Efficient 2-Dimensional Approximate Matching of Half-Rectangular Figures

Efficient algorithms exist for the approximate two dimensional matching problem for rectangles. This is the problem of finding all occurrences of an m × m pattern in an n × 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[formula][formula] + 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 these problems are presented.

Authors

• A. Amir
• M. Farach

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