--- _id: '2901' abstract: - lang: eng text: ' We introduce the M-modes problem for graphical models: predicting the M label configurations of highest probability that are at the same time local maxima of the probability landscape. M-modes have multiple possible applications: because they are intrinsically diverse, they provide a principled alternative to non-maximum suppression techniques for structured prediction, they can act as codebook vectors for quantizing the configuration space, or they can form component centers for mixture model approximation. We present two algorithms for solving the M-modes problem. The first algorithm solves the problem in polynomial time when the underlying graphical model is a simple chain. The second algorithm solves the problem for junction chains. In synthetic and real dataset, we demonstrate how M-modes can improve the performance of prediction. We also use the generated modes as a tool to understand the topography of the probability distribution of configurations, for example with relation to the training set size and amount of noise in the data. ' alternative_title: - ' JMLR: W&CP' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Zhu full_name: Yan, Zhu last_name: Yan - first_name: Dimitris full_name: Metaxas, Dimitris last_name: Metaxas - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. Computing the M most probable modes of a graphical model. In: Vol 31. JMLR; 2013:161-169.' apa: 'Chen, C., Kolmogorov, V., Yan, Z., Metaxas, D., & Lampert, C. (2013). Computing the M most probable modes of a graphical model (Vol. 31, pp. 161–169). Presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States: JMLR.' chicago: Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph Lampert. “Computing the M Most Probable Modes of a Graphical Model,” 31:161–69. JMLR, 2013. ieee: 'C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, and C. Lampert, “Computing the M most probable modes of a graphical model,” presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States, 2013, vol. 31, pp. 161–169.' ista: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. 2013. Computing the M most probable modes of a graphical model. AISTATS: Conference on Uncertainty in Artificial Intelligence, JMLR: W&CP, vol. 31, 161–169.' mla: Chen, Chao, et al. Computing the M Most Probable Modes of a Graphical Model. Vol. 31, JMLR, 2013, pp. 161–69. short: C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, JMLR, 2013, pp. 161–169. conference: end_date: 2013-05-01 location: Scottsdale, AZ, United States name: ' AISTATS: Conference on Uncertainty in Artificial Intelligence' start_date: 2013-04-29 date_created: 2018-12-11T12:00:14Z date_published: 2013-01-01T00:00:00Z date_updated: 2021-01-12T07:00:35Z day: '01' department: - _id: HeEd - _id: VlKo - _id: ChLa intvolume: ' 31' language: - iso: eng main_file_link: - open_access: '1' url: http://jmlr.org/proceedings/papers/v31/chen13a.html month: '01' oa: 1 oa_version: None page: 161 - 169 publication_status: published publisher: JMLR publist_id: '3846' quality_controlled: '1' scopus_import: 1 status: public title: Computing the M most probable modes of a graphical model type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2013' ... --- _id: '2939' abstract: - lang: eng text: In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ > 0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0, 1), the running time is O (C (1 - δ) Γ R d (n) log n), where C (1 - δ) Γ is the number of homology classes with persistence at least (1 - δ) Γ, n is the total number of simplices in the complex, d its dimension, and R d (n) is the complexity of computing the rank of an n × n matrix with O (d n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O (C (1 - δ) Γ n 2.376) algorithm, an O (C (1 - δ) Γ n 2.28) Las-Vegas algorithm, or an O (C (1 - δ) Γ n 2 + ε{lunate}) Monte-Carlo algorithm for an arbitrary ε{lunate} > 0. The space complexity of the Monte-Carlo version is bounded by O (d n) = O (n log n). acknowledgement: The authors thank Herbert Edelsbrunner for many helpful discussions and suggestions. Moreover, they are grateful for the careful reviews that helped to improve the quality of the paper. author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Chen C, Kerber M. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 2013;46(4):435-447. doi:10.1016/j.comgeo.2012.02.010' apa: 'Chen, C., & Kerber, M. (2013). An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2012.02.010' chicago: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” Computational Geometry: Theory and Applications. Elsevier, 2013. https://doi.org/10.1016/j.comgeo.2012.02.010.' ieee: 'C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,” Computational Geometry: Theory and Applications, vol. 46, no. 4. Elsevier, pp. 435–447, 2013.' ista: 'Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 46(4), 435–447.' mla: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” Computational Geometry: Theory and Applications, vol. 46, no. 4, Elsevier, 2013, pp. 435–47, doi:10.1016/j.comgeo.2012.02.010.' short: 'C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013) 435–447.' date_created: 2018-12-11T12:00:27Z date_published: 2013-05-01T00:00:00Z date_updated: 