Applying the Laplacian eigenfunction concept to pattern recognition

Abstract

It is demonstrated both theoretically and experimentally that Laplacian eigenfunction expansions on regions with no directional preference can be used to produce many new, interesting, and useful pattern recognition algorithms. Applications discussed in detail include invariant pattern recognition, accurate bilateral symmetry estimation of 3D volume data, and nonlinear joint transform correlation. This thesis focuses on Laplacian eigenfunction expansions on the unit disk and inside the unit sphere. Eigenfunctions of the 2D Laplacian on the unit disk are called disk harmonics, while eigenfunctions of the 3D Laplacian inside the unit sphere are called solid harmonics. Disk-harmonic coefficients are favourably compared, both theoretically and experimentally, with the commonly used Zernike and pseudo-Zernike moments for shift, scale, and rotation invariant pattern recognition. A method that exploits the symmetrical and group rotation properties of solid harmonics is developed to provide an accurate and robust estimate of the bilateral symmetry plane of 3D volume data. Results from experiments which estimated the symmetry plane of MRI human brain data are shown. A disk-harmonic expansion in the Fourier plane is used to improve the design of nonlinear joint transform correlators for real-time face recognition. The improved design is more tolerant to uniform intensity changes and distortions caused by in-plane and out-of-plane rotations, while maintaining the good discriminating power of highly nonlinear JTC's. Results from experiments using real faces with synthetic distortions and noise are shown. The improved performance of the device together with a feedback Ioop provides the potential for new applications such as real-time, hairstyle tolerant face recognition and real-time facial gesture recognition.