Preprocessing for the decomposition of images with normal offsets

The normal offset decomposition is a recent method to approximate images consisting of smoothly colored areas separated by smooth contours. In contrast to wavelet approximation methods, that perform suboptimally in this setting, this method is non-linear; the decomposition depends on the actual data. In every iteration new points are added by searching from the midpoint of the edges of the previous approximation along the normal direction until it pierces the surface that represents the image. The piercing points are attracted towards steep transitions and the edges that connect the new and old points line up against the contours in the image. The normal offset algorithm starts from an initial triangulation of the rectangular domain of the image. The choice of these initial points and triangles determines the quality of the resulting approximation. The most straightforward choice for the initial triangulation is two triangles that share a diagonal. However, other choices that are adapted to the specific image are more efficient because piercing points will only be placed on, or in the neighborhood of a discontinuity if there is an edge crossing the contour on the previous level. In this paper we investigate a method to find an initial triangulation that also makes use of the piercing procedure inherent to the normal offset decomposition algorithm.