Combinatorial methods for approximate image matching under translations and rotations

Given two{dimensional images T1::n; 1::n] and P1::m; 1::m] where m < n, we develop a fast rotation invariant ltration algorithm for nding the locations of approximate occurrences of P in T. In such an occurrence, each pixel of T should match the corresponding intervals of pixels deened by P. Our lter works by extracting linear sequences of intervals , called features, from P, and by searching these from T to nd candidate positions and orientations for a whole occurrence of P. We give exact combinatorial analysis of the problem. The number of relevant orientations for P is O(m 3) and number of diierent features of length u is O(u 2). These can be reduced to O(m) and O(u) respectively, with heuristics. We show that the optimal feature length is O(log m) and give O(jTj log m) worst case time ltering algorithm for the problem. We conclude with experimental results .