Fast and Robust QEF Minimization using Probabilistic Quadrics
Error quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad‐hoc regularization. While classical error quadrics measure the squ...
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| Vydáno v: | Computer graphics forum Ročník 39; číslo 2; s. 325 - 334 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Oxford
Blackwell Publishing Ltd
01.05.2020
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | Error quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad‐hoc regularization. While classical error quadrics measure the squared deviation from a set of ground truth planes or polygons, we treat the input data as genuinely uncertain information and embed error quadrics in a probabilistic setting (“probabilistic quadrics”) where the optimal point minimizes the expected squared error. We derive closed form solutions for the popular plane and triangle quadrics subject to (spatially varying, anisotropic) Gaussian noise. Probabilistic quadrics can be minimized robustly by solving a simple linear system — 50× faster than SVD. We show that probabilistic quadrics have superior properties in tasks like decimation and isosurface extraction since they favor more uniform triangulations and are more tolerant to noise while still maintaining feature sensitivity. A broad spectrum of applications can directly benefit from our new quadrics as a drop‐in replacement which we demonstrate with mesh smoothing via filtered quadrics and non‐linear subdivision surfaces. |
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| AbstractList | Error quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad‐hoc regularization. While classical error quadrics measure the squared deviation from a set of ground truth planes or polygons, we treat the input data as genuinely uncertain information and embed error quadrics in a probabilistic setting (“probabilistic quadrics”) where the optimal point minimizes the
expected
squared error. We derive closed form solutions for the popular plane and triangle quadrics subject to (spatially varying, anisotropic) Gaussian noise. Probabilistic quadrics can be minimized robustly by solving a simple linear system
— 50×
faster than SVD. We show that probabilistic quadrics have superior properties in tasks like decimation and isosurface extraction since they favor more uniform triangulations and are more tolerant to noise while still maintaining feature sensitivity. A broad spectrum of applications can directly benefit from our new quadrics as a drop‐in replacement which we demonstrate with mesh smoothing via filtered quadrics and non‐linear subdivision surfaces. Error quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad‐hoc regularization. While classical error quadrics measure the squared deviation from a set of ground truth planes or polygons, we treat the input data as genuinely uncertain information and embed error quadrics in a probabilistic setting (“probabilistic quadrics”) where the optimal point minimizes the expected squared error. We derive closed form solutions for the popular plane and triangle quadrics subject to (spatially varying, anisotropic) Gaussian noise. Probabilistic quadrics can be minimized robustly by solving a simple linear system — 50× faster than SVD. We show that probabilistic quadrics have superior properties in tasks like decimation and isosurface extraction since they favor more uniform triangulations and are more tolerant to noise while still maintaining feature sensitivity. A broad spectrum of applications can directly benefit from our new quadrics as a drop‐in replacement which we demonstrate with mesh smoothing via filtered quadrics and non‐linear subdivision surfaces. |
| Author | Kobbelt, L. Trettner, P. |
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| Cites_doi | 10.1109/VISUAL.1999.809869 10.1145/2898350 10.1145/566654.566586 10.1111/cgf.13597 10.1111/cgf.12531 10.1145/344779.344912 10.1109/ICACTE.2008.92 10.1145/258734.258849 10.1145/383259.383265 10.1145/1061347.1061350 10.1145/3306346.3323026 10.1016/j.cad.2012.04.005 10.1109/SIBGRAPI.2010.41 |
