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Approximation and processing of intensity images with discontinuity-preserving adaptive triangular meshes

Abstract:

A new algorithm for approximating intensity images with adaptive triangular meshes keeping image discontinuities and avoiding optimization is presented. The algorithm consists of two main stages. In the first stage, the original image is adaptively sampled at a set of points, taking into account both image discontinuities and curvatures. In the second stage, the sampled points are triangulated by applying a constrained 2D Delaunay algorithm. The obtained triangular meshes are compact representations that model the regions and discontinuities present in the original image with many fewer points. Thus, image processing operations applied upon those meshes can perform faster than upon the original images. As an example, four simple operations (translation, rotation, scaling and deformation) have been implemented in the 3D geometric domain and compared to their image domain counterparts.