Robust 3D Shape Correspondence in the Spectral Domain
Abstract
We present an algorithm for finding a meaningful vertex-to-vertex correspondence between two 3D shapes given as triangle meshes. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform scaling and rigid-body transformation. Invariance to shape bending is achieved by relying on geodesic point proximities on a mesh to capture its shape. To deal with stretching, we propose to use non-rigid alignment via thin-plate splines in the spectral domain. This is combined with a refinement step based on the geodesic proximities to improve dense correspondence. We show empirically that our algorithm outperforms previous spectral methods, as well as schemes that compute correspondence in the spatial domain via non-rigid iterative closest points or the use of local shape descriptors, e.g., 3D shape context
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Recent intrinsic techniques [36], [38], [39] use low dimensional embedding to by-pass the high-dimensionality problem by assuming a strong inelastic isometry constraint.
“Recent intrinsic techniques [36], [38], [39] use low dimensional embedding to by-pass the high-dimensionality problem by assuming a strong inelastic isometry constraint.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [36]
Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505 · see citing works
A Method for Registration of 3-D Shapes
Besl, P., & Mckay, N. D. (1992) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.121791 · Cited by 22,163 · see citing works
On Spectral Clustering: Analysis and an algorithm
Ng, A. Y., Jordan, M. I., & Weiss, Y. (2001) · Cited by 8,159 · see citing works
A performance evaluation of local descriptors
Mikolajczyk, K., & Schmid, C. (2005) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2005.188 · Cited by 6,723 · see citing works
Shape matching and object recognition using shape contexts
Belongie, S., Malik, J., & Puzicha, J. (2002) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.993558 · Cited by 6,306 · see citing works
The approximation of one matrix by another of lower rank
Eckart, C., & Young, G. (1936) · Psychometrika · doi:10.1007/bf02288367 · Cited by 4,497 · see citing works
Efficient variants of the ICP algorithm
Rusinkiewicz, S., & Levoy, M. (2002) · Proceedings Third International Conference on 3-D Digital Imaging and Modeling · doi:10.1109/im.2001.924423 · Cited by 3,945 · see citing works
Using spin images for efficient object recognition in cluttered 3D scenes
Johnson, A., & Hebert, M. (1999) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.765655 · Cited by 2,656 · see citing works
A new point matching algorithm for non-rigid registration
Chui, H., & Rangarajan, A. (2003) · Computer Vision and Image Understanding · doi:10.1016/s1077-3142(03)00009-2 · Cited by 1,560 · see citing works
Spectral grouping using the nystrom method
Fowlkes, C. C., Belongie, S., Chung, F., & Malik, J. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.1262185 · Cited by 1,310 · see citing works
Deformation transfer for triangle meshes
Sumner, R. W., & Popović, J. (2004) · ACM Transactions on Graphics · doi:10.1145/1015706.1015736 · Cited by 1,059 · see citing works
An eigendecomposition approach to weighted graph matching problems
Umeyama, S. (1988) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.6778 · Cited by 740 · see citing works
Gelfand, N., Mitra, N. J., Guibas, L., & Pottmann, H. (2005) · doi:10.2312/sgp/sgp05/197-206 · Cited by 545 · see citing works
On bending invariant signatures for surfaces
Elad, A., & Kimmel, R. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1233902 · Cited by 467 · see citing works
An algorithm for associating the features of two images
Scott, G. L., & Longuet-Higgins, H. C. (1991) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.1991.0045 · Cited by 442 · see citing works
Feature-based correspondence: an eigenvector approach
Shapiro, L. S., & Brady, J. M. (1992) · Image and Vision Computing · doi:10.1016/0262-8856(92)90043-3 · Cited by 428 · see citing works
Cross-parameterization and compatible remeshing of 3D models
Kraevoy, V., & Sheffer, A. (2004) · ACM Transactions on Graphics · doi:10.1145/1015706.1015811 · Cited by 323 · see citing works
Fundamentals of spherical parameterization for 3D meshes
Gotsman, C., Gu, X. D., & Sheffer, A. (2003) · ACM SIGGRAPH Conference Papers (SIGGRAPH) · doi:10.1145/1201775.882276 · Cited by 269 · see citing works
