  In this paper a hierarchical model for pixel clustering and image
segmentation is developed. In the model an image is hierarchically structured.
The original image is treated as a set of nested images, which are capable to
reversibly merge with each other. An object is defined as a structural element
of an image, so that, an image is regarded as a maximal object. The simulating
of none-hierarchical optimal pixel clustering by hierarchical clustering is
studied. To generate a hierarchy of optimized piecewise constant image
approximations, estimated by the standard deviation of approximation from the
image, the conversion of any hierarchy of approximations into the hierarchy
described in relation to the number of intensity levels by convex sequence of
total squared errors is proposed.
