Fuzzy Image Enhancement

1. Contrast Adaptation

In recent years, many researchers have applied the fuzzy set theory to develop new techniques for contrast improvement. Following, some of these approaches are briefly described.

1.1. Contrast Improvement with INT- Operator (Pal/King 1981/1983)

1. Step: Define the membership funktion

2. Step: Modify the membership values

3. Step: Generate new gray-levels

1.2. Contrast Improvement using Fuzzy Expected Value (Craig and Schneider 1992)

1. Step: Calculate the image histogram

2. Step: Determine the fuzzy expected value (FEV)

3. Step: Calculate the distance of gray-levels from FEV

4. Step: Generate new gray-levels

1.3. Contrast Improvement with Fuzzy Histogram Hyperbolization (Tizhoosh 1995/1997)

1. Step: Setting the shape of membership function (regrading to the actual image)

2. Step: Setting the value of fuzzifier Beta (a linguistic hedge)

3. Step: Calculation of membership values

4. Step: Modification of the membership values by linguistic hedge

5. Step: Generation of new gray-levels

1.4. Contrast Improvement based on Fuzzy If-Then Ruels (Tizhoosh 1997)

1. Step: Setting the parameter of inference system (input features, membership functions,..)

2. Step: Fuzzification of the actual pixel (memberships to the dark, gray and bright sets of pixels)

3. Step: Inference (e.g. if dark then darker, if gray then gray, if bright then brighter)

4. Step: Defuzzification of the inference result by the use of three singletons

1.5. Locally Adaptive Contrast Enhancement (Tizhoosh et al. 1997)

In many cases, the global fuzzy techniques fail to deliver satisfactory results. Therefore, a locally adaptive implementation is necessary to achieve better results. See some examples and a comparison with calssical approach.

 
2. Sharpening/Noise Reduction

In the literature, we can also find some new fuzzy techniques for sharpening and noise reduction: 

• A Fuzzy Filter for Images Corrupted By Impulse Noise
  Russo, F., Ramponi, G., SPLetters(3), No. 6, June 1996, pp. 168-170

• A design method of fuzzy weighted median filters
  Taguchi, A.[Akira], ICIP96(16A9), 1996

• Weighted fuzzy mean filter for image processing
  Lee, C.-S., Kuo Y.-H., Yau, P.-T., Fuzzy Sets and Systems, vol.89, no.2, pp. 157-180, 1997

• A robust approach to image enhancement based on fuzzy logic
  Choi, Y.S., Krishnapuram, R., IEEE Trans. on Image Processing, vol. 6, No. 6, pp. 808-825, 1997
  

See also Subjective Image Enhancement.