Abstract

Efficient algorithms exist for the approximate two dimensional matching problem for rectangles. This is the problem of finding all occurrences of an m \Theta m pattern in an n \Theta n text with no more than k mismatch, insertion, and deletion errors. In computer vision it is important to generalize this problem to non-rectangular figures. We make progress towards this goal by defining half-rectangular figures of height m and area a. The approximate two dimensional matching problem for half-rectangular patterns can be solved using a dynamic programming approach in time O(an 2 ). We show an O(kn 2 p m log m p k log k + k 2 n 2 ) algorithm which combines convolutions with dynamic programming. Note that our algorithm is superior to previous known solutions for k m 1=3 . At the heart of the algorithm are the Smaller Matching Problem and the k-Aligned Ones with Location Problem. These are interesting problems in their own right. Efficient algorithms to solve both t...

Citations