Applying backpropagation neural networks to fringe analysis

Abstract

Advances in image processing and optics technology, allied to the development of algorithmic techniques such as the fast Fourier transform and phase stepping, have allowed automatic fringe analysis to be successfully applied to many problems in visual inspection and noncontact surface measurement. However, when confronted with complicated or noisy images the algorithmic techniques tend to be less successful, implying an alternative approach may be necessary. Neural networks offer such an alternative. They have already been applied with some success to such conceptually similar pattern recognition problems, as the classification of fingerprints, the recognition of facial expressions and the identification of hand-written characters. Here, neural networks are applied to two simple fringe analysis problems. Firstly, to find the radius of a one-dimensional curved surface from its simulated fringe projection intensity distribution and, secondly, to identify four lensshaped objects of different radii of curvature from real fringe patterns obtained under different illumination conditions. In the first experiment, the backpropagation and radial basis function network paradigms are compared. In the second case, backpropagation is compared with the fuzzy-artmap paradigm. Performance criteria are the number of training data presentations, the accuracy of interpolation in the simulation experiment and the classification precision for the real data.