In this paper, using a coding theoretic approach, we implement Rissanen's concept of minimum description length (MDL) for segmenting an image into piecewise homogeneous regions. Our image model is a Gaussian random field whose mean and variance functions are piecewise constant across the image. The image pixels are (conditionally) independent and Gaussian, given the mean and variance functions. The model is intended to capture variations in both intensity (mean value) and texture (variance). We adopt a multi-scale tree based approach to develop two segmentation algorithms, using MDL to penalize overly complex segmentations. One algorithm is based on an adaptive (greedy) rectangular partitioning scheme. The second algorithm is an optimally-pruned wedgelet decorated dyadic partitioning. We compare the two schemes with an alternative constant variance dyadic CART (classification and regression tree) scheme which accounts only for variations in mean, and demonstrate their performance with SAR image segmentation problems.