In this paper we discussed problems associated with segmentation based on edge detection by performing a least-squares fit to either the local mean or texture of a SAR image. An important stage in the discussion is the extent to which this algorithm represents an optimum process. We therefore study typical statistical properties of a SAR image of the Amazon rain forest and establish corresponding optimum estimators. We demonstrate that the amplitude is not far from optimum for segmenting the mean by least-squares fitting while both the normalized log of the intensity and the amplitude contrast approximate a maximum likelihood texture measure. We next compare the statistics of these measures with equivalent Gaussians to establish the extent to which a least-squares fit represents the maximum likelihood method for determining edge height and position. Finally theoretical predictions are compared with texture segmentation results on the rain forest example.