A performance study of the tangent distance method in transformation-invariant image classification

A common problem in image analysis is the transformation-invariant estimation of the similarity between a query image and a set of reference images representing different classes. This typically requires the comparison of the distance between the query image and the transformation manifolds of the reference images. The tangent distance algorithm is a popular method that estimates the manifold distance by employing a linear approximation of the transformation manifolds. In this paper, we present a performance analysis of the tangent distance method in image classification applications for general transformation models. In particular, we characterize the misclassification error in terms of the geometric properties of the individual manifolds such as their curvature, as well as their relative properties such as the separation between them. We then extend our results to a multi-scale analysis where the images are smoothed with a low-pass filter and study the effect of smoothing on the misclassification error. Our theoretical results are confirmed by experiments and may find use in the selection of algorithm parameters in multiscale transformation-invariant image analysis methods.