Schreiner, J., Asirvatham, A., Praun, E., & Hoppe, H. (2004) · ACM Transactions on Graphics · doi:10.1145/1015706.1015812 · Cited by 267 · see citing works
Consistent mesh parameterizations
Praun, E., Sweldens, W., & Schröder, P. (2001) · ACM SIGGRAPH Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH) · doi:10.1145/383259.383277 · Cited by 261 · see citing works
Spectral surface reconstruction from noisy point clouds
Kolluri, R., Shewchuk, J. R., & O’Brien, J. F. (2004) · Symposium on Geometry Processing · doi:10.1145/1057432.1057434 · Cited by 246 · see citing works
Recent Advances in Mesh Morphing
Alexa, M. (2002) · Computer Graphics Forum · doi:10.1111/1467-8659.00575 · Cited by 239 · see citing works
3D Shape Matching with 3D Shape Contexts
Körtgen, M., Park, G.-J., Novotni, M., & Klein, R. (2003) · Cited by 227 · see citing works
Segmentation of 3D meshes through spectral clustering
Liu, R., & Zhang, H. (2004) · doi:10.1109/pccga.2004.1348360 · Cited by 217 · see citing works
Self-citationAn eigenspace projection clustering method for inexact graph matching
Caelli, T., & Kosinov, S. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.1265866 · Cited by 208 · see citing works
The Correlated Correspondence Algorithm for Unsupervised Registration of Nonrigid Surfaces
Anguelov, D., Srinivasan, P., Pang, H.-C., Koller, D., Thrun, S., & Davis, J. (2004) · Cited by 197 · see citing works
Harmonic Guidance for Surface Deformation
Zayer, R., Rössl, C., Karni, Z., et al. (2005) · Computer Graphics Forum · doi:10.1111/j.1467-8659.2005.00885.x · Cited by 193 · see citing works
Fundamentals of spherical parameterization for 3D meshes
Gotsman, C., Gu, X. D., & Sheffer, A. (2003) · ACM Transactions on Graphics · doi:10.1145/882262.882276 · Cited by 192 · see citing works
Spectral correspondence for point pattern matching
Carcassoni, M., & Hancock, E. R. (2002) · Pattern Recognition · doi:10.1016/s0031-3203(02)00054-7 · Cited by 175 · see citing works
Multi-scale features for approximate alignment of point-based surfaces
Li, X., & Guskov, I. (2005) · doi:10.5555/1281920.1281955 · Cited by 167 · see citing works
A refined ICP algorithm for robust 3-D correspondence estimation
Zinßer, T., Schmidt, J., & Niemann, H. J. (2004) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2003.1246775 · Cited by 153 · see citing works
Curvature maps for local shape comparison
Gatzke, T., Grimm, C. M., Garland, M., et al. (2006) · doi:10.1109/smi.2005.13 · Cited by 123 · see citing works
Kraevoy, V., Sheffer, A., & Gotsman, C. (2003) · ACM SIGGRAPH Conference Papers (SIGGRAPH) · doi:10.1145/1201775.882271 · Cited by 118 · see citing works
Correspondence matching with modal clusters
Carcassoni, M., & Hancock, E. R. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1251153 · Cited by 69 · see citing works
Cross-parameterization and compatible remeshing of 3D models
Kraevoy, V., & Sheffer, A. (2004) · ACM SIGGRAPH Conference Papers (SIGGRAPH) · doi:10.1145/1186562.1015811 · Cited by 60 · see citing works
Sub-sampling for Efficient Spectral Mesh Processing
Liu, R., Jain, V., & Zhang, H. (2006) · Lecture notes in computer science · doi:10.1007/11784203_15 · Cited by 22 · see citing works
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Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid
Tam, G. K. L., Cheng, Z.-Q., Lai, Y.-K., Langbein, F. C., Liu, Y., Marshall, D., Martin, R. R., Sun, X.-F., & Rosin, P. L. (2013) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2012.310 · Cited by 679 · see citing works
Minimum-Distortion Isometric Shape Correspondence Using EM Algorithm
Sahillioglu, Y., & Yemez, Y. (2012) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2012.26 · Cited by 53 · see citing works
- Authors
- Jain, V., & Zhang, H.
- Affiliations
- Simon Fraser University (CA)
- ORCID
- Venue
- IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06)
- Publisher
- IEEE
- Published
- 2006-07-10
- Pages
- 19-19
- OpenAlex
- W2137733660
- Cited by
- 148
- References
- 36
- Citations by year
- 2024: 1 · 2022: 3 · 2021: 3 · 2020: 3 · 2019: 4 · 2018: 7 · 2017: 7 · 2016: 10 · 2015: 8 · 2014: 14 · 2013: 12 · 2012: 18
- FWCI
- 29.24
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- IEEE International Conference on Shape Modeling and Applications (publishedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computational Geometry and Mesh Generation
- Keywords
- 3D shape correspondence, triangular meshes, spectral domain, thin-plate splines, shape matching
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