Piecewise linear image coding using surface triangulation and geometric compression

The provably NP-hard problem of finding optimal piecewise linear approximation for images is extended from 1D curve fitting to 2D surface fitting by a dual-agent algorithm. The results not only yield a storage-efficient codec for range, or intensity, images but also a surface triangulation technique to generate a succinct, accurate and visually pleasant 3D visualization model. Compared with the traditional piecewise linear image coding (PLIC) algorithms, triangulation of a range image is more adaptive due to conformity of the shape, orientation and size of triangles with the image contents. The triangularization algorithm presented here differs from previous approaches in that it strives to minimize the total number of triangles (or vertices) needed to approximate the image surface while keeping the deviation of any intensity value to within a prescribed error tolerance. Unlike most methods of bottom-up triangularization, which could bog down before any mesh simplification even begins, this algorithm fits the surface in a top-down manner, avoiding the generation of most unnecessary triangles. When combined with an efficient 3D triangulation-encoding scheme, the algorithm achieves compact code length with guaranteed error bound, thus providing a more faithful representation of all image features. A variety of benchmark test images have been experimented with and compared.

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