GEOMETRIC DATA ANALYSIS: AN INTERACTIVE GRAPHICS PROGRAM FOR SHAPE COMPARISON

Abstract

This chapter provides an overview of the geometric data analysis in an interactive graphics program for shape comparison. The method of least squares was used to solve the problem of finding a common location and orientation of two shapes to compare their similarities and differences. There are situations in which robust methods such as the repeated median technique are far superior to least squares, especially in the detection of localized shape differences. The chapter presents least squares and robust methods, and an interactive computer program written in FORTRAN with graphics capabilities. The chapter also presents the mathematical methods involved in each fitting process. It further presents two examples to illustrate the use of the program and to show the kinds of graphic results that can be obtained. The chapter describes the work involved in setting up the program to run on a computer installation and provides an overall description of how to use the system. Two shapes, each consisting of n homologous points, can be rotated, scaled, and translated to obtain a close fit to each other by several methods. The least squares and robust fits can be very different. The robust fit shows clearly the localized systematic nature of the shape differences.