Research and Advances

Optimal histogram matching by monotone gray level transformation

This paper investigates the problem of optimal histogram matching using monotone gray level transformation, which always assigns all picture points of a given gray level i to another gray level T(i) such that if i ≥ j, then T(i) ≥ T(j). The objective is to find a transformed digital picture of a given picture such that the sum of absolute errors between the gray level histogram of the transformed picture and that of a reference picture is minimized. This is equivalent to placing k1 linearly ordered objects of different sizes one by one into k2 linearly ordered boxes of assorted sizes, such that the accumulated error of space underpacked or overpacked in the boxes is minimized; the placement function is monotonic, which ensures a polynomial time solution to this problem. A tree search algorithm for optimal histogram matching is presented which has time complexity O(k1 × k2). If the monotone property is dropped, then the problem becomes NP-complete, even if it is restricted to k2 = 2.


Author Archives

Research and Advances

The reconstruction of binary patterns from their projections

Given the horizontal and vertical projections of a finite binary pattern f, can we reconstruct the original pattern f? In this paper we give a characterization of patterns that are reconstructable from their projections. Three algorithms are developed to reconstruct both unambiguous and ambiguous patterns. It is shown that an unambiguous pattern can be perfectly reconstructed in time m × n and that a pattern similar to an ambiguous pattern can also be constructed in time m × n, where m, n are the dimensions of the pattern frame.

Shape the Future of Computing

ACM encourages its members to take a direct hand in shaping the future of the association. There are more ways than ever to get involved.

Get Involved