We consider the problem of recognizing CAD models at arbitrary orientations observed via the projective transformation on an imaging sensor with noise. Bounds on codebook size are established through the rate-distortion curve for a distortion measure derived from the Hilbert-Schmidt norm for elements of the orthogonal group.

Quadtree decomposition is a simple technique used to obtain an image representation at different resolution levels. This representation can be useful for a variety of image processing and image compression algorithms. This paper presents a simple way to get better compression performances (in MSE sense) via quadtree decomposition, by using near to optimal choice of the threshold for quadtree decomposition; and bit allocation procedure based on the equations derived from rate-distortion theory. The rate-distortion performance of the improved algorithm is calculated for some Gaussian field, and it is examined vie simulation over benchmark gray-level images. In both these cases, significant improvement in the compression performances is shown.