Detecting foreground components in grey level images for shift invariant and topology preserving pyramids

A method to single out foreground components in a grey level image and to build a shift invariant and topology preserving pyramid is presented. A single threshold is generally not enough to separate foreground components, perceived as individual entities. Our process is based on iterated identification and removal of pixels causing merging of foreground components with different grey levels. This is the first step to generate a pyramid which, within the limits of decreasing resolution, is shift invariant and topology preserving. Translation dependency is reduced by taking into account the four positions of the partition grid used to build lower resolutions. Topology preservation is favoured by identifying on the highest resolution pyramid level all foreground components and, then, by forcing their preservation, compatibly with the resolution, through lower resolution pyramid levels.