Sparse Non-rigid Registration of 3D Shapes
Non‐rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non‐rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a s...
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| Published in: | Computer graphics forum Vol. 34; no. 5; pp. 89 - 99 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Oxford
Blackwell Publishing Ltd
01.08.2015
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| ISSN: | 0167-7055, 1467-8659 |
| Online Access: | Get full text |
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| Abstract | Non‐rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non‐rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an ℓ2‐norm regularization on the local transformation differences. However, the ℓ2‐norm regularization tends to bias the solution towards outliers and noise with heavy‐tailed distribution, which is verified by the poor goodness‐of‐fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non‐rigid registration (SNR) method with an ℓ1‐norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi‐resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large‐scale deformations as well as outliers and noise. |
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| AbstractList | Non‐rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non‐rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an ℓ 2 ‐norm regularization on the local transformation differences. However, the ℓ 2 ‐norm regularization tends to bias the solution towards outliers and noise with heavy‐tailed distribution, which is verified by the poor goodness‐of‐fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non‐rigid registration (SNR) method with an ℓ 1 ‐norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi‐resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large‐scale deformations as well as outliers and noise. Non-rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non-rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an 2-norm regularization on the local transformation differences. However, the 2-norm regularization tends to bias the solution towards outliers and noise with heavy-tailed distribution, which is verified by the poor goodness-of-fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non-rigid registration (SNR) method with an 1-norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi-resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large-scale deformations as well as outliers and noise. Non-rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non-rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an sub(2)-norm regularization on the local transformation differences. However, the sub(2)-norm regularization tends to bias the solution towards outliers and noise with heavy-tailed distribution, which is verified by the poor goodness-of-fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non-rigid registration (SNR) method with an sub(1)-norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi-resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large-scale deformations as well as outliers and noise. Non‐rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non‐rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an ℓ2‐norm regularization on the local transformation differences. However, the ℓ2‐norm regularization tends to bias the solution towards outliers and noise with heavy‐tailed distribution, which is verified by the poor goodness‐of‐fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non‐rigid registration (SNR) method with an ℓ1‐norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi‐resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large‐scale deformations as well as outliers and noise. |
| Author | Lai, Yu-Kun Li, Kun Yang, Jingyu Li, Ke |