2023-02-23T11:24:10Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2012.02.010 intvolume: ' 46' issue: '4' language: - iso: eng month: '05' oa_version: None page: 435 - 447 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '3796' quality_controlled: '1' related_material: record: - id: '3367' relation: earlier_version status: public scopus_import: 1 status: public title: An output sensitive algorithm for persistent homology type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 46 year: '2013' ... --- _id: '3129' abstract: - lang: eng text: "Let K be a simplicial complex and g the rank of its p-th homology group Hp(K) defined with ℤ2 coefficients. We show that we can compute a basis H of Hp(K) and annotate each p-simplex of K with a binary vector of length g with the following property: the annotations, summed over all p-simplices in any p-cycle z, provide the coordinate vector of the homology class [z] in the basis H. The basis and the annotations for all simplices can be computed in O(n ω ) time, where n is the size of K and ω < 2.376 is a quantity so that two n×n matrices can be multiplied in O(n ω ) time. The precomputed annotations permit answering queries about the independence or the triviality of p-cycles efficiently.\r\n\r\nUsing annotations of edges in 2-complexes, we derive better algorithms for computing optimal basis and optimal homologous cycles in 1 - dimensional homology. Specifically, for computing an optimal basis of H1(K) , we improve the previously known time complexity from O(n 4) to O(n ω  + n 2 g ω − 1). Here n denotes the size of the 2-skeleton of K and g the rank of H1(K) . Computing an optimal cycle homologous to a given 1-cycle is NP-hard even for surfaces and an algorithm taking 2 O(g) nlogn time is known for surfaces. We extend this algorithm to work with arbitrary 2-complexes in O(n ω ) + 2 O(g) n 2logn time using annotations.\r\n" alternative_title: - LNCS author: - first_name: Oleksiy full_name: Busaryev, Oleksiy last_name: Busaryev - first_name: Sergio full_name: Cabello, Sergio last_name: Cabello - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Tamal full_name: Dey, Tamal last_name: Dey - first_name: Yusu full_name: Wang, Yusu last_name: Wang citation: ama: 'Busaryev O, Cabello S, Chen C, Dey T, Wang Y. Annotating simplices with a homology basis and its applications. In: Vol 7357. Springer; 2012:189-200. doi:10.1007/978-3-642-31155-0_17' apa: 'Busaryev, O., Cabello, S., Chen, C., Dey, T., & Wang, Y. (2012). Annotating simplices with a homology basis and its applications (Vol. 7357, pp. 189–200). Presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki, Finland: Springer. https://doi.org/10.1007/978-3-642-31155-0_17' chicago: Busaryev, Oleksiy, Sergio Cabello, Chao Chen, Tamal Dey, and Yusu Wang. “Annotating Simplices with a Homology Basis and Its Applications,” 7357:189–200. Springer, 2012. https://doi.org/10.1007/978-3-642-31155-0_17. ieee: 'O. Busaryev, S. Cabello, C. Chen, T. Dey, and Y. Wang, “Annotating simplices with a homology basis and its applications,” presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki, Finland, 2012, vol. 7357, pp. 189–200.' ista: 'Busaryev O, Cabello S, Chen C, Dey T, Wang Y. 2012. Annotating simplices with a homology basis and its applications. SWAT: Symposium and Workshops on Algorithm Theory, LNCS, vol. 7357, 189–200.' mla: Busaryev, Oleksiy, et al. Annotating Simplices with a Homology Basis and Its Applications. Vol. 7357, Springer, 2012, pp. 189–200, doi:10.1007/978-3-642-31155-0_17. short: O. Busaryev, S. Cabello, C. Chen, T. Dey, Y. Wang, in:, Springer, 2012, pp. 189–200. conference: end_date: 2012-07-06 location: Helsinki, Finland name: 'SWAT: Symposium and Workshops on Algorithm Theory' start_date: 2012-07-04 date_created: 2018-12-11T12:01:33Z date_published: 2012-06-19T00:00:00Z date_updated: 2021-01-12T07:41:15Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-642-31155-0_17 external_id: arxiv: - '1107.3793' intvolume: ' 7357' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1107.3793 month: '06' oa: 1 oa_version: Preprint page: 189 - 200 publication_status: published publisher: Springer publist_id: '3569' quality_controlled: '1' scopus_import: 1 status: public title: Annotating simplices with a homology basis and its applications type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7357 year: '2012' ... --- _id: '3127' abstract: - lang: eng text: "When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques.\r\n We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data, we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations." article_processing_charge: No author: - first_name: Novi full_name: Quadrianto, Novi last_name: Quadrianto - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen citation: ama: 'Quadrianto N, Lampert C, Chen C. The most persistent soft-clique in a set of sampled graphs. In: Proceedings of the 29th International Conference on Machine Learning. ML Research Press; 2012:211-218.' apa: 'Quadrianto, N., Lampert, C., & Chen, C. (2012). The most persistent soft-clique in a set of sampled graphs. In Proceedings of the 29th International Conference on Machine Learning (pp. 211–218). Edinburgh, United Kingdom: ML Research Press.' chicago: Quadrianto, Novi, Christoph Lampert, and Chao Chen. