On the Optimality of Spectral Compression of Meshes

Spectral compression of triangle meshes has shown good results in practice, but there has been little or no theoretical support for the optimality of this compression. We show that for certain classes of geometric mesh models, spectral decomposition using the eigenvectors of the symmetric Laplacian of the connectivity graph is equivalent to principal component analysis. The key component of the proof is that the Laplacian is identical, up to a constant factor, to the inverse covariance matrix of the distribution of valid mesh geometries. Hence spectral compression is optimal in the MSE sense.