Finite Element and Meshfree Applications to Image Processing

This work presents a sample of three image processing methods, two of which are implemented using the finite element method and one of which involves a meshfree method. While the common way in which images are stored using pixels (2D) and voxels (3D) provides a natural setting for finite difference methods, we discuss some of the advantages of other types of numerical implementations of mathematical models. The first part of this dissertation describes how a meshfree method in a high dimensional space can be applied to image denoising. The second part of this work discusses a method for robustly creating a good quality tetrahedral mesh from a 3D image. The third section explains how this mesh can be incorporated into a finite element image registration method.