1Anisotropic Mesh Adaptation for Image Representation and Scaling

Abstract—Triangular meshes have gained much interest in image representation and have been widely used in image processing. This paper introduces a particular anisotropic mesh adaptation (AMA) method to image representation and image scaling. The AMA method is based on metric-specified mesh adaptation and finite element interpolation for Delaunay trian-gles. An initial triangular mesh is generated based on the desired number of points, and the mesh is then adapted according to a metric tensor that controls the size, shape and orientation of the triangles. Finally, the image is reconstructed from the mesh using finite element interpolation. The method is denoted as AMA-L if linear interpolation is used and AMA-Q if quadratic interpolation is used in the reconstruction, respectively. Different than many other methods, the AMA method starts with a triangular mesh directly and then adapts the mesh to represent the image. This AMA method has clear mathematical framework and can im-prove computational efficiency and accuracy in image processing. The AMA representation method provides comparable results with other content-based adaptive schemes but requires lower computational cost, and the AMA scaling method uses finite element interpolation and is comparable to vectorization. Index Terms—Image representation, image scaling, anisotropic mesh adaptation, finite element interpolation, triangular mesh I