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Proceedings Paper

Maximum-likelihood estimation for the discrete Boolean random function
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Paper Abstract

Gray-scale textures can be viewed as random surfaces in gray-scale space. One method of constructing such surfaces is the Boolean random function model wherein a surface is formed by taking the maximum of shifted random functions. This model is a generalization of the Boolean random set model in which a binary image is formed by the union of randomly positioned shapes. The Boolean random set model is composed of two independent random processes: a random shape process and a point process governing the placement of grains. The union of the randomly shifted grains forms a binary texture of overlapping objects. For the Boolean random function model, the random set or grain is replaced by a random function taking values among the admissible gray values. The maximum over all the randomly shifted functions produces a model of a rough surface that is appropriate for some classes of textures. The Boolean random function model is analyzed by viewing its behavior on intersecting lines. Under mild conditions in the discrete setting, 1D Boolean random set models are induced on intersecting lines. The discrete 1D model has been completely characterized in previous work. This analysis is used to derive a maximum- likelihood estimation for the Boolean random function.

Paper Details

Date Published: 8 October 1996
PDF: 8 pages
Proc. SPIE 2823, Statistical and Stochastic Methods for Image Processing, (8 October 1996); doi: 10.1117/12.253458
Show Author Affiliations
John C. Handley, Xerox Corp. (United States)
Edward R. Dougherty, Rochester Institute of Technology (United States)

Published in SPIE Proceedings Vol. 2823:
Statistical and Stochastic Methods for Image Processing
Edward R. Dougherty; Francoise J. Preteux; Jennifer L. Davidson, Editor(s)

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