| Author_xml | – sequence: 1 givenname: Jingyu surname: Yang fullname: Yang, Jingyu organization: School of Electronic Information Engineering, Tianjin University, Tianjin, China – sequence: 2 givenname: Ke surname: Li fullname: Li, Ke organization: School of Electronic Information Engineering, Tianjin University, Tianjin, China – sequence: 3 givenname: Kun surname: Li fullname: Li, Kun email: lik@tju.edu.cn organization: School of Computer Science and Technology, Tianjin University, Tianjin, China – sequence: 4 givenname: Yu-Kun surname: Lai fullname: Lai, Yu-Kun organization: School of Computer Science and Informatics, Cardiff University, Wales, UK |
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| Cites_doi | 10.1145/258734.258849 10.1111/j.1467-8659.2011.02023.x 10.1109/TIP.2013.2262292 10.1109/ICCV.2009.5459161 10.1111/cgf.12178 10.1145/882262.882311 10.1145/1618452.1618521 10.1109/CVPR.2012.6247673 10.1109/ICRA.2012.6225077 10.1111/j.1467-8659.2008.01282.x 10.1109/TVCG.2012.310 10.1111/j.1467-8659.2008.01287.x 10.1111/j.1467-8659.2008.01137.x 10.1016/S1077-3142(03)00009-2 10.1145/566654.566626 10.1109/3DV.2014.80 10.1109/ISMAR.2011.6092378 10.1016/j.media.2014.03.002 10.1007/s11432-009-0045-5 10.1109/JPROC.2009.2037655 10.1109/CVPR.2007.383165 10.1145/1360612.1360696 10.1145/2517967 10.1561/2200000016 10.1109/TPAMI.2010.46 10.1016/j.cagd.2009.09.001 10.1016/j.cviu.2014.04.011 10.1145/2601097.2601165 10.1145/1276377.1276478 |
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| Copyright | 2015 The Author(s) Computer Graphics Forum © 2015 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2015 The Eurographics Association and John Wiley & Sons Ltd. |
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| References | Flöry S., Hofer M.: Surface fitting and registration of point clouds using approximations of the unsigned distance function. Comput. Aided Geom. Des. 27, 1 (2010), 60-77. 2 Pekelny Y., Gotsman C.: Articulated object reconstruction and markerless motion capture from depth video. Computer Graphics Forum 27, 2 (2008), 399-408. 2 Sumner R.W., Schmid J., Pauly M.: Embedded deformation for shape manipulation. ACM Trans. Graph. 26, 3 (2007), 80. 1, 3 Yang J., Peng Y., Xu W., Dai Q.: Ways to sparse representation: an overview. Science in China series F: information sciences 52, 4 (2009), 695-703. 5 Bronstein A.M., Bronstein M.M., Kimmel R.: Numerical geometry of non-rigid shapes. Springer Science & Business Media, 2008. 2, 7 Li H., Sumner R.W., Pauly M.: Global correspondence optimization for non-rigid registration of depth scans. Computer graphics forum 27, 5 (2008), 1421-1430. 1, 2, 3, 8, 10 Allen B., Curless B., Popović Z.: Articulated body deformation from range scan data. ACM Trans. Graph. 21, 3 (2002), 612-619. 2 Elad M., Figueiredo M.A., Ma Y.: On the role of sparse and redundant representations in image processing. Proceedings of the IEEE 98, 6 (2010), 972-982. 3 Süssmuth J., Winter M., Greiner G.: Reconstructing animated meshes from time-varying point clouds. Computer Graphics Forum 27, 5 (2008), 1469-1476. 2 Tam G.K., Cheng Z.-Q., Lai Y.-K., Langbein F.C., Liu Y., Marshall D., Martin R.R., Sun X.-F., Rosin P.L.: Registration of 3D point clouds and meshes: a survey from rigid to nonrigid. IEEE Trans. Vis. Comp. Graph. 19, 7 (2013), 1199-1217. 2 Vlasic D., Baran I., Matusik W., Popović J.: Articulated mesh animation from multi-view silhouettes. ACM Trans. Graph. 27, 3 (2008), 97. 2, 7 Papazov C., Burschka D.: Deformable 3D shape registration based on local similarity transforms. In Computer Graphics Forum (2011), vol. 30, pp. 1493-1502. 2 Chui H., Rangarajan A.: A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding 89, 2 (2003), 114-141. 2 Li H., Adams B., Guibas L.J., Pauly M.: Robust single-view geometry and motion reconstruction. ACM Trans. Graph. 28, 5 (2009), 175. 2, 6 Wand M., Adams B., Ovsjanikov M., Berner A., Bokeloh M., Jenke P., Guibas L., Seidel H.-P., Schilling A.: Efficient reconstruction of nonrigid shape and motion from real-time 3D scanner data. ACM Trans. Graph. 28, 2 (2009), 15. 2 Tam G.K., Martin R.R., Rosin P.L., Lai Y-K.: Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry. ACM Trans. Graph. 