Computing Shape DNA using the closest point method
For computer graphics and shape analysis, this provides a numerical method for computing shape DNA, though the results are preliminary and lack quantitative comparisons.
The paper applies the closest point method to compute the Laplace-Beltrami spectrum for shape identification, showing it can effectively distinguish objects and cluster similar shapes using multi-dimensional scaling.
We demonstrate an application of the closest point method where the truncated spectrum of the Laplace--Beltrami operator of an object is used to identify the object. The effectiveness of the method is analyzed as well as the default algorithm, `eigs', in MATLAB which computes the eigenvalues of a given matrix. We also cluster "similar" objects via multi-dimensional scaling algorithm and empirically measure its effectiveness.