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

Volume

43

Issue

8

fYear

1995

fDate

8/1/1995 12:00:00 AM

Firstpage

1955

Lastpage

1965

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;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.403354

Filename

403354