2016, pp. 211–30, doi:<a href=\"https://doi.org/10.1007/978-3-319-24726-7_10\">10.1007/978-3-319-24726-7_10</a>.","ista":"Pokrass J, Bronstein AM, Bronstein MM, Sprechmann P, Sapiro G. 2016.Sparse Models for Intrinsic Shape Correspondence. In: Perspectives in Shape Analysis. Mathematics and Visualization, , 211–230.","chicago":"Pokrass, Jonathan, Alex M. Bronstein, Michael M. Bronstein, Pablo Sprechmann, and Guillermo Sapiro. “Sparse Models for Intrinsic Shape Correspondence.” In <i>Perspectives in Shape Analysis</i>, edited by Michael Breuß, Alfred Bruckstein, Petros Maragos, and Stefanie Wuhrer, 1st ed., 211–30. Cham: Springer International Publishing, 2016. <a href=\"https://doi.org/10.1007/978-3-319-24726-7_10\">https://doi.org/10.1007/978-3-319-24726-7_10</a>.","ama":"Pokrass J, Bronstein AM, Bronstein MM, Sprechmann P, Sapiro G. Sparse Models for Intrinsic Shape Correspondence. In: Breuß M, Bruckstein A, Maragos P, Wuhrer S, eds. <i>Perspectives in Shape Analysis</i>. 1st ed. Cham: Springer International Publishing; 2016:211-230. doi:<a href=\"https://doi.org/10.1007/978-3-319-24726-7_10\">10.1007/978-3-319-24726-7_10</a>","ieee":"J. Pokrass, A. M. Bronstein, M. M. Bronstein, P. Sprechmann, and G. Sapiro, “Sparse Models for Intrinsic Shape Correspondence,” in <i>Perspectives in Shape Analysis</i>, 1st ed., M. Breuß, A. Bruckstein, P. Maragos, and S. Wuhrer, Eds. Cham: Springer International Publishing, 2016, pp. 211–230.","short":"J. Pokrass, A.M. Bronstein, M.M. Bronstein, P. Sprechmann, G. Sapiro, in:, M. Breuß, A. Bruckstein, P. Maragos, S. Wuhrer (Eds.), Perspectives in Shape Analysis, 1st ed., Springer International Publishing, Cham, 2016, pp. 211–230."},"_id":"18328","place":"Cham","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-10-22T08:17:06Z","doi":"10.1007/978-3-319-24726-7_10","type":"book_chapter","date_published":"2016-10-01T00:00:00Z","publisher":"Springer International Publishing","language":[{"iso":"eng"}],"month":"10","oa_version":"None","date_created":"2024-10-15T11:20:53Z","extern":"1","editor":[{"first_name":"Michael","full_name":"Breuß, Michael","last_name":"Breuß"},{"full_name":"Bruckstein, Alfred","first_name":"Alfred","last_name":"Bruckstein"},{"full_name":"Maragos, Petros","first_name":"Petros","last_name":"Maragos"},{"last_name":"Wuhrer","full_name":"Wuhrer, Stefanie","first_name":"Stefanie"}],"publication_identifier":{"isbn":["9783319247243"],"eisbn":["9783319247267"],"eissn":["2197-666X"],"issn":["1612-3786"]},"article_processing_charge":"No","page":"211-230","abstract":[{"text":"We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor do we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to establish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non-trivial use of sparse models in shape correspondence. We formulate the problem of permuted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown correspondence in functional representation. We also propose a robust variant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects.","lang":"eng"}],"publication_status":"published","status":"public","edition":"1","alternative_title":["Mathematics and Visualization"],"OA_type":"closed access","scopus_import":"1","year":"2016","title":"Sparse Models for Intrinsic Shape Correspondence","day":"01","publication":"Perspectives in Shape Analysis"},{"quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2025-04-15T08:37:54Z","author":[{"first_name":"David","full_name":"Günther, David","last_name":"Günther"},{"last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Seidel","first_name":"Hans-Peter","full_name":"Seidel, Hans-Peter"},{"first_name":"Tino","full_name":"Weinkauf, Tino","last_name":"Weinkauf"}],"acknowledgement":"This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.","citation":{"short":"D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.","ieee":"D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the simplification of the Morse-Smale complex,” in <i>Topological Methods in Data Analysis and Visualization III.