An Analysis of Pairwise Geometric Histograms for View-Based Object Recognition

A pairwise geometric histogram (PGH) encodes the probability of geometric co-occurrences between any line and the set of lines defining an object. An object therefore has a set of PGHs associated with it, one histogram for each line. We describe here the way in which the probability of geometric co-occurrence is calculated and entered in the histograms, the different ways these histograms can be denned and the completeness 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 algorithm. We conclude that the methods suggested in a previous paper for object recognition and location provide a complete solution to the problem of recognition of edge based descriptors for fixed 2D projected views of rigid objects.