Noise-Adaptive Shape Reconstruction from Raw Point Sets
We propose a noise‐adaptive shape reconstruction method specialized to smooth, closed shapes. Our algorithm takes as input a defect‐laden point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noise‐adaptive distance function to the inferred shape, whic...
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| Published in | Computer graphics forum Vol. 32; no. 5; pp. 229 - 238 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford, UK
Blackwell Publishing Ltd
01.08.2013
Wiley |
| Subjects | |
| Online Access | Get full text |
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| Abstract | We propose a noise‐adaptive shape reconstruction method specialized to smooth, closed shapes. Our algorithm takes as input a defect‐laden point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noise‐adaptive distance function to the inferred shape, which relies on the assumption that the inferred shape is a smooth submanifold of known dimension. Second, we estimate the sign and confidence of the function at a set of seed points, through minimizing a quadratic energy expressed on the edges of a uniform random graph. Third, we compute a signed implicit function through a random walker approach with soft constraints chosen as the most confident seed points computed in previous step. |
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| AbstractList | We propose a noise-adaptive shape reconstruction method specialized to smooth, closed shapes. Our algorithm takes as input a defect-laden point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noise-adaptive distance function to the inferred shape, which relies on the assumption that the inferred shape is a smooth submanifold of known dimension. Second, we estimate the sign and confidence of the function at a set of seed points, through minimizing a quadratic energy expressed on the edges of a uniform random graph. Third, we compute a signed implicit function through a random walker approach with soft constraints chosen as the most confident seed points computed in previous step. We propose a noise-adaptive shape reconstruction method specialized to smooth, closed shapes. Our algorithm takes as input a defect-laden point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noise-adaptive distance function to the inferred shape, which relies on the assumption that the inferred shape is a smooth submanifold of known dimension. Second, we estimate the sign and confidence of the function at a set of seed points, through minimizing a quadratic energy expressed on the edges of a uniform random graph. Third, we compute a signed implicit function through a random walker approach with soft constraints chosen as the most confident seed points computed in previous step. [PUBLICATION ABSTRACT] |
| Author | Giraudot, Simon Alliez, Pierre Cohen-Steiner, David |
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| Cites_doi | 10.1007/s10208-011-9098-0 10.1016/j.comgeo.2005.10.006 10.1109/TPAMI.2006.233 10.1109/3DIMPVT.2012.84 10.1109/TVCG.2009.13 10.1016/j.comgeo.2006.11.008 10.1145/1882261.1866176 10.1111/j.1467-8659.2011.02030.x 10.1145/1057432.1057434 10.1111/j.1467-8659.2010.01782.x 10.1007/s00371-009-0395-4 10.1145/1857907.1857911 10.1142/S0218195910003438 10.1111/j.1467-8659.2012.03060.x 10.1111/j.1467-8659.2012.03174.x |
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| Copyright | 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd. Distributed under a Creative Commons Attribution 4.0 International License |
