An approximation algorithm for two-dimensional (2-D) signals, e.g. images, is presented. This approximation is obtained by partitioning the original signal into adjacent regions with each region being approximated in the least square sense by a 2-D analytical function. The segmentation procedure is controlled iteratively to insure at each step the best possible quality between the original image and the segmented one. The segmentation is based on two successive steps: splitting the original picture into adjacent squares of different size, then merging them in an optimal way into the final region configuration. Some results are presented when the approximation is performed by polynomial functions.