Statistics of the morphological pattern-spectrum mean and variance for a normal-sized convex-base random Boolean image

Francis M. Sand; Edward R. Dougherty

doi:10.1117/12.58369

1 April 1992 Statistics of the morphological pattern-spectrum mean and variance for a normal-sized convex-base random Boolean image

Francis M. Sand, Edward R. Dougherty

Author Affiliations +

Proceedings Volume 1658, Nonlinear Image Processing III; (1992) https://doi.org/10.1117/12.58369
Event: SPIE/IS&T 1992 Symposium on Electronic Imaging: Science and Technology, 1992, San Jose, CA, United States

Abstract

The morphological pattern spectrum (or, granulometric size distribution) results from iteratively opening an image and at each step recording the area of the opened image. Owing to the manner in which the size distribution is normalized, it defines a probability distribution function, and possesses moments. If a binary image is considered as a random process, then the moments of the pattern spectrum are random variables, and it is these random moments that are employed as shape and texture signatures in image classification and segmentation. In the present paper, the moments of these moments are studied for a random Boolean model that has been employed in various applications. Both exact and asymptotic methods are developed to express the mean and variance of the pattern-spectrum mean and variance.

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Francis M. Sand and Edward R. Dougherty "Statistics of the morphological pattern-spectrum mean and variance for a normal-sized convex-base random Boolean image", Proc. SPIE 1658, Nonlinear Image Processing III, (1 April 1992); https://doi.org/10.1117/12.58369

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