33, 1 (2014), 4. 4, 9 Allen B., Curless B., Popović Z.: The space of human body shapes: reconstruction and parameterization from range scans. ACM Trans. Graph. 22, 3 (2003), 587-594. 2 Myronenko A., Song X.: Point set registration: Coherent point drift. IEEE Trans. Pattern Analy. Mach. Intell. 32, 12 (2010), 2262-2275. 2 Yu Y., Zhang S., Li K., Metaxas D., Axel L.: Deformable models with sparsity constraints for cardiac motion analysis. Medical Image Analysis 18, 6 (2014), 927-937. 3 Yang A. Y, Zhou Z., Balasubramanian A.G., Sastry S.S., Ma Y: Fast ℓ1-minimization algorithms for robust face recognition. IEEE Trans. Image Processing 22, 8 (2013), 3234-3246. 5 Boyd S., Parikh N., Chu E., Peleato B., Eckstein J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning 3, 1 (2011), 1-122. 5 Salti S., Tombari F., Di Stefano L.: SHOT: unique signatures of histograms for surface and texture description. Computer Vision and Image Understanding 125 (2014), 251-264. 4, 9 Zollhöfer M., Niessner M., Izadi S., Rhemann C., Zach C., Fisher M., Wu C., Fitzgibbon A., Loop C., Theobalt C., Stamminger M.: Real-time non-rigid reconstruction using an RGB-D camera. ACM Trans. Graph. 33, 4 (2014). 1 Bertsekas D.P.: Constrained optimization and lagrange multiplier methods. Computer Science and Applied Mathematics, Boston: Academic Press 1 (1982). 5 Bouaziz S., Tagliasacchi A., Pauly M.: Sparse iterative closest point. Computer Graphics Forum 32, 5 (2013), 113-123. 1, 3, 10 2010; 98 2010; 32 2012 2013; 22 2011 2009 2008 1997 2011; 30 2007 2006 1992 2003 2002 2011; 3 2009; 28 2013; 19 2010; 27 2009; 52 1982; 1 2013; 32 2002; 21 2008; 27 2014 2014; 18 2009; 2 2014; 125 2014; 33 2003; 22 2007; 26 2003; 89 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_19_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_11_2 e_1_2_7_10_2 Bertsekas D.P. (e_1_2_7_6_2) 1982; 1 e_1_2_7_26_2 e_1_2_7_27_2 e_1_2_7_28_2 e_1_2_7_29_2 e_1_2_7_25_2 e_1_2_7_24_2 e_1_2_7_30_2 e_1_2_7_23_2 e_1_2_7_31_2 e_1_2_7_22_2 e_1_2_7_32_2 e_1_2_7_21_2 e_1_2_7_33_2 e_1_2_7_20_2 Bishop C.M. (e_1_2_7_7_2) 2006 e_1_2_7_35_2 e_1_2_7_36_2 e_1_2_7_37_2 e_1_2_7_38_2 Wand M. (e_1_2_7_34_2) 2009; 2 Bronstein A.M. (e_1_2_7_5_2) 2008 |
| References_xml | – reference: Wand M., Adams B., Ovsjanikov M., Berner A., Bokeloh M., Jenke P., Guibas L., Seidel H.-P., Schilling A.: Efficient reconstruction of nonrigid shape and motion from real-time 3D scanner data. ACM Trans. Graph. 28, 2 (2009), 15. 2 – reference: Allen B., Curless B., Popović Z.: Articulated body deformation from range scan data. ACM Trans. Graph. 21, 3 (2002), 612-619. 2 – reference: Yu Y., Zhang S., Li K., Metaxas D., Axel L.: Deformable models with sparsity constraints for cardiac motion analysis. Medical Image Analysis 18, 6 (2014), 927-937. 3 – reference: Bronstein A.M., Bronstein M.M., Kimmel R.: Numerical geometry of non-rigid shapes. Springer Science & Business Media, 2008. 2, 7 – reference: Flöry S., Hofer M.: Surface fitting and registration of point clouds using approximations of the unsigned distance function. Comput. Aided Geom. Des. 27, 1 (2010), 60-77. 2 – reference: Chui H., Rangarajan A.: A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding 89, 2 (2003), 114-141. 2 – reference: Bertsekas D.P.: Constrained optimization and lagrange multiplier methods. Computer Science and Applied Mathematics, Boston: Academic Press 1 (1982). 5 – reference: Elad M., Figueiredo M.A., Ma Y.: On the role of sparse and redundant representations in image processing. Proceedings of the IEEE 98, 6 (2010), 972-982. 3 – reference: Tam G.K., Martin R.R., Rosin P.L., Lai Y-K.: Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry. ACM Trans. Graph. 33, 1 (2014), 4. 4, 9 – reference: Sumner R.W., Schmid J., Pauly M.: Embedded deformation for shape manipulation. ACM Trans. Graph. 26, 3 (2007), 80. 1, 3 – reference: Pekelny Y., Gotsman C.: Articulated object reconstruction and markerless motion capture from depth video. Computer Graphics Forum 27, 2 (2008), 399-408. 