  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.
