## Abstract

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}√ m log m √ 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 these problems are presented.

Original language | English |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Information and Computation |

Volume | 118 |

Issue number | 1 |

DOIs | |

State | Published - Apr 1995 |