Feature-Preserving Image Restoration from Adaptive Triangular Meshes

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