Application of differential mapping and wavelet transform
Igor V. Ternovskiy, Tomasz P. Jannson · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1997
In this paper, the relationship between wavelet transform and Differential Mapping Singularities Theory (DMST) is discussed in the context of image compression. DMST maps 3D surfaces accurately, with exact results, and to construct an image compression algorithm based on an expanded set of operations. This set includes shift, scaling rotation, and homogeneous nonlinear transformations. This approach permits the mathematical description of a full set of singularities that describe edges and other specific points of objects. The edges and specific points (degenerate critical points) are the product of mapping smooth 3D surfaces, which can be described by a simple set of polynomials that are suitable for image compression and Automatic Target Recognition.