Image Smoothing Based on Fuzzy Reasoning. I. Theory.
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概要
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<I>Image smoothing can remove random statistical noise in images, but it simultaneously degrades the edge sharpness. It is hence necessary for image smoothing to achieve the best combination of the two conflicting factors, noise removal and edge preservation. For this purpose, fuzzy reasoning based on fuzzy set theory is applied to image smoothing. A proper way of smoothing for each pixel is inferred from linguistic rules of the form"If...then...", thus differing from usual smoothing methods based on analytical rules</I>.<BR><I>In the present smoothing method, three fuzzy sets, 'small' (S), 'medium' (M) and'large' (L), are defined by the magnitude of the gradients at the pixels; further, three smoothing filters denoted by SM</I><SUB>1</SUB>, <I>SM</I><SUB>2</SUB> <I>and SM</I><SUB>3</SUB> <I>are proposed as suitable ones for pixels belonging to S, M and L respectively, How suitable SM</I><SUB>1</SUB><I>is for S is expressed by the fuzzy set M</I><SUB>1</SUB>. <I>Similarly, degrees of suitability of SM</I><SUB>2</SUB> <I>and SM</I><SUB>3</SUB> <I>for M and L are expressed by the fuzzy sets M</I><SUB>2</SUB> <I>and M</I><SUB>3</SUB>.<BR><I>The above relation between S and SM</I><SUB>1</SUB><I>is described using M</I><SUB>1</SUB> <I>by the following fuzzy reasoning rule: "If ED (edge magnitude) at a pixel is S then WS (a way of smoothing) for this pixel is M</I><SUB>1</SUB>"<I>or simply"If ED=S then WS-M</I><SUB>1</SUB>. <I>Here, "WS=M</I><SUB>1</SUB>"<I>is the fuzzy statement of" (If ED=S then) SM</I><SUB>1</SUB> <I>is suitable". Similar rules hold between M and M</I><SUB>2</SUB>, <I>and L and M</I><SUB>3</SUB>. <I>From the three reasoning rules, a proper way of smoothing for each pixel is inferred if the magnitude of gradient at the pixel is given</I>.<BR><I>From results for preliminary experiments, it is suggested that the present smoothing algorithm can well combine noise removal and edge preservation, and its computation time is not considerable although it uses the three smoothing filters. It is thus expected that the smoothing algorithm possesses usefulness and practicality</I>.
- 社団法人 日本アイソトープ協会の論文
社団法人 日本アイソトープ協会 | 論文
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