During the binary segmentation an image transforms into a binary representation, in which the regions of interest as objects (or their parts) for further analysis are detected as connected components. The underlying image model for binary segmentation and analysis is composed of two separated parts: the first one is to model image domain by using notions and operations of mathematical morphology and the second one is to model the values of intensity function, defined on this domain. The proposed morphological operator transforms gray-scale images into binary ones by comparing image local properties within the structuring elements or structuring regions with a tolerance threshold, giving eroded objects as connected components and dilated contours for further analysis. Since the implementation of this operation is rather complicated, fast algorithms to calculate local properties of intensity function (e.g. mean, square deviation, median, absolute deviation, etc.), using spatial recursion, have been developed. They give a speed-up of order O(N), where N equals L X L is the structuring element size, for computing, e.g. local mean and variance, as compared with their naive calculation.