Learning geometric hashing functions for model-based object recognition

A major problem associated with geometric hashing and methods which have emerged from it is the non-uniform distribution of invariants over the hash space. This problem can affect the performance of the method significantly. Finding a "good" geometric hash function which redistributes the invariants uniformly over the hash space is not easy. In this paper, a new approach is proposed for alleviating the above problem. It is based on the use of an "elastic hash table" which is implemented as a self-organizing feature map neural network (SOFM-NN). In contrast to existing approaches which try to redistribute the invariants over the hash bins, we proceed oppositely, spreading the hash bins over the invariants. During training, the SOFM-NN resembles an elastic net which deforms over the hash space. The objective of the deformation process is to spread more hash bins in hash space areas which are heavily occupied and less hash bins in lower density areas. The advantage of the proposed approach is that it is a process that adapts to the invariants through learning. Hence, it makes absolutely no assumptions about the statistical characteristics of the invariants and the geometric hash function is actually computed through learning. Furthermore, the well known "topology preserving" property of the SOFM-NN guarantees that the computed geometric hash function should be well behaved. Finally, the proposed approach is inherently parallelizable.<>