1 November 1990 Role of shape in morphological bases for digital moving-average filters
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Abstract
A digital moving-average filter with nonnegative mask weights that sum to unity is a gray-scale morphological filter. As such it possesses a representation as a maximum of erosions over its morphological basis. The present paper investigates the special properties of the digital movingaverage morphological basis these properties being for the most part combinatoric in nature. Shapes of digital structuring elements are related to the filter weights by means of shape classes. This is accomplished by defining a characteristic of a signal relative to the filter weights and then characterizing basis elements by means of the characteristic. The notion of shape is then extended to a more general class of morphological filters. The concept of a morphological quasi-average is introduced and the power of such filters to approximate morphological filters is addressed.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Edward R. Dougherty, Edward R. Dougherty, Eugene J. Kraus, Eugene J. Kraus, } "Role of shape in morphological bases for digital moving-average filters", Proc. SPIE 1350, Image Algebra and Morphological Image Processing, (1 November 1990); doi: 10.1117/12.23572; https://doi.org/10.1117/12.23572
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