[{"citation":{"chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.","ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 48(8), 606–621.","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier, 2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015). Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010","ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.","ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” Computational Geometry: Theory and Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Dominique","full_name":"Attali, Dominique","last_name":"Attali"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724"},{"full_name":"Devillers, Olivier","last_name":"Devillers","first_name":"Olivier"},{"last_name":"Glisse","full_name":"Glisse, Marc","first_name":"Marc"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"}],"publist_id":"5305","title":"Homological reconstruction and simplification in R3","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"}],"year":"2015","publication":"Computational Geometry: Theory and Applications","day":"03","page":"606 - 621","date_created":"2018-12-11T11:54:06Z","doi":"10.1016/j.comgeo.2014.08.010","date_published":"2015-06-03T00:00:00Z","publisher":"Elsevier","quality_controlled":"1","date_updated":"2023-02-23T10:59:19Z","department":[{"_id":"HeEd"}],"_id":"1805","type":"journal_article","status":"public","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"volume":48,"issue":"8","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"2812"}]},"abstract":[{"lang":"eng","text":"We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard."}],"oa_version":"None","scopus_import":1,"intvolume":" 48","month":"06"},{"scopus_import":1,"month":"06","intvolume":" 10","abstract":[{"text":"We present a software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes. It aligns the shapes with each other, constructs a geometric graph representation together with the function that records the time of growth, and organizes the branches into a hierarchy that reflects the order of creation. The software includes the automatic computation of structural and dynamic traits for each root in the system enabling the quantification of growth on fine-scale. These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth.","lang":"eng"}],"oa_version":"Published Version","related_material":{"record":[{"relation":"research_data","id":"9737","status":"public"}]},"volume":10,"issue":"6","license":"https://creativecommons.org/licenses/by/4.0/","publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"d20f26461ca575276ad3ed9ce4bfc787","file_id":"5150","file_size":1850825,"date_updated":"2020-07-14T12:45:16Z","creator":"system","file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf","date_created":"2018-12-12T10:15:30Z"}],"language":[{"iso":"eng"}],"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"454","_id":"1793","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:16Z","date_updated":"2023-02-23T14:06:33Z","ddc":["000"],"publisher":"Public Library of Science","quality_controlled":"1","oa":1,"doi":"10.1371/journal.pone.0127657","date_published":"2015-06-01T00:00:00Z","date_created":"2018-12-11T11:54:02Z","has_accepted_license":"1","year":"2015","day":"01","publication":"PLoS One","article_number":"e0127657","author":[{"last_name":"Symonova","full_name":"Symonova, Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","first_name":"Olga"},{"last_name":"Topp","full_name":"Topp, Christopher","first_name":"Christopher"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"publist_id":"5318","title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","citation":{"ista":"Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.","chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.","short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots,” PLoS One, vol. 10, no. 6. Public Library of Science, 2015.","apa":"Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657","ama":"Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6). doi:10.1371/journal.pone.0127657","mla":"Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657, Public Library of Science, 2015, doi:10.1371/journal.pone.0127657."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"_id":"9737","type":"research_data_reference","status":"public","citation":{"mla":"Symonova, Olga, et al. Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2. Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.s001.","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots for the maize root shown in fig 2.” Public Library of Science, 2015.","short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","apa":"Symonova, O., Topp, C., & Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657.s001","ama":"Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001","chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.s001.","ista":"Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots for the maize root shown in fig 2, Public Library of Science, 10.1371/journal.pone.0127657.s001."},"date_updated":"2023-02-23T10:14:42Z","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","author":[{"last_name":"Symonova","full_name":"Symonova, Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","first_name":"Olga"},{"last_name":"Topp","full_name":"Topp, Christopher","first_name":"Christopher"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"article_processing_charge":"No","title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"oa_version":"Published Version","publisher":"Public Library of Science","month":"06","year":"2015","day":"01","date_published":"2015-06-01T00:00:00Z","doi":"10.1371/journal.pone.0127657.s001","related_material":{"record":[{"status":"public","id":"1793","relation":"used_in_publication"}]},"date_created":"2021-07-28T06:20:13Z"},{"acknowledgement":"F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation.","oa_version":"None","abstract":[{"lang":"eng","text":"Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology."