ACM Transactions on Graphics (TOG)
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Pose-consistent 3D shape segmentation based on a quantum mechanical feature descriptor
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
A new shape diffusion descriptor for brain classification
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Graph characterization using gaussian wave packet signature
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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This paper presents a novel analysis and application of the eigensystem of the edge-based Laplacian of a graph. The advantage of using the edge-based Laplacian over its vertex-based counterpart is that it significantly expands the set of differential operators that can be implemented in the graph domain. We commence by presenting a new mesh characterization based on the adjacency matrix of the mesh that captures both the geometric and topological properties of the shape. We use the edge-based eigenvalues to develop a novel method for defining pose-invariant signatures for non-rigid three-dimensional shapes based on the edge-based heat kernel. To illustrate the utility of our method, we perform numerous experiments applying the method to correspondence matching and classifying non-rigid three-dimensional shapes represented in terms of meshes.