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” In Proceedings of the 29th International Conference on Machine Learning, 211–18. ML Research Press, 2012. ieee: N. Quadrianto, C. Lampert, and C. Chen, “The most persistent soft-clique in a set of sampled graphs,” in Proceedings of the 29th International Conference on Machine Learning, Edinburgh, United Kingdom, 2012, pp. 211–218. ista: 'Quadrianto N, Lampert C, Chen C. 2012. The most persistent soft-clique in a set of sampled graphs. Proceedings of the 29th International Conference on Machine Learning. ICML: International Conference on Machine Learning, 211–218.' mla: Quadrianto, Novi, et al. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 211–18. short: N. Quadrianto, C. Lampert, C. Chen, in:, Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 211–218. conference: end_date: 2012-07-01 location: Edinburgh, United Kingdom name: 'ICML: International Conference on Machine Learning' start_date: 2012-06-26 date_created: 2018-12-11T12:01:33Z date_published: 2012-06-01T00:00:00Z date_updated: 2023-10-17T11:55:06Z day: '01' department: - _id: ChLa - _id: HeEd language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1206.4652 month: '06' oa: 1 oa_version: Preprint page: 211-218 publication: Proceedings of the 29th International Conference on Machine Learning publication_status: published publisher: ML Research Press publist_id: '3572' quality_controlled: '1' scopus_import: '1' status: public title: The most persistent soft-clique in a set of sampled graphs type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '3269' abstract: - lang: eng text: The unintentional scattering of light between neighboring surfaces in complex projection environments increases the brightness and decreases the contrast, disrupting the appearance of the desired imagery. To achieve satisfactory projection results, the inverse problem of global illumination must be solved to cancel this secondary scattering. In this paper, we propose a global illumination cancellation method that minimizes the perceptual difference between the desired imagery and the actual total illumination in the resulting physical environment. Using Gauss-Newton and active set methods, we design a fast solver for the bound constrained nonlinear least squares problem raised by the perceptual error metrics. Our solver is further accelerated with a CUDA implementation and multi-resolution method to achieve 1–2 fps for problems with approximately 3000 variables. We demonstrate the global illumination cancellation algorithm with our multi-projector system. Results show that our method preserves the color fidelity of the desired imagery significantly better than previous methods. article_processing_charge: No article_type: original author: - first_name: Yu full_name: Sheng, Yu last_name: Sheng - first_name: Barbara full_name: Cutler, Barbara last_name: Cutler - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Joshua full_name: Nasman, Joshua last_name: Nasman citation: ama: Sheng Y, Cutler B, Chen C, Nasman J. Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. 2011;30(4):1261-1268. doi:10.1111/j.1467-8659.2011.01985.x apa: Sheng, Y., Cutler, B., Chen, C., & Nasman, J. (2011). Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. Wiley-Blackwell. https://doi.org/10.1111/j.1467-8659.2011.01985.x chicago: Sheng, Yu, Barbara Cutler, Chao Chen, and Joshua Nasman. “Perceptual Global Illumination Cancellation in Complex Projection Environments.” Computer Graphics Forum. Wiley-Blackwell, 2011. https://doi.org/10.1111/j.1467-8659.2011.01985.x. ieee: Y. Sheng, B. Cutler, C. Chen, and J. Nasman, “Perceptual global illumination cancellation in complex projection environments,” Computer Graphics Forum, vol. 30, no. 4. Wiley-Blackwell, pp. 1261–1268, 2011. ista: Sheng Y, Cutler B, Chen C, Nasman J. 2011. Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. 30(4), 1261–1268. mla: Sheng, Yu, et al. “Perceptual Global Illumination Cancellation in Complex Projection Environments.” Computer Graphics Forum, vol. 30, no. 4, Wiley-Blackwell, 2011, pp. 1261–68, doi:10.1111/j.1467-8659.2011.01985.x. short: Y. Sheng, B. Cutler, C. Chen, J. Nasman, Computer Graphics Forum 30 (2011) 1261–1268. date_created: 2018-12-11T12:02:22Z date_published: 2011-07-19T00:00:00Z date_updated: 2021-01-12T07:42:16Z day: '19' department: - _id: HeEd doi: 10.1111/j.1467-8659.2011.01985.x intvolume: ' 30' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://www.cs.cmu.edu/%7Eshengyu/download/egsr2011_paper.pdf month: '07' oa: 1 oa_version: Published Version page: 1261 - 1268 publication: Computer Graphics Forum publication_status: published publisher: Wiley-Blackwell publist_id: '3377' quality_controlled: '1' scopus_import: 1 status: public title: Perceptual global illumination cancellation in complex projection environments type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2011' ... --- _id: '3267' abstract: - lang: eng text: 'We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We study the problem with different measures: volume, diameter and radius. For volume, that is, the 1-norm of a cycle, two main results are presented. First, we prove that the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). The latter result leads to the inapproximability of the problem of computing the nonbounding cycle with the smallest volume and computing cycles representing a homology basis with the minimal total volume. As for the other two measures defined by pairwise geodesic distance, diameter and radius, we show that the localization problem is NP-hard for diameter but is polynomial for radius. Our work is restricted to homology over the ℤ2 field.' