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In this work, we propose computational models and algorithms for point cloud registration with non-rigid transformation.
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Convergent discrete laplace-beltrami operator over triangular surfaces
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A nonmonotone line search technique and its application to unconstrained optimization
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A theoretical and computational framework for isometry invariant recognition of point cloud data
F. Mémoli and G. Sapiro · 2005
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Harmonic surface mapping with Laplace-Beltrami eigenmaps
Y. Shi, R. Lai, K. Kern, N. Sicotte, I. Dinov, and A. W. Toga · 2008
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Numerical geometry of non-rigid shapes
A. M. Bronstein, M. M. Bronstein, and R. Kimmel · 2008
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Optimal transport: old and new
Cédric Villani · 2008
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Computing teichm u ¨ \ddot{u} ller shape space
M. Jin, W. Zeng, F. Luo, and X. Gu · 2009
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Hierarchical shape segmentation and registration via topological features of laplace-beltrami eigenfunctions
M. Reuter · 2009
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A concise and provabley informative multi-scale signature baded on heat diffusion
J. Sun, M. Ovsjanikov, and L. Guibas · 2009
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Diffusion maps
R. R. Coifman and S. Lafon · 2006
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Laplace-Beltrami spectra as Shape-DNA of surfaces and solids
M. Reuter, F.E. Wolter, and N. Peinecke · 2006
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Laplace-beltrami eigenfunctions: Towards an algorithm that understands geometry
B. Levy · 2006
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Spectral surface quadrangulation
S. Dong, P-T. Bremer, M. Garland, V. Pascucci, and J. C. Hart · 2006
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Smooth functional and structural maps on the neocortex via orthonormal bases of the Laplace-Beltrami operator
A. Qiu, D. Bitouk, and M. I. Miller · 2006
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Efficient computation of isometry-invariant distances between surfaces
A. M. Bronstein, M. M. Bronstein, and R. Kimmel · 2006
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Laplace-beltrami nodal counts: a new signature for 3d shape analysis
R. Lai, Y. Shi, I. Dinov, T. F. Chan, and A. W. Toga · 2009
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Constructing Laplace operator from point clouds in ℝ d \mathbb{R}^{d}
Mikhail Belkin, Jian Sun, and Yusu Wang · 2009
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Local histogram based segmentation using the wasserstein distance
Kangyu Ni, Xavier Bresson, Tony Chan, and Selim Esedoglu · 2009
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A gromov-hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching
A. M. Bronstein, M. M. Bronstein, R. Kimmel, M. Mahmoudi, and G. Sapiro · 2010
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Robust surface reconstruction via laplace-beltrami eigen-projection and boundary deformation
Y. Shi, R. Lai, J. Morra, I. Dinov, P. Thompson, and A. W. Toga · 2010
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Scale-invariant heat kernel signatures for non-rigid shape recognition
M. M. Bronstein and I. Kokkinos · 2010
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Metric-induced optimal embedding for intrinsic 3D shape analysis
R. Lai, Y. Shi, K. Scheibel, S. Fears, R. Woods, A. W. Toga, and T. F. Chan · 2010
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A spectral notion of Gromov-Wasserstein distances and related methods
F. Mémoli · 2011
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Solving eigenvalue problems on curved surfaces using the closest point method
C. B. Macdonald, J. Brandman, and S. J. Ruuth · 2011
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Wasserstein regularization of imaging problem
Julien Rabin and Gabriel Peyré · 2011
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Geometric understanding of point clouds using laplace-beltrami operator
J. Liang, R. Lai, T. Wong, and H. Zhao · 2012
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Wasserstein barycenter and its application to texture mixing
Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot · 2012
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Solving partial differential equations on point clouds
Jian Liang and Hongkai Zhao · 2013
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A local mesh method for sloving PDEs on point clouds
R. Lai, J. Liang, and H. Zhao · 2013
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Area preserving brain mapping
Zhengyu Su, Wei Zeng, Rui Shi, Yalin Wang, Jian Sun, and Xianfeng Gu · 2013
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A user’s guide to optimal transport
Luigi Ambrosio and Nicola Gigli · 2013
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A feasible method for optimization with orthogonality constraints
Zaiwen Wen and Wotao Yin · 2013
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Affine invariant non-rigid shape analysis
D. Raviv and R. Kimmel · 2014
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