Constant-time hough transform on the processor arrays with reconfigurable bus systems

We develop constant-time algorithms to compute the Hough transform on a processor array with a reconfigurable bus system (abbreviated to PARBS). The PARBS is a comptuation model which consists of a processor array and a reconfigurable bus system. It is a very powerful computation model in that many problems can be solved efficiently. In this paper, we introduce the concept of iterative-PARBS which is similar to the FOR-loop construct in sequential programming languages. The iterative-PARBS is a building block in which the processing data can be routed through it several times. We can think it as a "hardware subroutine". Based on this scheme, we are able to explore constant-time Hough transform algorithms on PARBS. The following new results are derived in this study: 1) The sum of n bits can be computed in O(1) times on a PARBS with O(n^1+e{open}) processors for any fixed e{open}>0. 2) The weights of each simple path of an n*n image can be computed in O(1) time on a 3-D PARBS with O(n^2+e{open}) processors for any fixed e{open}>0. 3) The p angle Hough transform of an n*n image can be computed in O(1) time on a PARBS with O(p*n^2+e{open}) processors for any fixed e{open}>0 with p copies of the image pretiled. 4) The p angle Hough transform of an n*n image can be computed in O(1) time on a PARBS with O(p*n³) processors.