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| Copyright | 2020 The Author(s) Computer Graphics Forum © 2020 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2020 The Eurographics Association and John Wiley & Sons Ltd. |
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| References | 2001 2017; 36 2000 2013; 32 2010 2002; 21 1998 1997 2019; 38 2008 2016 2015 2004 2014 1992; 87 2012; 44 2016; 35 2005; 24 1999 e_1_2_9_10_2 e_1_2_9_21_2 e_1_2_9_20_2 e_1_2_9_12_2 e_1_2_9_23_2 e_1_2_9_11_2 Mathai A. (e_1_2_9_14_2) 1992 e_1_2_9_22_2 e_1_2_9_7_2 Thiery J.‐M. (e_1_2_9_19_2) 2013; 32 e_1_2_9_6_2 e_1_2_9_5_2 e_1_2_9_4_2 e_1_2_9_3_2 Calderon S. (e_1_2_9_2_2) 2017; 36 e_1_2_9_9_2 e_1_2_9_8_2 e_1_2_9_13_2 e_1_2_9_16_2 e_1_2_9_15_2 e_1_2_9_18_2 e_1_2_9_17_2 |
| References_xml | – volume: 24 start-page: 209 issue: 2 year: 2005 end-page: 239 article-title: Quadric‐based simplification in any dimension publication-title: ACM Trans. Graph. – volume: 38 start-page: 663 issue: 1 year: 2019 end-page: 677 article-title: Filtered quadrics for high‐speed geometry smoothing and clustering publication-title: Computer Graphics Forum – volume: 44 start-page: 1072 issue: 11 year: 2012 end-page: 1082 article-title: Variational mesh segmentation via quadric surface fitting publication-title: Comput. Aided Des. – volume: 36 issue: 5 year: 2017 article-title: Bounding proxies for shape approximation publication-title: ACM Transactions on Graphics (Proc. SIGGRAPH 2017) – start-page: 528 year: 2008 end-page: 532 – volume: 35 start-page: 30:1 issue: 3 year: 2016 end-page: 30:13 article-title: Animated mesh approximation with sphere‐meshes publication-title: ACM Trans. Graph. – volume: 87 issue: 12 year: 1992 – volume: 32 issue: 6 year: 2013 article-title: Sphere‐meshes: Shape approximation using spherical quadric error metrics publication-title: ACM Transaction on Graphics (Proc. SIGGRAPH Asia 2013) – volume: 38 start-page: 35:1 issue: 4 year: 2019 end-page: 35:11 article-title: Gaussianproduct subdivision surfaces publication-title: ACM Trans. Graph. – start-page: 57 year: 2001 end-page: 66 – start-page: 70 year: 2004 end-page: 76 – start-page: 209 year: 1997 end-page: 216 – volume: 21 start-page: 339 issue: 3 year: 2002 end-page: 346 article-title: Dual contouring of hermite data publication-title: ACM Trans. Graph. – start-page: 247 year: 2010 end-page: 254 – start-page: 259 year: 2000 end-page: 262 – year: 2016 – year: 2014 – start-page: 279 year: 1998 end-page: 286 – year: 2015 – year: 2010 – year: 1999 – ident: e_1_2_9_6_2 doi: 10.1109/VISUAL.1999.809869 – ident: e_1_2_9_11_2 – ident: e_1_2_9_20_2 doi: 10.1145/2898350 – ident: e_1_2_9_8_2 doi: 10.1145/566654.566586 – ident: e_1_2_9_12_2 doi: 10.1111/cgf.13597 – ident: e_1_2_9_17_2 doi: 10.1111/cgf.12531 – ident: e_1_2_9_7_2 – ident: e_1_2_9_4_2 – ident: e_1_2_9_10_2 doi: 10.1145/344779.344912 – ident: e_1_2_9_13_2 doi: 10.1109/ICACTE.2008.92 – ident: e_1_2_9_3_2 doi: 10.1145/258734.258849 – volume: 32 issue: 6 year: 2013 ident: e_1_2_9_19_2 article-title: Sphere‐meshes: Shape approximation using spherical quadric error metrics publication-title: ACM Transaction on Graphics (Proc. SIGGRAPH Asia 2013) – ident: e_1_2_9_15_2 – ident: e_1_2_9_18_2 – ident: e_1_2_9_23_2 – volume: 36 issue: 5 year: 2017 ident: e_1_2_9_2_2 article-title: Bounding proxies for shape approximation publication-title: ACM Transactions on Graphics (Proc. SIGGRAPH 2017) – ident: e_1_2_9_9_2 doi: 10.1145/383259.383265 – ident: e_1_2_9_5_2 doi: 10.1145/1061347.1061350 – ident: e_1_2_9_16_2 doi: 10.1145/3306346.3323026 – volume-title: Quadratic Forms in Random Variables: Theory and Applications year: 1992 ident: e_1_2_9_14_2 – ident: e_1_2_9_22_2 doi: 10.1016/j.cad.2012.04.005 – ident: e_1_2_9_21_2 doi: 10.1109/SIBGRAPI.2010.41 |
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| SubjectTerms | Algorithms CCS Concepts Computing methodologies → Mesh models; Mesh geometry models Error analysis Ground truth Normal distribution Optimization Random noise Regularization Robustness Singular value decomposition Triangles |
| Title | Fast and Robust QEF Minimization using Probabilistic Quadrics |
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