--- _id: '481' abstract: - lang: eng text: We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist. Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings. acknowledgement: 'Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.' author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229. doi:10.1142/S0218195916600050 apa: Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195916600050 chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050. ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017. ista: Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 26(3–4), 211–229. mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050. short: T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229. date_created: 2018-12-11T11:46:43Z date_published: 2017-04-13T00:00:00Z date_updated: 2023-02-21T16:06:22Z day: '13' ddc: - '004' - '514' - '516' department: - _id: HeEd doi: 10.1142/S0218195916600050 file: - access_level: open_access checksum: f79e8558bfe4b368dfefeb8eec2e3a5e content_type: application/pdf creator: system date_created: 2018-12-12T10:09:34Z date_updated: 2020-07-14T12:46:35Z file_id: '4758' file_name: IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf file_size: 769296 relation: main_file file_date_updated: 2020-07-14T12:46:35Z has_accepted_license: '1' intvolume: ' 26' issue: 3-4 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 211 - 229 publication: International Journal of Computational Geometry and Applications publication_status: published publisher: World Scientific Publishing publist_id: '7338' pubrep_id: '949' quality_controlled: '1' related_material: record: - id: '10892' relation: earlier_version status: public scopus_import: 1 status: public title: Planar matchings for weighted straight skeletons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2017' ... --- _id: '1272' abstract: - lang: eng text: We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams. acknowledgement: 'This work was supported by Austrian Science Fund (FWF): P25816-N15.' author: - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 2016;13(5):712-721. doi:10.1080/16864360.2016.1150718 apa: Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718 chicago: Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications. Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718. ieee: M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” Computer-Aided Design and Applications, vol. 13, no. 5. Taylor and Francis, pp. 712–721, 2016. ista: Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721. mla: Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis, 2016, pp. 712–21, doi:10.1080/16864360.2016.1150718. short: M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721. date_created: 2018-12-11T11:51:04Z date_published: 2016-09-02T00:00:00Z date_updated: 2021-01-12T06:49:32Z day: '02' ddc: - '004' - '516' department: - _id: HeEd doi: 10.1080/16864360.2016.1150718 file: - access_level: open_access checksum: c746f3a48edb62b588d92ea5d0fd2c0e content_type: application/pdf creator: system date_created: 2018-12-12T10:16:20Z date_updated: 2020-07-14T12:44:42Z file_id: '5206' file_name: IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf file_size: 1678369 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 13' issue: '5' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '09' oa: 1 oa_version: Published Version page: 712 - 721 publication: Computer-Aided Design and Applications publication_status: published publisher: Taylor and Francis publist_id: '6048' pubrep_id: '694' quality_controlled: '1' scopus_import: 1 status: public title: Generalized offsetting of planar structures using skeletons tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 13 year: '2016' ... --- _id: '1424' abstract: - lang: eng text: We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data. acknowledgement: This work was partially supported by the Austrian Science FUnd, project no. KLI 00012. alternative_title: - Advances in Neural Information Processing Systems author: - first_name: Roland full_name: Kwitt, Roland last_name: Kwitt - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Marc full_name: Niethammer, Marc last_name: Niethammer - first_name: Weili full_name: Lin, Weili last_name: Lin - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 citation: ama: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems; 2015:3070-3078.' apa: 'Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information Processing Systems.' chicago: Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer. “Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural Information Processing Systems, 2015. ieee: 'R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological data analysis-A kernel perspective,” presented at the NIPS: Neural Information Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.' ista: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological data analysis-A kernel perspective. NIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 28, 3070–3078.' mla: Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective. Vol. 28, Neural Information Processing Systems, 2015, pp. 3070–78. short: R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information Processing Systems, 2015, pp. 3070–3078. conference: end_date: 