ABSTRACT
This chapter describes the matching of two configurations using regression, making connections with general shape spaces and shape distances. It considers shape matching and affine shape matching and describes particular application of matching electrophoresis gels. The chapter also considers generalized matching where a random sample of objects is available. It looks at some shape distributions which can be used for inference. Inference for random samples is relatively straightforward and some classical inference procedures were given by J. T. Kent and K. V. Mardia and I. L. Dryden. Statistical inference on population mean shape and population shape covariance using probability distributions in the general shape space is an alternative to generalized matching by minimizing objective functions. Shape analysis is particularly useful in the prior modeling of the deformable templates and registration analysis is useful in the final automatic matching procedure. The chapter explores the work to consider robustness issues and provide smoothed matching.
