Shape recognition based on eigenvalues of the Laplacian

This chapter offers a theoretical overview of the characteristics of the eigenvalues of four well-known linear operators and assess their usefulness as reliable tools for shape recognition. A shape recognition technique can also be classified as either information-preserving or non-preserving depending on whether full recovery of the shape being analyzed is possible from the extracted feature vectors. The boundary conditions in Saito's problem emerge by requiring the Laplacian to commute with the expression of Green's function for free space. Rather than providing a comprehensive review of methods of computation of the eigenvalues of the membrane problem and the other associated problems described previously, we mention the techniques that were most prominent recently and others that provide future hope. A total of 288 hand-drawn images of disks, triangles, rectangles, ellipses, diamonds, and squares of different sizes and orientations were scanned into the compute.