2015-12-12 location: Montreal, Canada name: 'NIPS: Neural Information Processing Systems' start_date: 2015-12-07 date_created: 2018-12-11T11:51:56Z date_published: 2015-12-01T00:00:00Z date_updated: 2021-01-12T06:50:38Z day: '01' department: - _id: HeEd intvolume: ' 28' language: - iso: eng main_file_link: - open_access: '1' url: https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective month: '12' oa: 1 oa_version: Submitted Version page: 3070 - 3078 publication_status: published publisher: Neural Information Processing Systems publist_id: '5782' quality_controlled: '1' status: public title: Statistical topological data analysis-A kernel perspective type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2015' ... --- _id: '1483' abstract: - lang: eng text: Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes. author: - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Roland full_name: Kwitt, Roland last_name: Kwitt citation: ama: 'Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106' apa: 'Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106' chicago: Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106. ieee: 'J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.' ista: 'Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.' mla: Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106. short: J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748. conference: end_date: 2015-06-12 location: Boston, MA, USA name: 'CVPR: Computer Vision and Pattern Recognition' start_date: 2015-06-07 date_created: 2018-12-11T11:52:17Z date_published: 2015-10-14T00:00:00Z date_updated: 2021-01-12T06:51:03Z day: '14' department: - _id: HeEd doi: 10.1109/CVPR.2015.7299106 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1412.6821 month: '10' oa: 1 oa_version: Preprint page: 4741 - 4748 publication_identifier: eisbn: - '978-1-4673-6964-0 ' publication_status: published publisher: IEEE publist_id: '5709' scopus_import: 1 status: public title: A stable multi-scale kernel for topological machine learning type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ... --- _id: '1584' abstract: - lang: eng text: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442.' mla: 'Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.' date_created: 2018-12-11T11:52:51Z date_published: 2015-07-01T00:00:00Z date_updated: 2023-02-23T10:05:22Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.01.004 file: - access_level: open_access checksum: 5b33719a86f7f4c8e5dc62c1b6893f49 content_type: application/pdf creator: system date_created: 2018-12-12T10:17:36Z date_updated: 2020-07-14T12:45:03Z file_id: '5292' file_name: IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf file_size: 508379 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 48' issue: '5' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 429 - 442 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5587' pubrep_id: '475' quality_controlled: '1' related_material: record: - id: '1582' relation: other status: public scopus_import: 1 status: public title: 'Reprint of: Weighted straight skeletons in the plane' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1582' abstract: - lang: eng text: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133. doi:10.1016/j.comgeo.2014.08.006' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133.' mla: 'Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:10.1016/j.comgeo.2014.08.006.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.' date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2023-02-23T10:05:27Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2014.08.006 file: - access_level: open_access checksum: c1ef67f6ec925e12f73a96b8fe285ab4 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:28Z date_updated: 2020-07-14T12:45:02Z file_id: '5215' file_name: IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf file_size: 505987 relation: main_file file_date_updated: 2020-07-14T12:45:02Z has_accepted_license: '1' intvolume: ' 48' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 120 - 133 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5589' pubrep_id: '474' quality_controlled: '1' related_material: record: - id: '1584' relation: other status: public scopus_import: 1 status: public title: Weighted straight skeletons in the plane tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1583' abstract: - lang: eng text: We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021 apa: Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021 chicago: Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021. ieee: T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” Information Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015. ista: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247. mla: Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021. short: T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247. date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2021-01-12T06:51:45Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.ipl.2014.09.021 file: - access_level: open_access checksum: 2779a648610c9b5c86d0b51a62816d23 content_type: application/pdf creator: system date_created: 2018-12-12T10:18:45Z date_updated: 2020-07-14T12:45:03Z file_id: '5367' file_name: IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf file_size: 270137 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 115' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 243 - 247 publication: Information Processing Letters publication_status: published publisher: Elsevier publist_id: '5588' pubrep_id: '473' quality_controlled: '1' scopus_import: 1 status: public title: A simple algorithm for computing positively weighted straight skeletons of monotone polygons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 115 year: '2015' ... --- _id: '1590' abstract: - lang: eng text: 'The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Thomas full_name: Hackl, Thomas last_name: Hackl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber citation: ama: 'Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28' apa: 'Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., & Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28' chicago: Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28. ieee: O. Aichholzer et al., “Representing directed trees as straight skeletons,” in Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–347. ista: 'Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.' mla: Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:10.1007/978-3-319-27261-0_28. short: O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347. conference: end_date: 2015-09-26 location: Los Angeles, CA, United States name: 'GD: International Symposium on Graph Drawing' start_date: 2015-09-24 date_created: 2018-12-11T11:52:54Z date_published: 2015-11-27T00:00:00Z date_updated: 2022-01-28T09:10:37Z day: '27' department: - _id: HeEd doi: 10.1007/978-3-319-27261-0_28 intvolume: ' 9411' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1508.01076 month: '11' oa: 1 oa_version: Preprint page: 335 - 347 publication: Graph Drawing and Network Visualization publication_identifier: eisbn: - 978-3-319-27261-0 isbn: - 978-3-319-27260-3 publication_status: published publisher: Springer Nature publist_id: '5581' quality_controlled: '1' scopus_import: '1' status: public title: Representing directed trees as straight skeletons type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9411 year: '2015' ... --- _id: '1816' 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. acknowledgement: 'Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.' author: - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Peter full_name: Meerwald, Peter last_name: Meerwald - first_name: Roland full_name: Kwitt, Roland last_name: Kwitt citation: 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 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 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. 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. 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. short: S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86. date_created: 2018-12-11T11:54:10Z date_published: 2014-03-16T00:00:00Z date_updated: 2021-01-12T06:53:23Z day: '16' ddc: - '000' department: - _id: HeEd doi: 10.1142/S0218195914500034 file: - access_level: open_access checksum: be45c133ab4d43351260e21beaa8f4b1 content_type: application/pdf creator: system date_created: 2018-12-12T10:08:43Z date_updated: 2020-07-14T12:45:17Z file_id: '4704' file_name: IST-2016-443-v1+1_S0218195914500034.pdf file_size: 991734 relation: main_file file_date_updated: 2020-07-14T12:45:17Z has_accepted_license: '1' intvolume: ' 24' issue: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 61 - 86 publication: International Journal of Computational Geometry and Applications publication_status: published publisher: World Scientific Publishing publist_id: '5290' pubrep_id: '443' quality_controlled: '1' scopus_import: 1 status: public title: Topology-preserving watermarking of vector graphics tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2014' ... --- _id: '10892' abstract: - lang: eng text: "In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.\r\nUsing our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings." acknowledgement: 'T. Biedl was supported by NSERC and the Ross and Muriel Cheriton Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature; 2014:117-127. doi:10.1007/978-3-319-13075-0_10' apa: 'Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889, pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10' chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” In 25th International Symposium, ISAAC 2014, 8889:117–27. Springer Nature, 2014. https://doi.org/10.1007/978-3-319-13075-0_10. ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” in 25th International Symposium, ISAAC 2014, Jeonju, Korea, 2014, vol. 8889, pp. 117–127. ista: 'Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 8889, 117–127.' mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” 25th International Symposium, ISAAC 2014, vol. 8889, Springer Nature, 2014, pp. 117–27, doi:10.1007/978-3-319-13075-0_10. short: T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127. conference: end_date: 2014-12-17 location: Jeonju, Korea name: 'ISAAC: International Symposium on Algorithms and Computation' start_date: 2014-12-15 date_created: 2022-03-21T07:09:03Z date_published: 2014-11-08T00:00:00Z date_updated: 2023-02-23T12:20:55Z day: '08' department: - _id: HeEd doi: 10.1007/978-3-319-13075-0_10 intvolume: ' 8889' language: - iso: eng month: '11' oa_version: None page: 117-127 publication: 25th International Symposium, ISAAC 2014 publication_identifier: eisbn: - '9783319130750' eissn: - 1611-3349 isbn: - '9783319130743' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '481' relation: later_version status: public scopus_import: '1' status: public title: Planar matchings for weighted straight skeletons type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8889 year: '2014' ... --- _id: '2209' abstract: - lang: eng text: "A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straight-line graph for which this was the straight skeleton? We show how to reduce this problem to the problem of finding a line that intersects a set of convex polygons. We can find these convex polygons and all such lines in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number of edges of the input graph. We also explain how our approach can be used for recognizing Voronoi diagrams of points, thereby completing a partial solution provided by Ash and Bolker in 1985.\r\n" alternative_title: - '2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) ' author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 citation: ama: 'Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: IEEE; 2013:37-46. doi:10.1109/ISVD.2013.11' apa: 'Biedl, T., Held, M., & Huber, S. (2013). Recognizing straight skeletons and Voronoi diagrams and reconstructing their input (pp. 37–46). Presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia: IEEE. https://doi.org/10.1109/ISVD.2013.11' chicago: Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. https://doi.org/10.1109/ISVD.2013.11. ieee: 'T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.' ista: 'Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) , , 37–46.' mla: Biedl, Therese, et al. Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input. IEEE, 2013, pp. 37–46, doi:10.1109/ISVD.2013.11. short: T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46. conference: end_date: 2013-07-10 location: St. Petersburg, Russia name: 'ISVD: Voronoi Diagrams in Science and Engineering' start_date: 2013-07-08 date_created: 2018-12-11T11:56:20Z date_published: 2013-12-01T00:00:00Z date_updated: 2021-01-12T06:56:00Z day: '01' department: - _id: HeEd doi: 10.1109/ISVD.2013.11 language: - iso: eng month: '12' oa_version: None page: 37 - 46 publication_identifier: eisbn: - '978-0-7695-5037-4 ' publication_status: published publisher: IEEE publist_id: '4763' quality_controlled: '1' scopus_import: 1 status: public title: Recognizing straight skeletons and Voronoi diagrams and reconstructing their input type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ... --- _id: '2210' abstract: - lang: eng text: 'A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon. In this paper, we ask the reverse question: Given the straight skeleton (in form of a tree with a drawing in the plane, but with the exact position of the leaves unspecified), can we reconstruct the polygon? We show that in most cases there exists at most one polygon; in the remaining case there is an infinite number of polygons determined by one angle that can range in an interval. We can find this (set of) polygon(s) in linear time in the Real RAM computer model.' author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 citation: ama: 'Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons. In: 29th European Workshop on Computational Geometry. TU Braunschweig; 2013:95-98.' apa: 'Biedl, T., Held, M., & Huber, S. (2013). Reconstructing polygons from embedded straight skeletons. In 29th European Workshop on Computational Geometry (pp. 95–98). Braunschweig, Germany: TU Braunschweig.' chicago: Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons from Embedded Straight Skeletons.” In 29th European Workshop on Computational Geometry, 95–98. TU Braunschweig, 2013. ieee: T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight skeletons,” in 29th European Workshop on Computational Geometry, Braunschweig, Germany, 2013, pp. 95–98. ista: 'Biedl T, Held M, Huber S. 2013. Reconstructing polygons from embedded straight skeletons. 29th European Workshop on Computational Geometry. EuroCG: European Workshop on Computational Geometry, 95–98.' mla: Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.” 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98. short: T. Biedl, M. Held, S. Huber, in:, 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98. conference: end_date: 2013-03-20 location: Braunschweig, Germany name: 'EuroCG: European Workshop on Computational Geometry' start_date: 2013-03-17 date_created: 2018-12-11T11:56:21Z date_published: 2013-03-01T00:00:00Z date_updated: 2021-01-12T06:56:00Z day: '01' department: - _id: HeEd language: - iso: eng main_file_link: - open_access: '1' url: http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf month: '03' oa: 1 oa_version: Submitted Version page: 95 - 98 publication: 29th European Workshop on Computational Geometry publication_status: published publisher: TU Braunschweig publist_id: '4762' status: public title: Reconstructing polygons from embedded straight skeletons type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ...