Theory of Fuzzy Image Processing

Fuzzy image processing is a collection of different areas of fuzzy set theory, fuzzy logic and fuzzy measure theory. The following topics represent the most important theoretical components of fuzzy image processing:

• Fuzzy Geometry (Metric, topology, ...)

• Measures of Fuzziness and Image Information (entropy, correlation, divergence, expected values, ...)

• Fuzzy Inference Systems (image fuzzification, inference, image defuzzification)

• Fuzzy Clustering (Fuzzy c-means, possibilistic c-means, ...)

• Fuzzy Mathematical Morphology (Fuzzy ersion, fuzzy dilation, ...)

• Fuzzy Measure Theory (Sugeno measure/integral, possibility measures, necessity measures,...)

• Fuzzy Grammars

• Combined Approaches (Neural fuzzy/fuzzy neural approaches, fuzzy genetic algorithms, fuzzy wavelet analysis)

• Extension of classical methods (Fuzzy Hough transform, fuzzy median filtering, ...)

To use the these components systematically, we need to develop a new image understanding. The image fuzzification, therefore, plays a pivotal role in all image processing systems that apply any of these components. Tizhoosh distinguishes in his book between the following kinds of image fuzzification:

1. Histogram-based gray-level fuzzification (or briefly histogram fuzzification)
   Example: brightness in image enhancement (see Fig. 1)

2. Local fuzzification (Example: edge detection)

3. Feature fuzzification (Scene analysis, object recognition)