Progressive refinement using local variance estimators

When transmitting an image over a slow communications link, it is desired to provide the best display possible in early stages of the transmission. Progressive refinement attempts to continuously minimize the deviation between the image and its displayed approximation. It is shown that this minimization is accomplished by transmitting average values of regions of the image at increasingly fine levels of resolution. The optimal refinement strategy is to subdivide the region which maximizes the product of area and pixel variance. Typically, the receiving process cannot determine the pixel variance. Estimators of the variance can be computed from information already received are developed. They are applied to refinement over the spatial distribution of values and simultaneously to refinement over their gray-scale quantization. The estimators are shown to apply equally well to monochrome and full-color image. These techniques are implemented with no transmission overhead and are shown to generate qualitatively and quantitatively superior displays