ABSTRACT

We will briefly review in this chapter some of the necessary mathematical tools used in modern variational image analysis. This includes topics on Tikhonov regularization, maximum a posteriori estimate, convolution, Fourier transform, topologies on Banach spaces, function spaces, calculus of variations and energy minimization, geometric curve evolution, variational level set methods, numerical analysis by finite differences and the gradient descent method, and more. However, this chapter is not a substitute for the much more detailed existing textbooks on these topics. Thus, we strongly encourage the interested reader to consult many of the cited textbooks.