Detection of Lines by Combinatorial Optimization

As far as adopting the voting process is concerned, the maintenance of the accumulator during the computation cannot be neglected. We propose a Hough transform without the accumulator, since the maintenance of the accumulator during the computation is an expensive task. We first formulate the fitting of lines on a plane as a mathematical programming problem. Second, we introduce a relaxation method to solve this problem. Our method is based on the mathematical property that the grouping of sample points is achieved by the permutation for the sequence of the sample points.