An Approach to Pattern Matching of Curved Shapes

Quantitative Analysis of Similarity of Curvatures

Abstract

A new method for pattern matching of curved shape on the inner product space by using the Fourier transform was proposed.
Sampled data points interpolated by spline functions were transformed onto the frequency domain by Fourier transform. Thereafter, the spectra were processed by convolution and then retransformed onto the real time domain. The crossinner products of the two sets of data versus the autoinner product is a measure of similarity between the two.
Patterns of the upper first premolars, two profile pictures of a patient who received a surgical operation, twin's mandibles, and three pairs of upper central incisors and faces were compared by taking the ratio of the inner products. The results thus obtained supported the validity of this method.
From these findings, a conclusion was drawn that the ratio of the inner products is a reasonable index of the identity or similarity of the curvatures.