Pretopological operators for gray-level image analysis

This paper deals with new operators for gray-level image analysis. These operators are based on concepts of pretopology and they extend mathematical morphology operators. Instead of using one structuring element, these new operators use a basis of several structuring elements. If this basis is composed of only one element, these operators are equivalent to mathematical mor- phology ones. This article presents the pretopological representation space and four pretopological structures of operators. Relations between these new operators and the corresponding morpholog- ical operators are described and compared. Properties and examples are displayed.

[1]  Michel Lamure,et al.  Pretopology as an extension of graph theory : the case of strong connectivity , 2001 .

[2]  G. Matheron.  Random Sets and Integral Geometry , 1976 .

[3]  Stéphane Bonnevay,et al.  A pretopological approach for structural analysis , 2002, Inf. Sci..

[4]  Stéphane Bonnevay,et al.  A pretopological approach for structuring data in non-metric spaces , 1999, Electron. Notes Discret. Math..

[5]  Henk J. A. M. Heijmans.  A note on the umbra transform in gray-scale morphology , 1993, Pattern Recognit. Lett..

[6]  Stanley R Sternberg,et al.  Grayscale morphology , 1986 .

[7]  A C C Gibbs,et al.  Data Analysis , 2009, Encyclopedia of Database Systems.

[8]  Henk J. A. M. Heijmans,et al.  The algebraic basis of mathematical morphology. I Dilations and erosions , 1990, Comput. Vis. Graph. Image Process..

[9]  Soo-Chang Pei,et al.  Hierarchical image representation by mathematical morphology subband decomposition , 1995, Pattern Recognit. Lett..

[10]  Stéphane Bonnevay,et al.  Data Analysis Based on Minimal Closed Subsets , 2000 .

[11]  Henk J. A. M. Heijmans,et al.  The algebraic basis of mathematical morphology : II. Openings and closings , 1991, CVGIP Image Underst..

[12]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[13]  Michel Lamure.  Espaces abstraits et reconnaissance des formes : application au traitement des images digitales , 1987 .

[14]  Xinhua Zhuang,et al.  Image Analysis Using Mathematical Morphology , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  J. Serra.  Introduction to mathematical morphology , 1986 .

[16]  Henk J. A. M. Heijmans,et al.  Theoretical Aspects of Gray-Level Morphology , 1991, IEEE Trans. Pattern Anal. Mach. Intell..