2-D binary locally monotonic regression

We introduce binary locally monotonic regression as a first step in the study of the application of local monotonicity for image estimation. Given an algorithm that generates a similar locally monotonic image from a given image, we can specify both the scale of the image features retained and the image smoothness. In contrast to the median filter and to morphological filters, a locally monotonic regression produces the optimally similar locally monotonic image. Locally monotonic regression is a computationally expensive technique, and the restriction to binary-range signals allows the use of Viterbi-type algorithms. Binary locally monotonic regression is a powerful tool that can be used in the solution of the image estimation, image enhancement, and image segmentation problems.