Anisotropic Mesh Adaptation for Image Representation

Triangular meshes have gained much interest in image representation and have been widely used in image processing. This paper introduces a framework of anisotropic mesh adaptation (AMA) methods to image representation. The AMA methods take the $M$-uniform mesh approach for mesh adaptation and use finite element interpolation for image reconstruction. Different than many other methods that connect sample points to form the mesh, the AMA methods start directly with a triangular mesh and then adapt the mesh based on a user-defined metric tensor to represent the image. The AMA methods have clear mathematical framework and provides flexibility for both mesh adaptation and image reconstruction. The numerical examples show that the AMA representation provides comparable or better results than some well-known content-based adaptive schemes. The framework will be useful for anisotropic mesh adaptation in image scaling and image processing with anisotropic diffusion filters.