</i>, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.","chicago":"Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf. “Notes on the Simplification of the Morse-Smale Complex.” In <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization. Cham: Springer Nature, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">https://doi.org/10.1007/978-3-319-04099-8_9</a>.","ista":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization III. , 135–150.","ama":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III.</i> Mathematics and Visualization. Cham: Springer Nature; 2014:135-150. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">10.1007/978-3-319-04099-8_9</a>","apa":"Günther, D., Reininghaus, J., Seidel, H.-P., &#38; Weinkauf, T. (2014). Notes on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III.</i> (pp. 135–150). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">https://doi.org/10.1007/978-3-319-04099-8_9</a>","mla":"Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.” <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">10.1007/978-3-319-04099-8_9</a>."},"place":"Cham","_id":"10817","month":"03","oa_version":"None","date_created":"2022-03-04T08:33:57Z","publication_identifier":{"eisbn":["9783319040998"],"isbn":["9783319040981"],"eissn":["2197-666X"],"issn":["1612-3786"]},"editor":[{"last_name":"Bremer","first_name":"Peer-Timo","full_name":"Bremer, Peer-Timo"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"},{"last_name":"Peikert","full_name":"Peikert, Ronald","first_name":"Ronald"}],"project":[{"call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"type":"book_chapter","doi":"10.1007/978-3-319-04099-8_9","date_published":"2014-03-19T00:00:00Z","publisher":"Springer Nature","language":[{"iso":"eng"}],"abstract":[{"text":"The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption.","lang":"eng"}],"publication_status":"published","status":"public","article_processing_charge":"No","page":"135-150","year":"2014","scopus_import":"1","title":"Notes on the simplification of the Morse-Smale complex","day":"19","publication":"Topological Methods in Data Analysis and Visualization III.","department":[{"_id":"HeEd"}],"series_title":"Mathematics and Visualization","ec_funded":1},{"type":"conference","doi":"10.1007/978-3-319-04099-8_16","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"date_published":"2014-03-19T00:00:00Z","publisher":"Springer","alternative_title":["Mathematics and Visualization"],"oa_version":"None","date_created":"2022-03-18T13:05:39Z","title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","month":"03","scopus_import":"1","year":"2014","publication":"Topological Methods in Data Analysis and Visualization III ","publication_identifier":{"issn":["1612-3786"],"eissn":["2197-666X"],"isbn":["9783319040981"],"eisbn":["9783319040998"]},"day":"19","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","citation":{"short":"V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262.","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature,” in <i>Topological Methods in Data Analysis and Visualization III </i>, 2014, pp. 249–262.","ista":"Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262.","ama":"Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In: <i>Topological Methods in Data Analysis and Visualization III </i>. Springer; 2014:249-262. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">10.1007/978-3-319-04099-8_16</a>","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In <i>Topological Methods in Data Analysis and Visualization III </i>, 249–62. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">https://doi.org/10.1007/978-3-319-04099-8_16</a>.","mla":"Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” <i>Topological Methods in Data Analysis and Visualization III </i>, Springer, 2014, pp. 249–62, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">10.1007/978-3-319-04099-8_16</a>.","apa":"Zobel, V., Reininghaus, J., &#38; Hotz, I. (2014). Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In <i>Topological Methods in Data Analysis and Visualization III </i> (pp. 249–262). Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">https://doi.org/10.1007/978-3-319-04099-8_16</a>"},"author":[{"last_name":"Zobel","first_name":"Valentin","full_name":"Zobel, Valentin"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"}],"article_processing_charge":"No","page":"249-262","_id":"10886","status":"public","abstract":[{"lang":"eng","text":"We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set."