Scaling Images and Image Features via the Renormalization Group

Abstract

The problem of obtaining high-quality images and image features at different scales is discussed. Emphasis is placed on a Markov image model described in a lattice by a Gaussian noise and a local regularization term depending upon the image discontinuities. An approximate self-similar property of the model is derived by a process of averaging over half of the lattice sites. This is known as the renormalization group approach. Two multiscale pyramid structures, one of images and the other of image discontinuities, are obtained. The coarse images generated by the proposed method are smooth and show good contrast. The approach, when applied in the reverse order, is capable of enlarging images, while accounting for the original image features. The quality of the derived pyramid is demonstrated by using it to help solve a segmentation problem.<<ETX>>