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The triangulation of images has become an active research area in recentyears for its compressive representation and ease of image processing andvisualization. However, little work has been done on how to faithfully recoverimage intensities from a triangulated mesh of an image, a process also known asimage restoration or decoding from meshes. The existing methods such as linearinterpolation, least-square interpolation, or interpolation based on radialbasis functions (RBFs) work to some extent, but often yield blurred features(edges, corners, etc.). The main reason for this problem is due to theisotropically-defined Euclidean distance that is taken into consideration inthese methods, without considering the anisotropicity of feature intensities inan image. Moreover, most existing methods use intensities defined at mesh nodeswhose intensities are often ambiguously defined on or near image edges (orfeature boundaries). In the current paper, a new method of restoring an imagefrom its triangulation representation is proposed, by utilizing anisotropicradial basis functions (ARBFs). This method considers not only the geometrical(Euclidean) distances but also the local feature orientations (anisotropicintensities). Additionally, this method is based on the intensities of meshfaces instead of mesh nodes and thus provides a more robust restoration. Thetwo strategies together guarantee excellent feature-preserving restoration ofan image with arbitrary super-resolutions from its triangulationrepresentation, as demonstrated by various experiments provided in the paper.

Adaptive Mesh Representation and Restoration of Biomedical Images