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman citation: ama: Chen C, Freedman D. Hardness results for homology localization. Discrete & Computational Geometry. 2011;45(3):425-448. doi:10.1007/s00454-010-9322-8 apa: Chen, C., & Freedman, D. (2011). Hardness results for homology localization. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-010-9322-8 chicago: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” Discrete & Computational Geometry. Springer, 2011. https://doi.org/10.1007/s00454-010-9322-8. ieee: C. Chen and D. Freedman, “Hardness results for homology localization,” Discrete & Computational Geometry, vol. 45, no. 3. Springer, pp. 425–448, 2011. ista: Chen C, Freedman D. 2011. Hardness results for homology localization. Discrete & Computational Geometry. 45(3), 425–448. mla: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” Discrete & Computational Geometry, vol. 45, no. 3, Springer, 2011, pp. 425–48, doi:10.1007/s00454-010-9322-8. short: C. Chen, D. Freedman, Discrete & Computational Geometry 45 (2011) 425–448. date_created: 2018-12-11T12:02:21Z date_published: 2011-01-14T00:00:00Z date_updated: 2023-02-21T16:07:10Z day: '14' department: - _id: HeEd doi: 10.1007/s00454-010-9322-8 intvolume: ' 45' issue: '3' language: - iso: eng month: '01' oa_version: None page: 425 - 448 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '3379' quality_controlled: '1' related_material: record: - id: '10909' relation: earlier_version status: public scopus_import: 1 status: public title: Hardness results for homology localization type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 45 year: '2011' ... --- _id: '3268' abstract: - lang: eng text: 'Algebraic topology is generally considered one of the purest subfield of mathematics. However, over the last decade two interesting new lines of research have emerged, one focusing on algorithms for algebraic topology, and the other on applications of algebraic topology in engineering and science. Amongst the new areas in which the techniques have been applied are computer vision and image processing. In this paper, we survey the results of these endeavours. Because algebraic topology is an area of mathematics with which most computer vision practitioners have no experience, we review the machinery behind the theories of homology and persistent homology; our review emphasizes intuitive explanations. In terms of applications to computer vision, we focus on four illustrative problems: shape signatures, natural image statistics, image denoising, and segmentation. Our hope is that this review will stimulate interest on the part of computer vision researchers to both use and extend the tools of this new field. ' alternative_title: - Computer Science, Technology and Applications author: - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen citation: ama: 'Freedman D, Chen C. Algebraic topology for computer vision. In: Computer Vision. Nova Science Publishers; 2011:239-268.' apa: Freedman, D., & Chen, C. (2011). Algebraic topology for computer vision. In Computer Vision (pp. 239–268). Nova Science Publishers. chicago: Freedman, Daniel, and Chao Chen. “Algebraic Topology for Computer Vision.” In Computer Vision, 239–68. Nova Science Publishers, 2011. ieee: D. Freedman and C. Chen, “Algebraic topology for computer vision,” in Computer Vision, Nova Science Publishers, 2011, pp. 239–268. ista: 'Freedman D, Chen C. 2011.Algebraic topology for computer vision. In: Computer Vision. Computer Science, Technology and Applications, , 239–268.' mla: Freedman, Daniel, and Chao Chen. “Algebraic Topology for Computer Vision.” Computer Vision, Nova Science Publishers, 2011, pp. 239–68. short: D. Freedman, C. Chen, in:, Computer Vision, Nova Science Publishers, 2011, pp. 239–268. date_created: 2018-12-11T12:02:22Z date_published: 2011-11-30T00:00:00Z date_updated: 2021-01-12T07:42:16Z day: '30' extern: '1' language: - iso: eng main_file_link: - url: http://www.hpl.hp.com/techreports/2009/HPL-2009-375.pdf month: '11' oa_version: None page: 239 - 268 publication: Computer Vision publication_status: published publisher: Nova Science Publishers publist_id: '3378' quality_controlled: '1' status: public title: Algebraic topology for computer vision type: book_chapter user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3367' abstract: - lang: eng text: In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ>0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0,1), the running time is O(C(1-δ)ΓR(n)log n), where C(1-δ)Γ is the number of homology classes with persistence at least (1-δ)Γ, n is the total number of simplices, and R(n) is the complexity of computing the rank of an n x n matrix with O(n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O(C(1-δ)Γn2.376) algorithm, a O(C(1-δ)Γn2.28) Las-Vegas algorithm, or