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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 shift-invariant.

The real-domain 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 real-domain 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 order-statistical 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 10-year 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

Researches before the blank

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