A Nonlinear Contour Preserving Transform for Geometrical Image Compression

Recently the performance of nonlinear transforms have been given a lot of attention to overcome the suboptimal n- terms approximation power of tensor product wavelet methods on higher dimensions. The suboptimal performance prevails when those transforms are used for a sparse representation of functions consisting of smoothly varying areas separated by smooth contours. This paper introduces a method creating normal meshes with nonsubdivision connectivity to approximate the nonsmoothness of such images efficiently. From a domain decomposition viewpoint, the method is a triangulation refinement method preserving contours. The so-called normal offset decomposition searches from the midpoint of the edges in the previous approximation along the normal direction until it pierces the surface that represents the image and adds the piercing points to the approximation. The transform is nonlinear as it depends on the actual image. In this paper, we propose a normal offset based compression algorithm for digital images. The discrete setting causes the transform to become redundant. We also propose a model to encode the obtained coefficients. We show rate distortion curves and compare the results with the JPEG2000 encoder.