Deep Structure of Images in Populations Via Geometric Models in Populations

We face the question of how to produce a scale space of image intensities relative to a scale space of objects or other characteristic image regions filling up the image space, when both images and objects are understood to come from a population. We argue for a schema combining a multi-scale image representation with a multi-scale representation of objects or regions. The objects or regions at one scale level are produced using soft-edged apertures, which are subdivided into sub-regions. The intensities in the regions are represented using histograms. Relevant probabilities of region shape and inter-relations between region geometry and of histograms are described, and the means is given of inter-relating the intensity probabilities and geometric probabilities by producing the probabilities of intensities conditioned on geometry.