In texture and pattern analysis, the granulometric size distribution is related to morphological features. The mean of this distribution--the pattern spectrum mean--can be used for feature analysis. In this paper, we treat the pattern spectrum as a random function and its moments as random variables. The grain model is as follows: the number of grains is held fixed for the image segment and grains are assumed convex. Generalization to the case of random number of grains is desirable; only limited results are available for this case so far. The statistical distribution of the pattern spectrum mean is studied under two alternative models: Normal and Gamma. The asymptotic distribution of the PSM is developed under each model. A special case of random numbers of grains per segment is analyzed.

Date Published: 1 April 1991
PDF: 11 pages
Proc. SPIE 1451, Nonlinear Image Processing II, (1 April 1991); doi: 10.1117/12.44319

Published in SPIE Proceedings Vol. 1451:
Nonlinear Image Processing II
Edward R. Dougherty; Gonzalo R. Arce; Charles G. Boncelet Jr., Editor(s)