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| References | Wang H., Scheidegger C. E., Silva C.: Bandwidth selection and reconstruction quality in point-based surfaces. IEEE Transactions on Visualization and Computer Graphics 15, 4 (2009), 572-582. Berger M., Silva C.: Medial kernels. Computer Graphics Forum 31 (2012), 795-804. Grady L.: Random walks for image segmentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on 28, 11 (2006), 1768-1783. Tagliasacchi A., Olson M., Zhang H., Hamarneh G., Cohen-Or D.: Vase: Volume-aware surface evolution for surface reconstruction from incomplete point clouds. Computer Graphics Forum 30, 5 (2011), 1563-1571. Avron H., Sharf A., Greif C., Cohen-Or D.: L1-sparse reconstruction of sharp point set surfaces. ACM Transactions on Graphics 29 (November 2010), 135:1-135:12. Sotoodeh S.: Outlier detection in laser scanner point clouds. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 5 (2006), 297-302. Shalom S., Shamir A., Zhang H., Cohen-Or D.: Cone carving for surface reconstruction. ACM Transactions on Graphics 29, 6 (Dec. 2010), 150:1-150:10. Unnikrishnan R., Lalonde J.-F., Vandapel N., Hebert M.: Scale selection for geometric fitting in noisy point clouds. International Journal on Computational Geometry and Applications 20, 5 (October 2010). Dey T. K., Goswami S.: Provable surface reconstruction from noisy samples. Comput. Geom. Theory Appl. 35, 1 (Aug. 2006), 124-141. Song Y.: Boundary fitting for 2D curve reconstruction. The Visual Computer 26 (2010), 187-204. Mullen P., De Goes F., Desbrun M., Cohen-Steiner D., Alliez P.: Signing the unsigned: Robust surface reconstruction from raw pointsets. Computer Graphics Forum 29, 5 (2010), 1733-1741. Proceedings of EUROGRAPHICS Symposium on Geometry Processing. Chazal F., Cohen-Steiner D., Mérigot Q.: Geometric inference for probability measures. Foundations of Computational Mathematics 11, 6 (2011), 733-751. July 2012 2010; 11 2010; 26 Dec. 2010; 29 2012 2010 2010; 29 Aug. 2006; 35 2006; 28 October 2010; 20 2011; 30 2011; 11 2007 2006; 5 2006 2004 2002 November 2010; 29 2012; 31 2009; 15 e_1_2_7_5_2 Sotoodeh S. (e_1_2_7_19_2) 2006; 5 Unnikrishnan R. (e_1_2_7_22_2) 2010; 20 e_1_2_7_4_2 e_1_2_7_3_2 e_1_2_7_2_2 e_1_2_7_9_2 e_1_2_7_8_2 e_1_2_7_7_2 e_1_2_7_6_2 e_1_2_7_18_2 e_1_2_7_17_2 e_1_2_7_16_2 e_1_2_7_15_2 e_1_2_7_14_2 e_1_2_7_13_2 e_1_2_7_12_2 e_1_2_7_23_2 e_1_2_7_11_2 e_1_2_7_10_2 e_1_2_7_21_2 e_1_2_7_20_2 |
| References_xml | – reference: Grady L.: Random walks for image segmentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on 28, 11 (2006), 1768-1783. – reference: Wang H., Scheidegger C. E., Silva C.: Bandwidth selection and reconstruction quality in point-based surfaces. IEEE Transactions on Visualization and Computer Graphics 15, 4 (2009), 572-582. – reference: Berger M., Silva C.: Medial kernels. Computer Graphics Forum 31 (2012), 795-804. – reference: Mullen P., De Goes F., Desbrun M., Cohen-Steiner D., Alliez P.: Signing the unsigned: Robust surface reconstruction from raw pointsets. Computer Graphics Forum 29, 5 (2010), 1733-1741. Proceedings of EUROGRAPHICS Symposium on Geometry Processing. – reference: Song Y.: Boundary fitting for 2D curve reconstruction. The Visual Computer 26 (2010), 187-204. – reference: Avron H., Sharf A., Greif C., Cohen-Or D.: L1-sparse reconstruction of sharp point set surfaces. ACM Transactions on Graphics 29 (November 2010), 135:1-135:12. – reference: Sotoodeh S.: Outlier detection in laser scanner point clouds. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 5 (2006), 297-302. – reference: Chazal F., Cohen-Steiner D., Mérigot Q.: Geometric inference for probability measures. Foundations of Computational Mathematics 11, 6 (2011), 733-751. – reference: Dey T. K., Goswami S.: Provable surface reconstruction from noisy samples. Comput. Geom. Theory Appl. 35, 1 (Aug. 2006), 124-141. – reference: Unnikrishnan R., Lalonde J.-F., Vandapel N., Hebert M.: Scale selection for geometric fitting in noisy point clouds. International Journal on Computational Geometry and Applications 20, 5 (October 2010). – reference: Tagliasacchi A., Olson M., Zhang H., Hamarneh G., Cohen-Or D.: Vase: Volume-aware surface evolution for surface reconstruction from incomplete point clouds. Computer Graphics Forum 30, 5 (2011), 1563-1571. – reference: Shalom S., Shamir A., Zhang H., Cohen-Or D.: Cone carving for surface reconstruction. ACM Transactions on Graphics 29, 6 (Dec. 2010), 150:1-150:10. – start-page: 11 year: 2004 end-page: 21 – volume: 29 start-page: 135:1 year: November 2010 end-page: 135:12 article-title: L1‐sparse reconstruction of sharp point set surfaces publication-title: ACM Transactions