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.


Adjacency Matrix Heat Kernel Feature Descriptor Graph Domain Dimensional Shape 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Furqan Aziz
    • 1
  • Richard C. Wilson
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkUK

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