ACM Computing Surveys (CSUR)
Computing 2-D Min, Median, and Max Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Directional Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Dilation, Erosion, Opening, and Closing Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological Operators with Discrete Line Segments
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Morphological Erosions and Openings: Fast Algorithms Based on Anchors
Journal of Mathematical Imaging and Vision
Computationally efficient, one-pass algorithm for morphological filters
Journal of Visual Communication and Image Representation
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The current best bound on the number of comparison operations needed to compute the running maximum or minimum over a p-element sliding data window is approximately three comparisons per output sample [1], [2], [3], [4]. This bound is probabilistic for the algorithms in [2], [3], [4] and is derived for their complexities on the average for independent, identically distributed (i.i.d.) input signals (uniformly i.i.d., in the case of the algorithm in [2]). The worst-case complexities of these algorithms are O(p). The worst-case complexity C1 = 3 驴 4驴/驴p comparisons per output sample for 1D signals is achieved in the Gil-Werman algorithm [1]. In this correspondence we propose a modification of the Gil-Werman algorithm with the same worst-case complexity but with a lower average complexity. A theoretical analysis shows that using the proposed modification the complexities of sliding Max or Min 1D and 2D filters over i.i.d. signals are reduced to C1 = 2.5 驴 3.5驴/驴p + 1驴/驴p2 and C2 = 5 驴 7驴/驴p + 2驴/驴p2 comparisons per output sample on the average, respectively. Simulations confirm the theoretical results. Moreover, experiments show that even for highly correlated data, namely, for real images the behavior of the algorithm remains the same as for i.i.d. signals.