A two-dimensional interpolation function for irregularly-spaced data
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SCAPE: shape completion and animation of people
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Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Efficient Computation of Isometry-Invariant Distances Between Surfaces
SIAM Journal on Scientific Computing
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Clustering and Embedding Using Commute Times
IEEE Transactions on Pattern Analysis and Machine Intelligence
A hierarchical segmentation of articulated bodies
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Graph nodes clustering based on the commute-time kernel
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Image segmentation based on k-means clustering and energy-transfer proximity
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part II
Discrete bi-Laplacians and biharmonic b-splines
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
SMI 2012: Full Local approximation of scalar functions on 3D shapes and volumetric data
Computers and Graphics
Motion-based mesh segmentation using augmented silhouettes
Graphical Models
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The hitchhiker's guide to the galaxy of mathematical tools for shape analysis
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A global algorithm to compute defect-tolerant geodesic distance
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Fast nonrigid 3D retrieval using modal space transform
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ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Geodesics in heat: A new approach to computing distance based on heat flow
ACM Transactions on Graphics (TOG)
Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry
ACM Transactions on Graphics (TOG)
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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Measuring distances between pairs of points on a 3D surface is a fundamental problem in computer graphics and geometric processing. For most applications, the important properties of a distance are that it is a metric, smooth, locally isotropic, globally “shape-aware,” isometry-invariant, insensitive to noise and small topology changes, parameter-free, and practical to compute on a discrete mesh. However, the basic methods currently popular in computer graphics (e.g., geodesic and diffusion distances) do not have these basic properties. In this article, we propose a new distance measure based on the biharmonic differential operator that has all the desired properties. This new surface distance is related to the diffusion and commute-time distances, but applies different (inverse squared) weighting to the eigenvalues of the Laplace-Beltrami operator, which provides a nice trade-off between nearly geodesic distances for small distances and global shape-awareness for large distances. The article provides theoretical and empirical analysis for a large number of meshes.