Abstract
Adaptive reconstructive τ -openings are to employed to recover signal from noise in the binary union-noise model. Openings are parameterized in accordance with Euclidean granulometric representation, the parameter being restricted to nonnegative integers. The filter-parameter space is treated as the countably infinite state space in a Markov chain whose transitions occur at each encounter with a grain when scanning the image. An upward or downward transition occurs when a noise or signal grain, respectively, is misrecognised.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dougherty, E. R., ‘Optimal Mean-Square N-Observation Digital Morphological Filters – Part I: Optimal Binary Filters,’ Computer Vision, Graphics, and Image Processing - Image Understanding, Vol. 55, No. 1, January, 1992.
Loce, R. P., and E. R. Dougherty, ‘Facilitation of Optimal Binary Morphological Filter Design Via Structuring-Element Libraries and Observation Constraints,’ Optical Engineering, Vol. 31, No. 5, May, 1992.
Loce, R. P., and E. R. Dougherty, ‘Optimal Morphological Restoration: The Morphological Filter Mean-Absolute-Error Theorem,’ Visual Communication and Image Representation,Vol. 3, No. 4, December, 1992.
Dougherty, E. R., and R. P. Loce, ‘Efficient Design Strategies for the Optimal Binary Digital Morphological Filter: Probabilities, Constraints, and Structuring-Element Libraries,’ Mathematical Morphology in Image Processing, ed. E. R. Dougherty, Marcel Dekker, New York, 1993.
Dougherty, E. R., and R. P. Loce, ‘Optimal Mean-Absolute-Error Hit-or-Miss Filters: Morphological Representation and Estimation of the Binary Conditional Expectation,’ Optical Engineering, Vol. 32, No. 4, April, 1993.
Dougherty, E. R., Haralick, R. M., Chen, Y., Agerskov, C., Jacobi, U., and P. H. Sloth, ‘Estimation of Optimal T-Opening Parameters Based on Independent Observation of Signal and Noise Pattern Spectra,’ Signal Processing, Vol. 29, December, 1992.
Cuciurean-Zapan, C. and E. R. Dougherty, ‘Optimal Openings for Overlapping Signal and Noise Grains,’ Proc. SPIE Image Algebra and Morphological Image Processing, Vol. 2300 July 1994.
Cuciurean-Zapan, C. and E. R. Dougherty, ‘Optimal Reconstructive r-Openings for Disjoint and Statistically Modeled Nondisjoint Grains,’ Morphological Imaging Laboratory Report, MIL-04–94, Rochester Institute of Technology, Rochester, N.Y. April 1994.
Schonfeld, D., and Goutsias, J., ‘Optimal Morphological Pattern Restoration from Noisy Binary Images,’ IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 1, January, 1991.
Salembier, P., ‘Structuring Element Adaptation for Morphological Filters,’ Visual Communication and Image Representation, Vol. 3, No. 2, June, 1992.
Chen, Y., and E. R. Dougherty, ‘Adaptive Reconstructive τ-Openings,’ Morphological Imaging Laboratory Report, MIL-05–94, Rochester Institute of Technology, Rochester, N.Y. May 1994.
Matheron, G., Random Sets and Integral Geometry, John Wiley, New York, 1975.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Chen, Y., Dougherty, E.R. (1994). Adaptive Parameterized Openings. In: Serra, J., Soille, P. (eds) Mathematical Morphology and Its Applications to Image Processing. Computational Imaging and Vision, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1040-2_5
Download citation
DOI: https://doi.org/10.1007/978-94-011-1040-2_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4453-0
Online ISBN: 978-94-011-1040-2
eBook Packages: Springer Book Archive