a O(C(1-δ)Γn2+ε) Monte-Carlo algorithm for an arbitrary ε>0. article_processing_charge: No author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Chen C, Kerber M. An output sensitive algorithm for persistent homology. In: ACM; 2011:207-216. doi:10.1145/1998196.1998228' apa: 'Chen, C., & Kerber, M. (2011). An output sensitive algorithm for persistent homology (pp. 207–216). Presented at the SoCG: Symposium on Computational Geometry, Paris, France: ACM. https://doi.org/10.1145/1998196.1998228' chicago: Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology,” 207–16. ACM, 2011. https://doi.org/10.1145/1998196.1998228. ieee: 'C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,” presented at the SoCG: Symposium on Computational Geometry, Paris, France, 2011, pp. 207–216.' ista: 'Chen C, Kerber M. 2011. An output sensitive algorithm for persistent homology. SoCG: Symposium on Computational Geometry, 207–216.' mla: Chen, Chao, and Michael Kerber. An Output Sensitive Algorithm for Persistent Homology. ACM, 2011, pp. 207–16, doi:10.1145/1998196.1998228. short: C. Chen, M. Kerber, in:, ACM, 2011, pp. 207–216. conference: end_date: 2011-06-15 location: Paris, France name: 'SoCG: Symposium on Computational Geometry' start_date: 2011-06-13 date_created: 2018-12-11T12:02:56Z date_published: 2011-06-13T00:00:00Z date_updated: 2023-02-23T11:05:04Z day: '13' department: - _id: HeEd doi: 10.1145/1998196.1998228 language: - iso: eng month: '06' oa_version: None page: 207 - 216 publication_status: published publisher: ACM publist_id: '3245' quality_controlled: '1' related_material: record: - id: '2939' relation: later_version status: public scopus_import: 1 status: public title: An output sensitive algorithm for persistent homology type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3271' abstract: - lang: eng text: In this paper we present an efficient framework for computation of persis- tent homology of cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is adapted to the setting of cubical complexes. The proposed approach enables efficient application of persistent homology in domains where the data is naturally given in a cubical form. By avoiding triangulation of the data, we significantly reduce the size of the complex. We also present a data-structure de- signed to compactly store and quickly manipulate cubical complexes. By means of numerical experiments, we show high speed and memory efficiency of our ap- proach. We compare our framework to other available implementations, showing its superiority. Finally, we report performance on selected 3D and 4D data-sets. alternative_title: - Theory, Algorithms, and Applications author: - first_name: Hubert full_name: Wagner, Hubert last_name: Wagner - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Erald full_name: Vuçini, Erald last_name: Vuçini citation: ama: 'Wagner H, Chen C, Vuçini E. Efficient computation of persistent homology for cubical data. In: Peikert R, Hauser H, Carr H, Fuchs R, eds. Topological Methods in Data Analysis and Visualization II. Springer; 2011:91-106. doi:10.1007/978-3-642-23175-9_7' apa: Wagner, H., Chen, C., & Vuçini, E. (2011). Efficient computation of persistent homology for cubical data. In R. Peikert, H. Hauser, H. Carr, & R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II (pp. 91–106). Springer. https://doi.org/10.1007/978-3-642-23175-9_7 chicago: Wagner, Hubert, Chao Chen, and Erald Vuçini. “Efficient Computation of Persistent Homology for Cubical Data.” In Topological Methods in Data Analysis and Visualization II, edited by Ronald Peikert, Helwig Hauser, Hamish Carr, and Raphael Fuchs, 91–106. Springer, 2011. https://doi.org/10.1007/978-3-642-23175-9_7. ieee: H. Wagner, C. Chen, and E. Vuçini, “Efficient computation of persistent homology for cubical data,” in Topological Methods in Data Analysis and Visualization II, R. Peikert, H. Hauser, H. Carr, and R. Fuchs, Eds. Springer, 2011, pp. 91–106. ista: 'Wagner H, Chen C, Vuçini E. 2011.Efficient computation of persistent homology for cubical data. In: Topological Methods in Data Analysis and Visualization II. Theory, Algorithms, and Applications, , 91–106.' mla: Wagner, Hubert, et al. “Efficient Computation of Persistent Homology for Cubical Data.” Topological Methods in Data Analysis and Visualization II, edited by Ronald Peikert et al., Springer, 2011, pp. 91–106, doi:10.1007/978-3-642-23175-9_7. short: H. Wagner, C. Chen, E. Vuçini, in:, R. Peikert, H. Hauser, H. Carr, R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II, Springer, 2011, pp. 91–106. date_created: 2018-12-11T12:02:23Z date_published: 2011-11-14T00:00:00Z date_updated: 2021-01-12T07:42:18Z day: '14' department: - _id: HeEd doi: 10.1007/978-3-642-23175-9_7 editor: - first_name: Ronald full_name: Peikert, Ronald last_name: Peikert - first_name: Helwig full_name: Hauser, Helwig last_name: Hauser - first_name: Hamish full_name: Carr, Hamish last_name: Carr - first_name: Raphael full_name: Fuchs, Raphael last_name: Fuchs language: - iso: eng month: '11' oa_version: None page: 91 - 106 publication: Topological Methods in Data Analysis and Visualization II publication_status: published publisher: Springer publist_id: '3375' quality_controlled: '1' scopus_import: 1 status: public