ABSTRACT
This chapter presents the basic mathematics underlying shape analysisand classification. It starts by presenting some elementary concepts, including propositional logic, functions and complex numbers, and follows by covering important topics in linear algebra, such as vector spaces, linear transformations and metric spaces. Since several properties of shapes exhibit a differential nature, a review of the main related concepts from differential geometry and multivariate calculus is subsequently presented. Next, the key operations known as convolution and correlation are introduced and exemplified, which is followed by a review of probability and statistics, including probability distributions, autocorrelation and the Karhunen-Loève transform. The chapter concludes by presenting the main issues in Fourier analysis, from the Fourier series to discrete convolution performed in the frequency domain.
