A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing

Spectral Transform 73

based on 1D discrete Laplacians and then looked at the problem

from a signal processing perspective and applied the algebraic tool

of spectral analysis to interpret compression, Laplacian smooth-

ing, and signal filtering. For those familiar with signal process-

ing and Fourier analysis, a connection appears to be obvious. In

particular, by looking at the plots of the eigenvectors of the 1D

discrete Laplacian operator (Equation (5.3)) in Figure 5.6, one no-

tices their resemblance to the sinusoidal curves of the Fourier or

DCT basis functions. We now make that connection explicit.

Typically, one introduces discrete Fourier transform ...