论文信息 - Some statistical properties of mathematical morphology

Some statistical properties of mathematical morphology

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. >

[1] T. Nodes,et al. The Output Distribution of Median Type Filters , 1984, IEEE Trans. Commun..

[2] Jaakko Astola,et al. Analysis of noise attenuation in morphological image processing , 1991, Electronic Imaging.

[3] R. Schafer,et al. Morphological systems for multidimensional signal processing , 1990, Proc. IEEE.

[4] Joseph Naor,et al. Multiple Resolution Texture Analysis and Classification , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5] Joseph Ronsin,et al. Compared performances of morphological, median type, and running mean filters , 1992, Other Conferences.

[6] Petros Maragos. A Representation Theory for Morphological Image and Signal Processing , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[7] Frank Y. Shih,et al. Image analysis using mathematical morphology: algorithms and architectures , 1988 .

[8] Jaakko Astola,et al. Morphological filtering of noisy images , 1990, Other Conferences.

[9] G. Arce,et al. Morphological filters: Statistics and further syntactic properties , 1987 .

[10] B I Justusson,et al. Median Filtering: Statistical Properties , 1981 .

[11] Jaakko Astola,et al. Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation , 1991, IEEE Trans. Signal Process..