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.

Citation Download Citation

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

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available