title: Efficient computation of persistent homology for cubical data type: book_chapter user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3270' abstract: - lang: eng text: 'The persistence diagram of a filtered simplicial com- plex is usually computed by reducing the boundary matrix of the complex. We introduce a simple op- timization technique: by processing the simplices of the complex in decreasing dimension, we can “kill” columns (i.e., set them to zero) without reducing them. This technique completely avoids reduction on roughly half of the columns. We demonstrate that this idea significantly improves the running time of the reduction algorithm in practice. We also give an output-sensitive complexity analysis for the new al- gorithm which yields to sub-cubic asymptotic bounds under certain assumptions.' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Chen C, Kerber M. Persistent homology computation with a twist. In: TU Dortmund; 2011:197-200.' apa: 'Chen, C., & Kerber, M. (2011). Persistent homology computation with a twist (pp. 197–200). Presented at the EuroCG: European Workshop on Computational Geometry, Morschach, Switzerland: TU Dortmund.' chicago: Chen, Chao, and Michael Kerber. “Persistent Homology Computation with a Twist,” 197–200. TU Dortmund, 2011. ieee: 'C. Chen and M. Kerber, “Persistent homology computation with a twist,” presented at the EuroCG: European Workshop on Computational Geometry, Morschach, Switzerland, 2011, pp. 197–200.' ista: 'Chen C, Kerber M. 2011. Persistent homology computation with a twist. EuroCG: European Workshop on Computational Geometry, 197–200.' mla: Chen, Chao, and Michael Kerber. Persistent Homology Computation with a Twist. TU Dortmund, 2011, pp. 197–200. short: C. Chen, M. Kerber, in:, TU Dortmund, 2011, pp. 197–200. conference: end_date: 2011-03-30 location: Morschach, Switzerland name: 'EuroCG: European Workshop on Computational Geometry' start_date: 2011-03-28 date_created: 2018-12-11T12:02:22Z date_published: 2011-01-01T00:00:00Z date_updated: 2021-01-12T07:42:17Z day: '01' department: - _id: HeEd language: - iso: eng month: '01' oa_version: None page: 197 - 200 publication_status: published publisher: TU Dortmund publist_id: '3376' quality_controlled: '1' status: public title: Persistent homology computation with a twist type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3313' abstract: - lang: eng text: Interpreting an image as a function on a compact sub- set of the Euclidean plane, we get its scale-space by diffu- sion, spreading the image over the entire plane. This gener- ates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian ker- nel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods. article_number: '6126271' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Chen C, Edelsbrunner H. Diffusion runs low on persistence fast. In: Proceedings of the IEEE International Conference on Computer Vision. IEEE; 2011. doi:10.1109/ICCV.2011.6126271' apa: 'Chen, C., & Edelsbrunner, H. (2011). Diffusion runs low on persistence fast. In Proceedings of the IEEE International Conference on Computer Vision. Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126271' chicago: Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.” In Proceedings of the IEEE International Conference on Computer Vision. IEEE, 2011. https://doi.org/10.1109/ICCV.2011.6126271. ieee: C. Chen and H. Edelsbrunner, “Diffusion runs low on persistence fast,” in Proceedings of the IEEE International Conference on Computer Vision, Barcelona, Spain, 2011. ista: 'Chen C, Edelsbrunner H. 2011. Diffusion runs low on persistence fast. Proceedings of the IEEE International Conference on Computer Vision. ICCV: International Conference on Computer Vision, 6126271.' mla: Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.” Proceedings of the IEEE International Conference on Computer Vision, 6126271, IEEE, 2011, doi:10.1109/ICCV.2011.6126271. short: C. Chen, H. Edelsbrunner, in:, Proceedings of the IEEE International Conference on Computer Vision, IEEE, 2011. conference: end_date: 2011-11-13 location: Barcelona, Spain name: 'ICCV: International Conference on Computer Vision' start_date: 2011-11-06 date_created: 2018-12-11T12:02:37Z date_published: 2011-11-06T00:00:00Z date_updated: 2021-01-12T07:42:35Z day: '06' ddc: - '000' department: - _id: HeEd doi: 10.1109/ICCV.2011.6126271 file: - access_level: open_access checksum: 6984684081ba123808b344f9f2e64a8f content_type: application/pdf creator: system date_created: 2018-12-12T10:17:28Z date_updated: 2020-07-14T12:46:07Z file_id: '5282' file_name: IST-2016-540-v1+1_2011-P-08-RunEmpty.pdf file_size: 614050 relation: main_file file_date_updated: 2020-07-14T12:46:07Z has_accepted_license: '1' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version publication: Proceedings of the IEEE International Conference on Computer Vision publication_status: published publisher: IEEE publist_id: '3327' pubrep_id: '540' quality_controlled: '1' scopus_import: 1 status: public title: Diffusion runs low on persistence fast type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '5386' abstract: - lang: eng text: 'We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.' alternative_title: - IST Austria Technical Report