2 – reference: Yang J., Peng Y., Xu W., Dai Q.: Ways to sparse representation: an overview. Science in China series F: information sciences 52, 4 (2009), 695-703. 5 – reference: Süssmuth J., Winter M., Greiner G.: Reconstructing animated meshes from time-varying point clouds. Computer Graphics Forum 27, 5 (2008), 1469-1476. 2 – reference: Myronenko A., Song X.: Point set registration: Coherent point drift. IEEE Trans. Pattern Analy. Mach. Intell. 32, 12 (2010), 2262-2275. 2 – reference: Papazov C., Burschka D.: Deformable 3D shape registration based on local similarity transforms. In Computer Graphics Forum (2011), vol. 30, pp. 1493-1502. 2 – reference: Li H., Sumner R.W., Pauly M.: Global correspondence optimization for non-rigid registration of depth scans. Computer graphics forum 27, 5 (2008), 1421-1430. 1, 2, 3, 8, 10 – reference: Salti S., Tombari F., Di Stefano L.: SHOT: unique signatures of histograms for surface and texture description. Computer Vision and Image Understanding 125 (2014), 251-264. 4, 9 – reference: Allen B., Curless B., Popović Z.: The space of human body shapes: reconstruction and parameterization from range scans. ACM Trans. Graph. 22, 3 (2003), 587-594. 2 – reference: Tam G.K., Cheng Z.-Q., Lai Y.-K., Langbein F.C., Liu Y., Marshall D., Martin R.R., Sun X.-F., Rosin P.L.: Registration of 3D point clouds and meshes: a survey from rigid to nonrigid. IEEE Trans. Vis. Comp. Graph. 19, 7 (2013), 1199-1217. 2 – reference: Bouaziz S., Tagliasacchi A., Pauly M.: Sparse iterative closest point. Computer Graphics Forum 32, 5 (2013), 113-123. 1, 3, 10 – reference: Vlasic D., Baran I., Matusik W., Popović J.: Articulated mesh animation from multi-view silhouettes. ACM Trans. Graph. 27, 3 (2008), 97. 2, 7 – reference: Li H., Adams B., Guibas L.J., Pauly M.: Robust single-view geometry and motion reconstruction. ACM Trans. Graph. 28, 5 (2009), 175. 2, 6 – reference: Boyd S., Parikh N., Chu E., Peleato B., Eckstein J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning 3, 1 (2011), 1-122. 5 – reference: Yang A. Y, Zhou Z., Balasubramanian A.G., Sastry S.S., Ma Y: Fast ℓ1-minimization algorithms for robust face recognition. IEEE Trans. Image Processing 22, 8 (2013), 3234-3246. 5 – reference: Zollhöfer M., Niessner M., Izadi S., Rhemann C., Zach C., Fisher M., Wu C., Fitzgibbon A., Loop C., Theobalt C., Stamminger M.: Real-time non-rigid reconstruction using an RGB-D camera. ACM Trans. Graph. 33, 4 (2014). 1 – volume: 89 start-page: 114 issue: 2 year: 2003 end-page: 141 article-title: A new point matching algorithm for non‐rigid registration publication-title: Computer Vision and Image Understanding – start-page: 1 year: 2007 end-page: 8 – volume: 27 start-page: 1469 issue: 5 year: 2008 end-page: 1476 article-title: Reconstructing animated meshes from time‐varying point clouds publication-title: Computer Graphics Forum – volume: 30 start-page: 1493 year: 2011 end-page: 1502 article-title: Deformable 3D shape registration based on local similarity transforms publication-title: Computer Graphics Forum – volume: 125 start-page: 251 year: 2014 end-page: 264 article-title: SHOT: unique signatures of histograms for surface and texture description publication-title: Computer Vision and Image Understanding – volume: 33 issue: 4 year: 2014 article-title: Real‐time non‐rigid reconstruction using an RGB‐D camera publication-title: ACM Trans. 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| SubjectTerms | 3-D graphics Analysis Categories and Subject Descriptors (according to ACM CCS) Estimates I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Hierarchy and geometric transformations Image processing systems Noise Outliers (statistics) Registration Regularization Scanning Sensors Studies Tasks Three dimensional Transformations |
| Title | Sparse Non-rigid Registration of 3D Shapes |
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