Patch-based variational image approximation

Vector graphic gives us a new solution to the representation of raster images. Among many types of vectorized representations, the most popular is mesh representation, which inherits the benefits of vector graphics. Inspired by mesh, we propose a novel patch-based representation for raster images, in which pixels are partitioned into regions, and pixels belonging to the same region are converted into a 3D point cloud and approximated by a 3D planar patch with proper boundaries in a variational way. The resulting patches are then encoded via a half-edge structure for storage. The key point is that the vertices of boundaries are not located on the very positions of sample points, i.e. converted pixels, but dependent on the optimal position of the patch, which theoretically reduces the fitting errors. Experiments show that our algorithm produces better results.