author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: Chen C, Freedman D, Lampert C. Enforcing Topological Constraints in Random Field Image Segmentation. IST Austria; 2011. doi:10.15479/AT:IST-2011-0002 apa: Chen, C., Freedman, D., & Lampert, C. (2011). Enforcing topological constraints in random field image segmentation. IST Austria. https://doi.org/10.15479/AT:IST-2011-0002 chicago: Chen, Chao, Daniel Freedman, and Christoph Lampert. Enforcing Topological Constraints in Random Field Image Segmentation. IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0002. ieee: C. Chen, D. Freedman, and C. Lampert, Enforcing topological constraints in random field image segmentation. IST Austria, 2011. ista: Chen C, Freedman D, Lampert C. 2011. Enforcing topological constraints in random field image segmentation, IST Austria, 69p. mla: Chen, Chao, et al. Enforcing Topological Constraints in Random Field Image Segmentation. IST Austria, 2011, doi:10.15479/AT:IST-2011-0002. short: C. Chen, D. Freedman, C. Lampert, Enforcing Topological Constraints in Random Field Image Segmentation, IST Austria, 2011. date_created: 2018-12-12T11:39:02Z date_published: 2011-03-28T00:00:00Z date_updated: 2023-02-23T11:22:48Z day: '28' ddc: - '000' department: - _id: ChLa doi: 10.15479/AT:IST-2011-0002 file: - access_level: open_access checksum: ad64c2add5fe2ad10e9d5c669f3f9526 content_type: application/pdf creator: system date_created: 2018-12-12T11:53:34Z date_updated: 2020-07-14T12:46:41Z file_id: '5495' file_name: IST-2011-0002_IST-2011-0002.pdf file_size: 26390601 relation: main_file file_date_updated: 2020-07-14T12:46:41Z has_accepted_license: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: '69' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '22' related_material: record: - id: '3336' relation: later_version status: public status: public title: Enforcing topological constraints in random field image segmentation type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3336' abstract: - lang: eng text: 'We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.' acknowledgement: The first author is supported by the Austrian Science Fund (FWF) grant No. P20134-N13. The authors would like to thank Sebastian Nowozin for helpful discussions. article_processing_charge: No author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Chen C, Freedman D, Lampert C. Enforcing topological constraints in random field image segmentation. In: CVPR: Computer Vision and Pattern Recognition. IEEE; 2011:2089-2096. doi:10.1109/CVPR.2011.5995503' apa: 'Chen, C., Freedman, D., & Lampert, C. (2011). Enforcing topological constraints in random field image segmentation. In CVPR: Computer Vision and Pattern Recognition (pp. 2089–2096). Colorado Springs, CO, United States: IEEE. https://doi.org/10.1109/CVPR.2011.5995503' chicago: 'Chen, Chao, Daniel Freedman, and Christoph Lampert. “Enforcing Topological Constraints in Random Field Image Segmentation.” In CVPR: Computer Vision and Pattern Recognition, 2089–96. IEEE, 2011. https://doi.org/10.1109/CVPR.2011.5995503.' ieee: 'C. Chen, D. Freedman, and C. Lampert, “Enforcing topological constraints in random field image segmentation,” in CVPR: Computer Vision and Pattern Recognition, Colorado Springs, CO, United States, 2011, pp. 2089–2096.' ista: 'Chen C, Freedman D, Lampert C. 2011. Enforcing topological constraints in random field image segmentation. CVPR: Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition, 2089–2096.' mla: 'Chen, Chao, et al. “Enforcing Topological Constraints in Random Field Image Segmentation.” CVPR: Computer Vision and Pattern Recognition, IEEE, 2011, pp. 2089–96, doi:10.1109/CVPR.2011.5995503.' short: 'C. Chen, D. Freedman, C. Lampert, in:, CVPR: Computer Vision and Pattern Recognition, IEEE, 2011, pp. 2089–2096.' conference: end_date: 2011-06-25 location: Colorado Springs, CO, United States name: 'CVPR: Conference on Computer Vision and Pattern Recognition' start_date: 2011-06-20 date_created: 2018-12-11T12:02:45Z date_published: 2011-07-22T00:00:00Z date_updated: 2023-02-23T12:23:56Z day: '22' department: - _id: HeEd - _id: ChLa doi: 10.1109/CVPR.2011.5995503 language: - iso: eng month: '07' oa_version: None page: 2089 - 2096 publication: 'CVPR: Computer Vision and Pattern Recognition' publication_identifier: eisbn: - 978-1-4577-0395-9 isbn: - 978-1-4577-0394-2 publication_status: published publisher: IEEE publist_id: '3294' quality_controlled: '1' related_material: record: - id: '5386' relation: earlier_version status: public scopus_import: '1' status: public title: Enforcing topological constraints in random field image segmentation type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '10909' abstract: - lang: eng text: We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We focus on the volume measure, that is, the 1-norm of a cycle. Two main results are presented. First, we prove the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). A side effect is the inapproximability of the problem of computing the nonbounding cycle with the smallest volume, and computing cycles representing a homology basis with the minimal total volume. We also discuss other geometric measures (diameter and radius) and show their disadvantages in homology localization. Our