}],"intvolume":" 31","month":"12","scopus_import":1,"quality_controlled":"1","publisher":"Academic Press","publication":"Journal of Complexity","language":[{"iso":"eng"}],"day":"01","publication_status":"published","year":"2015","date_created":"2018-12-11T11:54:02Z","related_material":{"record":[{"relation":"dissertation_contains","id":"1399","status":"public"}]},"issue":"6","volume":31,"date_published":"2015-12-01T00:00:00Z","doi":"10.1016/j.jco.2015.06.002","page":"773 - 797","_id":"1792","status":"public","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002.","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","mla":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002.","apa":"Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002","ama":"Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.","ieee":"F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797, 2015."},"date_updated":"2023-09-07T11:41:25Z","department":[{"_id":"HeEd"}],"title":"A Koksma-Hlawka inequality for general discrepancy systems","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian","last_name":"Pausinger","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768"},{"full_name":"Svane, Anne","last_name":"Svane","first_name":"Anne"}],"publist_id":"5320"},{"publisher":"Institute of Science and Technology Austria","alternative_title":["ISTA Thesis"],"month":"06","abstract":[{"text":"This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold.","lang":"eng"}],"oa_version":"None","page":"144","date_created":"2018-12-11T11:51:48Z","related_material":{"record":[{"relation":"part_of_dissertation","id":"1662","status":"public"},{"relation":"part_of_dissertation","id":"1792","status":"public"},{"id":"2255","status":"public","relation":"part_of_dissertation"}]},"date_published":"2015-06-01T00:00:00Z","publication_status":"published","year":"2015","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"day":"01","type":"dissertation","status":"public","_id":"1399","article_processing_charge":"No","author":[{"first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger"}],"publist_id":"5808","title":"On the approximation of intrinsic volumes","department":[{"_id":"HeEd"}],"citation":{"ista":"Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015.","ama":"Pausinger F. On the approximation of intrinsic volumes. 2015.","apa":"Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","short":"F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015.","ieee":"F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015.","mla":"Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute of Science and Technology Austria, 2015."},"date_updated":"2023-09-07T11:41:25Z","supervisor":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"publisher":"Springer","quality_controlled":"1","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.","date_created":"2022-03-21T07:11:23Z","date_published":"2014-03-19T00:00:00Z","doi":"10.1007/978-3-319-04099-8_4","page":"55-69","publication":"Topological Methods in Data Analysis and Visualization III ","day":"19","year":"2014","project":[{"name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"Toward the extraction of saddle periodic orbits","editor":[{"last_name":"Bremer","full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"},{"first_name":"Valerio","full_name":"Pascucci, Valerio","last_name":"Pascucci"},{"full_name":"Peikert, Ronald","last_name":"Peikert","first_name":"Ronald"}],"article_processing_charge":"No","author":[{"first_name":"Jens","full_name":"Kasten, Jens","last_name":"Kasten"},{"last_name":"Reininghaus","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"first_name":"Wieland","last_name":"Reich","full_name":"Reich, Wieland"},{"full_name":"Scheuermann, Gerik","last_name":"Scheuermann","first_name":"Gerik"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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 Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_4.","ieee":"J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization III , 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.","apa":"Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4","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. Topological Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4","mla":"Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4."},"intvolume":" 1","place":"Cham","month":"03","scopus_import":"1","oa_version":"None","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"}],"ec_funded":1,"volume":1,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["2197-666X"],"isbn":["9783319040981"],"issn":["1612-3786"],"eisbn":["9783319040998"]},"status":"public","type":"book_chapter","series_title":"Mathematics and Visualization","_id":"10893","department":[{"_id":"HeEd"}],"date_updated":"2022-06-21T12:01:47Z"},{"oa":1,"publisher":"World Scientific Publishing","quality_controlled":"1","acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","date_created":"2018-12-11T11:54:10Z","doi":"10.1142/S0218195914500034","date_published":"2014-03-16T00:00:00Z","page":"61 - 86","publication":"International Journal of Computational Geometry and Applications","day":"16","year":"2014","has_accepted_license":"1","title":"Topology-preserving watermarking of vector graphics","publist_id":"5290","author":[{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"last_name":"Meerwald","full_name":"Meerwald, Peter","first_name":"Peter"},{"last_name":"Kwitt","full_name":"Kwitt, Roland","first_name":"Roland"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2014. https://doi.org/10.1142/S0218195914500034.","ista":"Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 24(1), 61–86.","mla":"Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications, vol. 24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:10.1142/S0218195914500034.","ieee":"S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking of vector graphics,” International Journal of Computational Geometry and Applications, vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.","short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86.","apa":"Huber, S., Held, M., Meerwald, P., & Kwitt, R. (2014). Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195914500034","ama":"Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 2014;24(1):61-86. doi:10.1142/S0218195914500034"},"intvolume":" 24","month":"03","scopus_import":1,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques."}],"issue":"1","volume":24,"language":[{"iso":"eng"}],"file":[{"checksum":"be45c133ab4d43351260e21beaa8f4b1","file_id":"4704","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:08:43Z","file_name":"IST-2016-443-v1+1_S0218195914500034.pdf","creator":"system","date_updated":"2020-07-14T12:45:17Z","file_size":991734}],"publication_status":"published","pubrep_id":"443","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","_id":"1816","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:17Z","ddc":["000"],"date_updated":"2021-01-12T06:53:23Z"},{"year":"2014","publication_status":"published","day":"14","language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","page":"64 - 79","volume":53,"issue":"1","date_published":"2014-11-14T00:00:00Z","doi":"10.1007/s00454-014-9646-x","date_created":"2018-12-11T11:54:18Z","abstract":[{"lang":"eng","text":"We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an (Formula presented.) upper bound on the Ramsey number of a path with n ordered vertices."}],"oa_version":"Submitted Version","acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","scopus_import":1,"publisher":"Springer","main_file_link":[{"url":"http://arxiv.org/abs/1310.7004","open_access":"1"}],"oa":1,"month":"11","intvolume":" 53","citation":{"mla":"Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational Geometry, vol. 53, no. 1, Springer, 2014, pp. 64–79, doi:10.1007/s00454-014-9646-x.","short":"J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational Geometry 53 (2014) 64–79.","ieee":"J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey number of outerplanar graphs,” Discrete & Computational Geometry, vol. 53, no. 1. Springer, pp. 64–79, 2014.","apa":"Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x","ama":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79. doi:10.1007/s00454-014-9646-x","chicago":"Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational Geometry. Springer, 2014. https://doi.org/10.1007/s00454-014-9646-x.","ista":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey number of outerplanar graphs. 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Musin, “Functionals on triangulations of delaunay sets,” Moscow Mathematical Journal, vol. 14, no. 3. Independent University of Moscow, pp. 491–504, 2014.","short":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 491–504."},"title":"Functionals on triangulations of delaunay sets","article_processing_charge":"No","external_id":{"arxiv":["1211.7053"]},"publist_id":"5220","author":[{"last_name":"Dolbilin","full_name":"Dolbilin, Nikolai","first_name":"Nikolai"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Alexey","full_name":"Glazyrin, Alexey","last_name":"Glazyrin"},{"full_name":"Musin, Oleg","last_name":"Musin","first_name":"Oleg"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” Journal of Mathematical Sciences, vol. 203, no. 6, Springer, 2014, pp. 754–60, doi:10.1007/s10958-014-2165-8.","short":"V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner, O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.","ieee":"V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H. Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that preserves global topology,” Journal of Mathematical Sciences, vol. 203, no. 6. Springer, pp. 754–760, 2014.","apa":"Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y., Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 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Journal of Mathematical Sciences. 203(6), 754–760."},"title":"An algorithm for cartographic generalization that preserves global topology","article_processing_charge":"No","author":[{"full_name":"Alexeev, V V","last_name":"Alexeev","first_name":"V V"},{"first_name":"V G","last_name":"Bogaevskaya","full_name":"Bogaevskaya, V G"},{"full_name":"Preobrazhenskaya, M M","last_name":"Preobrazhenskaya","first_name":"M M"},{"first_name":"A Y","last_name":"Ukhalov","full_name":"Ukhalov, A Y"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Yakimova","full_name":"Yakimova, Olga","first_name":"Olga"}],"publist_id":"5165","acknowledgement":"We would like to offer our special thanks to students of the Department of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev for participation in developing the program and assistance in preparation of test data. This work was supported by grant 11.G34.31.0053 from the government of the Russian Federation.","publisher":"Springer","quality_controlled":"1","publication":"Journal of Mathematical Sciences","day":"16","year":"2014","date_created":"2018-12-11T11:54:46Z","doi":"10.1007/s10958-014-2165-8","date_published":"2014-11-16T00:00:00Z","page":"754 - 760","_id":"1929","status":"public","type":"journal_article","article_type":"original","date_updated":"2022-05-24T10:39:06Z","department":[{"_id":"HeEd"}],"oa_version":"None","abstract":[{"lang":"eng","text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales."}],"intvolume":" 203","month":"11","scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1072-3374"],"eissn":["1573-8795"]},"issue":"6","volume":203}]