Stable image segmentation

The article is devoted to so-called Segmentation Problem that occurs in domain of automatic recognition of digital images when detecting of visually perceived objects. For proved object detection and recognition the famous histogram Otsu’s method (1979) is combined with Mumford-Shah model (1985) of local (bottom up) segmentation basing on the optimal piecewise constant image approximations. The article presents the optimal approximations for the standard example of the real image obtained by exhaustive search of histogram thresholds in limited intensity ranges. To avoid an exhaustive search the spatial distribution of pixels in an image is taken into account. At that the stability condition for the segmented images is derived and tested on the standard image.