Computing Shape DNA using the closest point method
Rachel Han
TL;DR
This paper explores using the closest point method to compute the shape DNA of objects through Laplace--Beltrami spectra, analyzing its effectiveness and clustering similar objects with multi-dimensional scaling.
Contribution
It introduces a novel application of the closest point method for shape analysis and evaluates spectral clustering techniques for object identification.
Findings
Spectral features effectively identify objects.
Clustering via multi-dimensional scaling groups similar shapes.
The MATLAB 'eigs' algorithm performs reliably in spectral computations.
Abstract
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.
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Taxonomy
TopicsRobotics and Sensor-Based Localization · Computational Geometry and Mesh Generation · Machine Learning and Algorithms