Analysis and design of nonlinear image proc essing filters



Image processing filter is a trasformation of an input image to another image that resembles the input one but is more desireble. Noise removal and edge extraction and emphasis are typical image processing filters. The filters are regarded to apply an identical operation everywhere in the image, i. e. they are shiftinvariant.
The realdomain filter of the image processing filters makes a calculation using the pixel values in the neighborhood of each pixel, and assign the result to the corresponding pixel in the output image. The realdomain filters are categorized into "linear" filters or "nonlinear" ones according to the linearity of the calculation.
The linear filter has a long history of the researches on its analysis and design since the signal processing using electronic circuits was established. The nonlinear filters, however, have a lot of variations and there is no theory of analysis and design applicable commonly to all kinds of the nonlinear filters.
Median and orderstatistical filter is one of nonlinear filters. It is well known that the median filter is quite effective for the removal of impulsive noise, which is the replacement of a pixel with another value that is not related to the input image. There have been a lot of researches to develop variations that remove impulsive noise while preserving image details.
We developed methods of optimizing filter parameters using examples of a corrupted image and its ideal output, using the learning ability of neural networks. We also developed unsupervised optimization method without requiring the ideal outputs by employing appropriate restrictions to the parameters.
I started this research when I was a Ph. D. candidate. After a 10year blank, I restarted this research by a cooperation with Professor Mitsuji Muneyasu of Kansai University. The topics on "mathematical morphology and texture images" and "Pattern spectrum and filter optimization" were derived from this research.
The image of a cat on the left top of this page was often used as an example for my image processing researches when I was a Ph. D. candidate. A short story of this cat is one of the contents of this web site.
Selected publications
Recent researches
 M. Muneyasu, K. Shiohama, and A. Asano, "An Unsupervised Design Method for Weighted Median filters Based on Simulated Annealing," Proc. International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS) 2008, (2008. 12, in press.).
 A. Fujiki, A. Asano, and M. Muneyasu, "Unsupervised optimization of morphological filters for noise removal in texture images," Proc. Joint 3rd International Conference on Soft Computing and Intelligent Systems and 7th International Symposium on advanced Intelligent Systems (SCIS & ISIS 2006) 17941799 (2006. 9).
 A. Fujiki, A. Asano, and M. Muneyasu, "Unsupervised structuring element optimization of morphological opening for texture images," Proc. 2006 International Symposium on Nonlinear Theory and its Applications (NOLTA2006), 711714 (2006. 9).
 A. Fujiki, T. Hashimoto, M. Muneyasu, and A. Asano, "A design of window shapes and weights in weighted median filters for texture images," Proc. 2005 International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS 2005), 665668 (2005. 12).
 A. Asano, Y. Kobayashi, C. Muraki, and M. Muneyasu, "Optimization of gray scale morphological opening for noise removal in texture images," Proc. 47th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS2004), 1, 313316 (2004. 7).
Researches before the blank
 A. Asano, Y. Kasai, and S. Yokozeki, "Linear separability of positive selfdual logical filters," Optical Review, 2, 5, 327330 (1995. 7).
 A. Asano, T. Honda, and S. Yokozeki, "Simulator for Aid of TrialandError Design of Nonlinear Image Processing Filters," Optical Review, 2, 3, 163166 (1995. 5).
 A. Asano, T. Syudoh, and S. Yokozeki, "Efficient Algorithm for Learning Optimization of Morphological Filters," Optical Review, 2, 3, 159162 (1995. 5).
 A. Asano, K. Matsumura, K. Itoh, Y. Ichioka, and S. Yokozeki, "Optimization of morphological filters by learning," Opt. Commun., 112, 265270 (1994. 12).
 A. Asano, K. Itoh, and Y. Ichioka, "RONDO: RankOrder based Nonlinear Differential Operator," Pattern Recognition, 25, 9, 10431059 (1992. 9).
 A. Asano, K. Itoh, and Y. Ichioka, "Optimization of cascaded threshold logic filters for grayscale image processing," Opt. Commun., 88, 485493 (1992. 9).
 A. Asano and L. P. Yaroslavsky, "Experimental study on the fixed points of the RANK filter," Opt. Commun., 88, 199209 (1992. 3).
 A. Asano, K. Itoh, and Y. Ichioka, "Analysis of Nonlinear Filters Using Inductive Inference," Tech. Rep. Osaka Univ. 41, 2056, 221233 (1991. 10).
 A. Asano, K. Itoh, and Y. Ichioka, "Optimization of the weighted median filter by learning," Opt. Lett., 16, 3, 168170 (1991. 2).
 A. Asano, W. Zhang, K. Itoh, and Y. Ichioka, "Convergence properties of recursive rankorder filter and neural network," Pattern Recognit. Lett., 11, 8, 557560 (1990. 10).
 A. Asano, K. Itoh, and Y. Ichioka, "The Nearest Neighbor Median Filter: Some Deterministic Properties and Implementations," Pattern Recognition, 23, 10, 10591066 (1990. 10).
 A. Asano, K. Itoh, and Y. Ichioka, "Bipolar Morphology and Its Applications," Jpn. J. Appl. Phys. Part 2, 29, 7, 12701273 (1990. 7).
