Normal Offsets for digital image decomposition

This paper describes the use of normal offsets with regard to image compression. Given a gray scale image, the decomposition aims at a sparse representation i.e. lots of (nearly) zero coefficients. The class of images we want to represent have smoothly colored regions separated by edges-abrupt changes- along smooth lines. An image can also be seen as a surface lying in the three dimensional space. This surface can be approximated by a mesh. Usually a mesh is constructed given input data consisting of three coefficients, of which two of them represent the location in the domain and only one contains information about the geometry of the mesh. Normal offsets try to resolve this using only one coefficient is needed in order to compute another point, depending on already known mesh points. In this manner normal offsets are suitable for multiresolution purposes, i.e. getting a more and more accurate approximation when moving to higher resolution levels.