Maximum-likelihood estimation for the discrete Boolean random function

John C. Handley; Edward R. Dougherty

doi:10.1117/12.253458

8 October 1996 Maximum-likelihood estimation for the discrete Boolean random function

Proceedings Volume 2823, Statistical and Stochastic Methods for Image Processing; (1996) https://doi.org/10.1117/12.253458
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

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.

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John C. Handley and Edward R. Dougherty "Maximum-likelihood estimation for the discrete Boolean random function", Proc. SPIE 2823, Statistical and Stochastic Methods for Image Processing, (8 October 1996); https://doi.org/10.1117/12.253458

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KEYWORDS

Statistical modeling

Statistical analysis

Binary data

Image processing

Image segmentation

Mathematical modeling

Data modeling

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