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Signal and image processing using three-dimensional binary ranking transforms

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Abstract

Because binary mathematical morphology permits fast local neighborhood operations by flash conversion, it is used extensively in high-speed pattern-recognition computer systems. Further, since anyN-dimensional integer function may be represented by an (N + 1)-dimensional binary (bilevel) function, ordinary two-dimensional graylevel images become three-dimensional binary images. Thus these images may be processed by high-speed flash-conversion computers assuming that a sufficiently compact three-dimensional kernel can be devised. The tetradekahedron of the face-centered-cubic tessellation forms a perfect kernel in three-dimensions. Its neighborhood is compact. It has total symmetry with all 12 neighbors equidistant from the central element. Using this kernel a variety of useful three-dimensional morphological operations may be performed for target track detection, shaded graphics, data clustering, automated focusing, and spatial filtering.

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Authors and Affiliations

  1. Kensal Consulting, Tucson, Arizona, USA

    Kendall Preston Jr.

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

    Kendall Preston Jr.

Authors
  1. Kendall Preston Jr.
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Additional information

This research was supported by the National Cancer Institute (Grant CA45047), the National Science Foundation (Grant DCR8611863), the Office of Naval Research (Contract Number N001488K-0435-N143), and the Department of Defense (delivery order 00055, San Diego State University Foundation, under Contract 85-D0203 from the Naval Ocean Systems Center).

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Preston, K. Signal and image processing using three-dimensional binary ranking transforms. Circuits Systems and Signal Process 11, 137–151 (1992). https://doi.org/10.1007/BF01189224

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  • DOI: https://doi.org/10.1007/BF01189224

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