}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","publication_status":"published","date_updated":"2023-09-05T14:13:16Z"},{"series_title":"Mathematics and Visualization","volume":1,"department":[{"_id":"HeEd"}],"ec_funded":1,"scopus_import":"1","year":"2014","title":"Toward the extraction of saddle periodic orbits","day":"19","publication":"Topological Methods in Data Analysis and Visualization III ","article_processing_charge":"No","page":"55-69","publication_status":"published","abstract":[{"text":"Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data.","lang":"eng"}],"status":"public","intvolume":"         1","doi":"10.1007/978-3-319-04099-8_4","type":"book_chapter","publisher":"Springer","date_published":"2014-03-19T00:00:00Z","language":[{"iso":"eng"}],"month":"03","date_created":"2022-03-21T07:11:23Z","oa_version":"None","editor":[{"first_name":"Peer-Timo","full_name":"Bremer, Peer-Timo","last_name":"Bremer"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"},{"first_name":"Ronald","full_name":"Peikert, Ronald","last_name":"Peikert"}],"project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493"}],"publication_identifier":{"issn":["1612-3786"],"eissn":["2197-666X"],"eisbn":["9783319040998"],"isbn":["9783319040981"]},"author":[{"last_name":"Kasten","full_name":"Kasten, Jens","first_name":"Jens"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","full_name":"Reininghaus, Jan","first_name":"Jan"},{"first_name":"Wieland","full_name":"Reich, Wieland","last_name":"Reich"},{"last_name":"Scheuermann","full_name":"Scheuermann, Gerik","first_name":"Gerik"}],"citation":{"ieee":"J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in <i>Topological Methods in Data Analysis and Visualization III </i>, vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer, 2014, pp. 55–69.","short":"J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III , Springer, Cham, 2014, pp. 55–69.","mla":"Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” <i>Topological Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">10.1007/978-3-319-04099-8_4</a>.","apa":"Kasten, J., Reininghaus, J., Reich, W., &#38; Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III </i> (Vol. 1, pp. 55–69). Cham: Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">https://doi.org/10.1007/978-3-319-04099-8_4</a>","ama":"Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III </i>. Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">10.1007/978-3-319-04099-8_4</a>","ista":"Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III . vol. 1, 55–69.","chicago":"Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward the Extraction of Saddle Periodic Orbits.” In <i>Topological Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">https://doi.org/10.1007/978-3-319-04099-8_4</a>."},"acknowledgement":"First, we thank the reviewers of this paper for their ideas and critical comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions. This research is supported by the European Commission under the TOPOSYS project FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the European Science Foundation under the ACAT Research Network Program.","place":"Cham","_id":"10893","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-04-15T08:37:54Z"},{"year":"2013","scopus_import":"1","month":"04","oa_version":"None","title":"Group-Valued Regularization for Motion Segmentation of Articulated Shapes","date_created":"2024-10-15T11:20:54Z","day":"04","extern":"1","editor":[{"full_name":"Breuß, Michael","first_name":"Michael","last_name":"Breuß"},{"last_name":"Bruckstein","first_name":"Alfred","full_name":"Bruckstein, Alfred"},{"last_name":"Maragos","full_name":"Maragos, Petros","first_name":"Petros"}],"publication":"Innovations for Shape Analysis","publication_identifier":{"issn":["1612-3786"],"eisbn":["9783642341410"],"isbn":["9783642341403"]},"series_title":"MATHVISUAL","doi":"10.1007/978-3-642-34141-0_12","type":"book_chapter","alternative_title":["Mathematics and Visualization"],"publisher":"Springer Nature","date_published":"2013-04-04T00:00:00Z","language":[{"iso":"eng"}],"quality_controlled":"1","abstract":[{"lang":"eng","text":"Motion-based