on Graphics – volume: 30 start-page: 1563 issue: 5 year: 2011 end-page: 1571 article-title: Vase: Volume‐aware surface evolution for surface reconstruction from incomplete point clouds publication-title: Computer Graphics Forum – start-page: 524 year: 2012 end-page: 530 – volume: 5 start-page: 297 year: 2006 end-page: 302 article-title: Outlier detection in laser scanner point clouds publication-title: International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences – volume: 35 start-page: 124 issue: 1 year: Aug. 2006 end-page: 141 article-title: Provable surface reconstruction from noisy samples publication-title: Comput. Geom. Theory Appl. – volume: 28 start-page: 1768 issue: 11 year: 2006 end-page: 1783 article-title: Random walks for image segmentation publication-title: Pattern Analysis and Machine Intelligence, IEEE Transactions on – volume: 11 year: 2010 – volume: 29 start-page: 1733 issue: 5 year: 2010 end-page: 1741 article-title: Signing the unsigned: Robust surface reconstruction from raw pointsets publication-title: Computer Graphics Forum – start-page: 139 year: 2004 end-page: 147 – volume: 31 start-page: 795 year: 2012 end-page: 804 article-title: Medial kernels publication-title: Computer Graphics Forum – start-page: 163 year: 2002 end-page: 170 – volume: 29 start-page: 150:1 issue: 6 year: Dec. 2010 end-page: 150:10 article-title: Cone carving for surface reconstruction publication-title: ACM Transactions on Graphics – volume: 20 issue: 5 year: October 2010 article-title: Scale selection for geometric fitting in noisy point clouds publication-title: International Journal on Computational Geometry and Applications – start-page: 61 year: 2006 end-page: 70 – volume: 11 start-page: 733 issue: 6 year: 2011 end-page: 751 article-title: Geometric inference for probability measures publication-title: Foundations of Computational Mathematics – start-page: 100 year: 2007 end-page: 110 – volume: 15 start-page: 572 issue: 4 year: 2009 end-page: 582 article-title: Bandwidth selection and reconstruction quality in point‐based surfaces publication-title: IEEE Transactions on Visualization and Computer Graphics – year: July 2012 – volume: 26 start-page: 187 year: 2010 end-page: 204 article-title: Boundary fitting for 2D curve reconstruction publication-title: The Visual Computer – year: 2010 – year: 2012 – ident: e_1_2_7_2_2 – ident: e_1_2_7_6_2 doi: 10.1007/s10208-011-9098-0 – ident: e_1_2_7_16_2 – ident: e_1_2_7_7_2 doi: 10.1016/j.comgeo.2005.10.006 – ident: e_1_2_7_10_2 doi: 10.1109/TPAMI.2006.233 – ident: e_1_2_7_15_2 doi: 10.1109/3DIMPVT.2012.84 – ident: e_1_2_7_23_2 doi: 10.1109/TVCG.2009.13 – ident: e_1_2_7_3_2 – ident: e_1_2_7_17_2 doi: 10.1016/j.comgeo.2006.11.008 – ident: e_1_2_7_8_2 – ident: e_1_2_7_11_2 – ident: e_1_2_7_20_2 doi: 10.1145/1882261.1866176 – ident: e_1_2_7_21_2 doi: 10.1111/j.1467-8659.2011.02030.x – ident: e_1_2_7_12_2 doi: 10.1145/1057432.1057434 – ident: e_1_2_7_14_2 doi: 10.1111/j.1467-8659.2010.01782.x – volume: 5 start-page: 297 year: 2006 ident: e_1_2_7_19_2 article-title: Outlier detection in laser scanner point clouds publication-title: International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences – ident: e_1_2_7_18_2 doi: 10.1007/s00371-009-0395-4 – ident: e_1_2_7_4_2 doi: 10.1145/1857907.1857911 – volume: 20 issue: 5 year: 2010 ident: e_1_2_7_22_2 article-title: Scale selection for geometric fitting in noisy point clouds publication-title: International Journal on Computational Geometry and Applications doi: 10.1142/S0218195910003438 – ident: e_1_2_7_9_2 – ident: e_1_2_7_5_2 doi: 10.1111/j.1467-8659.2012.03060.x – ident: e_1_2_7_13_2 doi: 10.1111/j.1467-8659.2012.03174.x |
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| SubjectTerms | Algebraic Geometry Algorithms Computer graphics Computer science Confidence Graphs I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Boundary representations Mathematical analysis Mathematical models Mathematics Noise Reconstruction Seeds Studies |
| Title | Noise-Adaptive Shape Reconstruction from Raw Point Sets |
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