 
Summary: Efficient 2dimensional Approximate Matching of
Halfrectangular Figures \Lambda
Amihood Amir y Martin Farach z
Georgia Tech DIMACS
July 23, 1993
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 nonrectangular figures.
We make progress towards this goal by defining halfrectangular figures of height m
and area a. The approximate two dimensional matching problem for halfrectangular
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 Ÿ m 1=3 .