segmentation is an important tool for the analysis of articulated shapes. As such, it plays an important role in mechanical engineering, computer graphics, and computer vision. In this chapter, we study motion-based segmentation of 3D articulated shapes. We formulate motion-based surface segmentation as a piecewise-smooth regularization problem for the transformations between several poses. Using Lie-group representation for the transformation at each surface point, we obtain a simple regularized fitting problem. An Ambrosio-Tortorelli scheme of a generalized Mumford-Shah model gives us the segmentation functional without assuming prior knowledge on the number of parts or even the articulated nature of the object. Experiments on several standard datasets compare the results of the proposed method to state-of-the-art algorithms."}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication_status":"published","status":"public","date_updated":"2025-01-16T15:57:36Z","article_processing_charge":"No","author":[{"last_name":"Rosman","full_name":"Rosman, Guy","first_name":"Guy"},{"first_name":"Michael M.","full_name":"Bronstein, Michael M.","last_name":"Bronstein"},{"orcid":"0000-0001-9699-8730","full_name":"Bronstein, Alexander","first_name":"Alexander","last_name":"Bronstein","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6"},{"last_name":"Wolf","full_name":"Wolf, Alon","first_name":"Alon"},{"full_name":"Kimmel, Ron","first_name":"Ron","last_name":"Kimmel"}],"citation":{"mla":"Rosman, Guy, et al. “Group-Valued Regularization for Motion Segmentation of Articulated Shapes.” <i>Innovations for Shape Analysis</i>, edited by Michael Breuß et al., Springer Nature, 2013, pp. 263–81, doi:<a href=\"https://doi.org/10.1007/978-3-642-34141-0_12\">10.1007/978-3-642-34141-0_12</a>.","apa":"Rosman, G., Bronstein, M. M., Bronstein, A. M., Wolf, A., &#38; Kimmel, R. (2013). Group-Valued Regularization for Motion Segmentation of Articulated Shapes. In M. Breuß, A. Bruckstein, &#38; P. Maragos (Eds.), <i>Innovations for Shape Analysis</i> (pp. 263–281). Berlin, Heidelberg: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-642-34141-0_12\">https://doi.org/10.1007/978-3-642-34141-0_12</a>","chicago":"Rosman, Guy, Michael M. Bronstein, Alex M. Bronstein, Alon Wolf, and Ron Kimmel. “Group-Valued Regularization for Motion Segmentation of Articulated Shapes.” In <i>Innovations for Shape Analysis</i>, edited by Michael Breuß, Alfred Bruckstein, and Petros Maragos, 263–81. MATHVISUAL. Berlin, Heidelberg: Springer Nature, 2013. <a href=\"https://doi.org/10.1007/978-3-642-34141-0_12\">https://doi.org/10.1007/978-3-642-34141-0_12</a>.","ista":"Rosman G, Bronstein MM, Bronstein AM, Wolf A, Kimmel R. 2013.Group-Valued Regularization for Motion Segmentation of Articulated Shapes. In: Innovations for Shape Analysis. Mathematics and Visualization, , 263–281.","ama":"Rosman G, Bronstein MM, Bronstein AM, Wolf A, Kimmel R. Group-Valued Regularization for Motion Segmentation of Articulated Shapes. In: Breuß M, Bruckstein A, Maragos P, eds. <i>Innovations for Shape Analysis</i>. MATHVISUAL. Berlin, Heidelberg: Springer Nature; 2013:263-281. doi:<a href=\"https://doi.org/10.1007/978-3-642-34141-0_12\">10.1007/978-3-642-34141-0_12</a>","ieee":"G. Rosman, M. M. Bronstein, A. M. Bronstein, A. Wolf, and R. Kimmel, “Group-Valued Regularization for Motion Segmentation of Articulated Shapes,” in <i>Innovations for Shape Analysis</i>, M. Breuß, A. Bruckstein, and P. Maragos, Eds. Berlin, Heidelberg: Springer Nature, 2013, pp. 263–281.","short":"G. Rosman, M.M. Bronstein, A.M. Bronstein, A. Wolf, R. Kimmel, in:, M. Breuß, A. Bruckstein, P. Maragos (Eds.), Innovations for Shape Analysis, Springer Nature, Berlin, Heidelberg, 2013, pp. 263–281."