Abstract: A system is disclosed providing accurate compression, storage, transmission and reconstruction of both simulated and empirical data representing terrain and other physical or hypothetical signals or surfaces, in one or multiple dimensions. In one embodiment, a gradient of an original surface is generated, and the data representing that gradient is compressed, then stored and/or transmitted. Reconstruction of the gradient yields an accurate representation of the original gradient. An alternative embodiment includes taking a second gradient of the original surface before compression, in which case reconstruction yields the second gradient, from which the first gradient can also be recovered.

Abstract: A method and apparatus for compression and restoration of images, videos, surfaces, curves and, generally, pixel-based data sets, including: feature-based quantization using a set of N isocontours; compressing each of these N contours using a level set-based compression of curves or surfaces—and/or combining the quantization with a conventional method for compression of surfaces; and decompressing the compressed data using a nonoscillatory reconstruction. The method is naturally multiscale, but does not use wavelets or other multiscale-basis functions. The method performs compression and decompression (1) without excessive computational complexity, even in the presence of topological changes such as merging or breaking of isocontours as the scale changes, (2) with excellent image fidelity, (3) without unacceptable artifacts such as ringing, blurring, or blocking, (4) with simple and natural grid based ways of calculating geometric features such as normals, principal curvatures.

Abstract: A system is disclosed providing accurate compression, storage, transmission and reconstruction of both simulated and empirical data representing terrain and other physical or hypothetical signals or surfaces, in one or multiple dimensions. In one embodiment, a gradient of an original surface is generated, and the data representing that gradient is compressed, then stored and/or transmitted. Reconstruction of the gradient yields an accurate representation of the original gradient. An alternative embodiment includes taking a second gradient of the original surface before compression, in which case reconstruction yields the second gradient, from which the first gradient can also be recovered.

Abstract: A system is disclosed providing accurate compression, storage, transmission and reconstruction of both simulated and empirical data representing terrain and other physical or hypothetical signals or surfaces, in one or multiple dimensions. In one embodiment, a gradient of an original surface is generated, and the data representing that gradient is compressed, then stored and/or transmitted. Reconstruction of the gradient yields an accurate representation of the original gradient. An alternative embodiment includes taking a second gradient of the original surface before compression, in which case reconstruction yields the second gradient, from which the first gradient can also be recovered.

Abstract: A method and apparatus for compression and restoration of images, videos, surfaces, curves and, generally, pixel-based data sets, including: feature-based quantization using a set of N isocontours; compressing each of these N contours using a level set-based compression of curves or surfaces—and/or combining the quantization with a conventional method for compression of surfaces; and decompressing the compressed data using a nonoscillatory reconstruction. The method is naturally multiscale, but does not use wavelets or other multiscale-basis functions. The method performs compression and decompression (1) without excessive computational complexity, even in the presence of topological changes such as merging or breaking of isocontours as the scale changes, (2) with excellent image fidelity, (3) without unacceptable artifacts such as ringing, blurring, or blocking, (4) with simple and natural grid based ways of calculating geometric features such as normals, principal curvatures.