Image Compression with Anisotropic Diffusion
Journal of Mathematical Imaging and Vision
Beating the Quality of JPEG 2000 with Anisotropic Diffusion
Proceedings of the 31st DAGM Symposium on Pattern Recognition
Towards PDE-Based image compression
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Lossless and near-lossless image compression based on multiresolution analysis
Journal of Computational and Applied Mathematics
Original article: Recovering functions: A method based on domain decomposition
Mathematics and Computers in Simulation
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Two complementary geometric structures for the topographic representation of an image are developed in this work. The first one computes a description of the Morse-topological structure of the image, while the second one computes a simplified version of its drainage structure. The topographic significance of the Morse and drainage structures of digital elevation maps (DEMs) suggests that they can been used as the basis of an efficient encoding scheme. As an application, we combine this geometric representation with an interpolation algorithm and lossless data compression schemes to develop a compression scheme for DEMs. This algorithm achieves high compression while controlling the maximum error in the decoded elevation map, a property that is necessary for the majority of applications dealing with DEMs. We present the underlying theory and compression results for standard DEM data.