A systolic image difference algorithm for RLE-compressed images

Abstract

AbstractÐA new systolic algorithm which computes image differences in run-length encoded (RLE) format is described. The binary image difference operation is commonly used in many image processing applications including automated inspection systems, character recognition, fingerprint analysis, and motion detection. The efficiency of these operations can be improved significantly with the availability of a fast systolic system that computes the image difference as described in this paper. It is shown that for images with a high similarity measure, the time complexity of the systolic algorithm is small and, in some cases, constant with respect to the image size. A formal proof of correctness for the algorithm is also given.

<title>Design and implementation of an FPGA-based processor for compressed images</title>

“…Most systolic image processing algorithms proposed so far are based on operations on pixel data. Fortunately, some compression techniques such as RLE preserve part of the information pertaining to spatial locality allowing us to design a systolic system that finds the difference between two binary images represented in RLE [5].…”

A systolic algorithm to process compressed binary images

“…To make this definition useful we must make the observations that Corollary 3.1: if the runs of a bitstring are viewed as a set of smaller bitstrings, then the XOR of this set is the original bitstring [12], and Corollary 3.2: letting xor(A) represent the result of XORing the bitstrings contained in the set A, we have for arbitrary sets of bitstrings A and B that xor(A B) = xor(fxor(A), xor(B)g) [12]. Now we wish to use these corollaries to prove that the image difference produced by the algorithm is correct.…”

“…At no point in the algorithm will there exist a non-empty cell beyond location k1 + k2 where k1 is the number of runs in the first image and k2 is the number of runs in the second image [12]. …”

“…For notation we refer to the state of cell i before an iteration begins as cell [i].before, and the state of the cell after the first, second, and third steps as cell [ Note that parts three, four and five of the above corollary are included only because they are useful in proving the induction step. The proof of corollary 2.1 is by induction on the number of iterations and can be found in our technical report [12]. The first four parts are reasonably intuitive, however the fifth part may not be.…”

“…In the second case however, the number of errors is fixed at 6 runs each of size 4 pixels, thus while the sequential algorithm still takes large amounts of time, the systolic algorithm averages just over 5 iterations regardless of how large the image gets. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], and the length of error runs is 2-6).…”