},"place":"Berlin, Heidelberg","_id":"18351","page":"263-281"},{"editor":[{"last_name":"Breuß","first_name":"Michael","full_name":"Breuß, Michael"},{"full_name":"Bruckstein, Alfred","first_name":"Alfred","last_name":"Bruckstein"},{"last_name":"Maragos","first_name":"Petros","full_name":"Maragos, Petros"}],"publication_identifier":{"isbn":["9783642341403"],"eisbn":["9783642341410"],"issn":["1612-3786"]},"publication":"Innovations for Shape Analysis","day":"04","extern":"1","oa_version":"None","date_created":"2024-10-15T11:20:54Z","title":"Stable Semi-local Features for Non-rigid Shapes","year":"2013","month":"04","language":[{"iso":"eng"}],"alternative_title":["Mathematics and Visualization"],"publisher":"Springer Nature","date_published":"2013-04-04T00:00:00Z","doi":"10.1007/978-3-642-34141-0_8","type":"book_chapter","series_title":"MATHVISUAL","date_updated":"2025-01-16T15:50:22Z","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication_status":"published","abstract":[{"text":"Feature-based analysis is becoming a very popular approach for geometric shape analysis. Following the success of this approach in image analysis, there is a growing interest in finding analogous methods in the 3D world. Maximally stable component detection is a low computation cost and high repeatability method for feature detection in images.In this study, a diffusion-geometry based framework for stable component detection is presented, which can be used for geometric feature detection in deformable shapes.The vast majority of studies of deformable 3D shapes models them as the two-dimensional boundary of the volume of the shape. Recent works have shown that a volumetric shape model is advantageous in numerous ways as it better captures the natural behavior of non-rigid deformations. We show that our framework easily adapts to this volumetric approach, and even demonstrates superior performance.A quantitative evaluation of our methods on the SHREC’10 and SHREC’11 feature detection benchmarks as well as qualitative tests on the SCAPE dataset show its potential as a source of high-quality features. Examples demonstrating the drawbacks of surface stable components and the advantage of their volumetric counterparts are also presented.","lang":"eng"}],"page":"161 - 189","place":"Berlin, Heidelberg","_id":"18352","citation":{"apa":"Litman, R., Bronstein, A. M., &#38; Bronstein, M. M. (2013). Stable Semi-local Features for Non-rigid Shapes. In M. Breuß, A. Bruckstein, &#38; P. Maragos (Eds.), <i>Innovations for Shape Analysis</i> (pp. 161–189). Berlin, Heidelberg: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-642-34141-0_8\">https://doi.org/10.1007/978-3-642-34141-0_8</a>","mla":"Litman, Roee, et al. “Stable Semi-Local Features for Non-Rigid Shapes.” <i>Innovations for Shape Analysis</i>, edited by Michael Breuß et al., Springer Nature, 2013, pp. 161–89, doi:<a href=\"https://doi.org/10.1007/978-3-642-34141-0_8\">10.1007/978-3-642-34141-0_8</a>.","ista":"Litman R, Bronstein AM, Bronstein MM. 2013.Stable Semi-local Features for Non-rigid Shapes. In: Innovations for Shape Analysis. Mathematics and Visualization, , 161–189.","chicago":"Litman, Roee, Alex M. Bronstein, and Michael M. Bronstein. “Stable Semi-Local Features for Non-Rigid Shapes.” In <i>Innovations for Shape Analysis</i>, edited by Michael Breuß, Alfred Bruckstein, and Petros Maragos, 161–89. MATHVISUAL. Berlin, Heidelberg: Springer Nature, 2013. <a href=\"https://doi.org/10.1007/978-3-642-34141-0_8\">https://doi.org/10.1007/978-3-642-34141-0_8</a>.","ama":"Litman R, Bronstein AM, Bronstein MM. Stable Semi-local Features for Non-rigid Shapes. In: Breuß M, Bruckstein A, Maragos P, eds. <i>Innovations for Shape Analysis</i>. MATHVISUAL. Berlin, Heidelberg: Springer Nature; 2013:161-189. doi:<a href=\"https://doi.org/10.1007/978-3-642-34141-0_8\">10.1007/978-3-642-34141-0_8</a>","ieee":"R. Litman, A. M. Bronstein, and M. M. Bronstein, “Stable Semi-local Features for Non-rigid Shapes,” in <i>Innovations for Shape Analysis</i>, M. Breuß, A. Bruckstein, and P. Maragos, Eds. Berlin, Heidelberg: Springer Nature, 2013, pp. 161–189.","short":"R. Litman, A.M. Bronstein, M.M. Bronstein, in:, M. Breuß, A. Bruckstein, P. Maragos (Eds.), Innovations for Shape Analysis, Springer Nature, Berlin, Heidelberg, 2013, pp. 161–189."},"author":[{"last_name":"Litman","full_name":"Litman, Roee","first_name":"Roee"},{"first_name":"Alexander","full_name":"Bronstein, Alexander","last_name":"Bronstein","orcid":"0000-0001-9699-8730","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6"},{"last_name":"Bronstein","full_name":"Bronstein, Michael M.","first_name":"Michael M."}],"article_processing_charge":"No"}]