work is restricted to homology over the ℤ2 field. acknowledgement: Partially supported by the Austrian Science Fund under grantFSP-S9103-N04 and P20134-N13. article_processing_charge: No author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman citation: ama: 'Chen C, Freedman D. Hardness results for homology localization. In: Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics; 2010:1594-1604. doi:10.1137/1.9781611973075.129' apa: 'Chen, C., & Freedman, D. (2010). Hardness results for homology localization. In Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1594–1604). Austin, TX, United States: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973075.129' chicago: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” In Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, 1594–1604. Society for Industrial and Applied Mathematics, 2010. https://doi.org/10.1137/1.9781611973075.129. ieee: C. Chen and D. Freedman, “Hardness results for homology localization,” in Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, Austin, TX, United States, 2010, pp. 1594–1604. ista: 'Chen C, Freedman D. 2010. Hardness results for homology localization. Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 1594–1604.' mla: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2010, pp. 1594–604, doi:10.1137/1.9781611973075.129. short: C. Chen, D. Freedman, in:, Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2010, pp. 1594–1604. conference: end_date: 2010-01-19 location: Austin, TX, United States name: 'SODA: Symposium on Discrete Algorithms' start_date: 2010-01-17 date_created: 2022-03-21T08:24:07Z date_published: 2010-02-01T00:00:00Z date_updated: 2023-02-23T11:19:46Z day: '01' department: - _id: HeEd doi: 10.1137/1.9781611973075.129 language: - iso: eng month: '02' oa_version: None page: 1594-1604 publication: Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms publication_identifier: eisbn: - '9781611973075' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '3267' relation: later_version status: public scopus_import: '1' status: public title: Hardness results for homology localization type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2010' ... --- _id: '3782' abstract: - lang: eng text: In cortex surface segmentation, the extracted surface is required to have a particular topology, namely, a two-sphere. We present a new method for removing topology noise of a curve or surface within the level set framework, and thus produce a cortical surface with correct topology. We define a new energy term which quantifies topology noise. We then show how to minimize this term by computing its functional derivative with respect to the level set function. This method differs from existing methods in that it is inherently continuous and not digital; and in the way that our energy directly relates to the topology of the underlying curve or surface, versus existing knot-based measures which are related in a more indirect fashion. The proposed flow is validated empirically. acknowledgement: "Partially supported by the Austri an Science Fund unde r grant P20134-N13.\r\nWe thank Helena Molina-Abril for very helpful discussion. We thank anonymous reviewers for helpful comments." alternative_title: - LNCS author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman citation: ama: 'Chen C, Freedman D. Topology noise removal for curve  and surface evolution. In: Conference Proceedings MCV 2010. Vol 6533. Springer; 2010:31-42. doi:10.1007/978-3-642-18421-5_4' apa: 'Chen, C., & Freedman, D. (2010). Topology noise removal for curve  and surface evolution. In Conference proceedings MCV 2010 (Vol. 6533, pp. 31–42). Beijing, China: Springer. https://doi.org/10.1007/978-3-642-18421-5_4' chicago: Chen, Chao, and Daniel Freedman. “Topology Noise Removal for Curve  and Surface Evolution.” In Conference Proceedings MCV 2010, 6533:31–42. Springer, 2010. https://doi.org/10.1007/978-3-642-18421-5_4. ieee: C. Chen and D. Freedman, “Topology noise removal for curve  and surface evolution,” in Conference proceedings MCV 2010, Beijing, China, 2010, vol. 6533, pp. 31–42. ista: 'Chen C, Freedman D. 2010. Topology noise removal for curve  and surface evolution. Conference proceedings MCV 2010. MCV: Medical Computer Vision, LNCS, vol. 6533, 31–42.' mla: Chen, Chao, and Daniel Freedman. “Topology Noise Removal for Curve  and Surface Evolution.” Conference Proceedings MCV 2010, vol. 6533, Springer, 2010, pp. 31–42, doi:10.1007/978-3-642-18421-5_4. short: C. Chen, D. Freedman, in:, Conference Proceedings MCV 2010, Springer, 2010, pp. 31–42. conference: end_date: 2010-09-20 location: Beijing, China name: 'MCV: Medical Computer Vision' start_date: 2010-09-20 date_created: 2018-12-11T12:05:08Z date_published: 2010-12-31T00:00:00Z date_updated: 2021-01-12T07:52:10Z day: '31' department: - _id: HeEd doi: 10.1007/978-3-642-18421-5_4 intvolume: ' 6533' language: - iso: eng month: '12' oa_version: None page: 31 - 42 publication: ' Conference proceedings MCV 2010' publication_status: published publisher: Springer publist_id: '2445' quality_controlled: '1' scopus_import: 1 status: public title: Topology noise removal for curve and surface evolution type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 6533 year: '2010' ...