Shape Analysis Using the Edge-Based Laplacian [chapter]

Furqan Aziz, Richard C. Wilson, Edwin R. Hancock
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
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
more &raquo; ... genvalues 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/978-3-642-34166-3_42</a> <a target="_blank" rel="external noopener" href="">fatcat:xzv7e634znav3blzpovxrktw6m</a> </span>
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