Abstract

Training set selection is an integral part of filter design and can affect filter performance. The training set selection algorithm presented here is designed specifically for single-parameter out-of-plane rotation. It is assumed that the user can vary a single angle of rotation associated with a 3-D object model from which a projected image can be obtained yielding a set of training images. In the case of only in-plane rotation with N uniformly sampled training images, the resulting N × N correlation matrix (CM) of the normalized training samples would be Toeplitz. The eigenvectors and eigenvalues of this ideal CM take on simple forms. The training set selection algorithm presented here uses this ideal CM as a basis for training set selection performance. When a training set is selected, the eigenvalues and vectors for an ideal CM can be obtained and used to generate a corresponding ideal CM. This ideal matrix is then compared (on a mean-squared error basis) with the actual CM. This resulting performance parameter is then used to reselect another training set. This process repeats until the resulting CM is a good approximation to a Toeplitz matrix.

© 1988 Optical Society of America