Title :
Some statistical properties of mathematical morphology
Author :
Wang, Demin ; Haese-Coat, Véronique ; Bruno, Alain ; Ronsin, Joseph
Author_Institution :
Dept. of Electron. & Comput. Eng., Shandong Polytech. Univ., Jinan, China
fDate :
8/1/1995 12:00:00 AM
Abstract :
Analyzes the statistical properties of the basic binary and multilevel morphological operations with both 1-D and 2D structuring elements. Very simple expressions for the output distribution of erosion and opening are derived in the case of any independent identically or nonidentically distributed inputs. The probability relations between erosion and dilation, also between opening and closing, are developed. The output expectation bias and variances are analyzed and computed to show the efficiency of morphological operations for noise supression. As applications of theoretical results, the effects of the morphological operations on noisy signals are illustrated by several examples. The study reveals certain interesting phenomena. For example, the output variances of opening for some input distributions are greater than those of erosion, and morphological operations perform better than median filters in edge preservation
Keywords :
image processing; interference suppression; mathematical morphology; probability; statistical analysis; 1-D structuring elements; 2D structuring elements; binary morphological operations; closing; dilation; edge preservation; erosion; independent identically distributed inputs; independent nonidentically distributed input; mathematical morphology; morphological operations; multilevel morphological operations; noise supression; noisy signals; opening; output distribution; output expectation bias; output variances; probability relations; statistical properties; variances; Analysis of variance; Computer vision; Feature extraction; Filtering; Filters; Image edge detection; Morphological operations; Morphology; Probability; Shape;
Journal_Title :
Signal Processing, IEEE Transactions on
