ASSESSING THE COMPLETENESS PROPERTIES OF PAIRWISE GEOMETRIC HISTOGRAMS

A pairwise geometric histogram (PGH) encodes the probability of geomet ric co-occurrences between any line and the set of lines defining an o bject. An object therefore has a set of PGHs associated with it, one h istogram for each line. We describe here the way in which the probabil ity of geometric cooccurrence is calculated and entered in the histogr ams, the different ways these histograms can be defined and the comple teness properties of the set of histograms in terms of arbitrary shape representation. We show that this representation provides unambiguous shape representation by demonstrating an inverse reconstruction algor ithm. We conclude that the methods suggested in a previous paper for o bject recognition and location provide a complete solution to the prob lem of recognition of edge based descriptors for fixed 2D projected vi ews of rigid objects.