Representation of finite-range increasing filters in the context of computational morphology

Edward R. Dougherty; Divyendu Sinha

doi:10.1117/12.144773

21 May 1993 Representation of finite-range increasing filters in the context of computational morphology

Edward R. Dougherty, Divyendu Sinha

Proceedings Volume 1902, Nonlinear Image Processing IV; (1993) https://doi.org/10.1117/12.144773
Event: IS&T/SPIE's Symposium on Electronic Imaging: Science and Technology, 1993, San Jose, CA, United States

Abstract

The classical Matheron representation of gray-scale filters considers images to possess infinite range, in particular so that they are range translation invariant. A key aspect of the theory is that binary morphology algebraically embeds into gray-scale with binary images possessing gray range minus infinity and zero. While this structure causes no algebraic problems, it does create both topological and probabilistic difficulties. In particular, the theory of optimal gray- scale filters does not contain the theory of optimal binary filters as a special case, and the optimal gray-scale filter takes finite-range images, say [0,M], and yields images with range [-M,2M]. These anomalies are mitigated by the theory of computational morphology. Here, morphological filters preserve the gray range and possess very simple Matheron-type representations. Besides range preservation for finite-range images, the key difference in computational morphology is that a filter possesses a vector of bases, not a single basis. The salient feature remains, that of the filter being represented in terms of erosions.

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Edward R. Dougherty and Divyendu Sinha "Representation of finite-range increasing filters in the context of computational morphology", Proc. SPIE 1902, Nonlinear Image Processing IV, (21 May 1993); https://doi.org/10.1117/12.144773

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KEYWORDS

Binary data

Image filtering

Nonlinear image processing

Fuzzy logic

Optimization (mathematics)

Optimal filtering

Digital filtering

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