A fast morphological filtering algorithm

Abstract

AbstractThis paper proposes an algorithm for fast morphological filtering using structuring elements of arbitrary two‐dimensional shape. The conventional fast morphological filtering has the constraint that the structuring element should be decomposable. The proposed method solves this problem by adding the result for the area which becomes a new object of calculation as a result of the motion of the structuring element and deleting the result for the area which goes outside the object for calculation. The proposed method has the feature that the calculation result is retained for each area deleted simultaneously from the object of calculation, and then morphological filtering is realized. Compared to the conventional fast algorithm, the constraint is reduced in the sense that undecomposable structuring elements can be used, and the method can be applied to multivalued images. Furthermore, the processing speed is independent of the density resolution of the considered image. The computation complexity is O(4rs) for the case of a circular structuring element, for example, where r is the radius of the structuring element and s is the number of pixels in the original image. This paper presents an experiment for comparison between the proposed algorithm and the conventional algorithm. The experiment reveals that the proposed algorithm is approximately twice as fast as the conventional fast method. An experiment is also performed for ring‐shaped structuring elements, to which the conventional fast method is difficult to apply, and the result is compared to the conventional method without speed improvement. The results reveal that the processing time in the method without speed improvement increases when the number of pixels in the structuring element is increased, but it does not increase in the proposed method. Thus, the proposed method is more effective when the processing time required in the conventional method is long. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(14): 23–33, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10438