Unlike conventional photographic images that are characterized only by light intensity or signal energy, laser radar (ladar) range data, or other terrain imagery, contain distance information. Range images are traditionally processed for their three-dimensional content. Previous innovations in partial differential equation (PDE) and total variation based segmentation techniques show good results for conventional images. Fast, efficient variational segmentation techniques that use higher order image models are needed for the preprocessing of such data for applications including target detection and acquisition, compression, and image modeling. We develop a variational segmentation algorithm using higher-order piecewise smooth models for multichannel range imagery such as ladar images. The algorithm is computationally stable, and a fast solution may be found using the fast Cholesky decomposition and a modified binary search tree.

In this paper, a fast encoding algorithm is developed for fractal image compression. At each search entry in the domain pool, the mean square error (MSE) calculations of the given range block and the eight dihedral symmetries of the domain block are obtained simultaneously in the frequency domain, in which the redundant computations are all eliminated in the new encoding algorithm. It is shown in software simulation that the encoding time is about six times faster than that of the baseline method with almost the same PSNR for the retrieved image. The fast algorithm is performed to deal with the eight dihedral symmetries at each search entry. Therefore, it can be applied to various enhanced algorithms which are equipped with quadtree, classification, and other mechanisms.