Global Image Thresholding Adaptive Neuro-Fuzzy Inference System Trained with Fuzzy Inclusion and Entropy Measures
Abstract
:1. Introduction
2. ANFIS, Global Thresholding Techniques and the Main Parts of Our Previous Research
2.1. Global Thresholding Methods and Neural Networks in Image Segmentation
2.2. Fuzzy Subsethood and Entropy Measures
if and only ifin Zadeh’s sense, | (S1) |
Ifin Zadeh’s sense, then, | (S2) |
If, then, | (S3) |
and if, then |
If , then | (S3) |
and if , then |
2.3. Global and Local Thresholding Using Fuzzy Inclusion and Entropy Measures
Algorithm 1: (Global) |
|
- Group 1 N with and (very dark),
- Group 2 N with and
- Group 3 N with and
- Group 4 N with and
- Group 5 N with and (very bright)
- Group 6 N with and
- Group 7 N with and
- Group 8 N with and
Algorithm 2: (Local) |
|
2.4. Why ANFIS
3. First Global Thresholding ANFIS
3.1. Data Construction and Initial Evaluation
3.2. G(lobal) ANFIS 1—Adjusting Otsu’s Targets
4. Second Global Thresholding ANFIS—Experimenting on Public Databases
4.1. Public Databases Which We Used
4.2. Data Set Construction of G(lobal) ANFIS 2
4.3. Testing of G ANFIS 2
- 211 cases where (the difference varied from 0.76 to 0.01).
- 24 cases where (the difference varied from 0.17 to 0.01).
- 6 cases where the difference of and was zero.
- 202 cases where (the difference varied from 0.53 to 0.01),
- 20 cases where (the difference varied from 0.11 to 0.01),
- 19 cases where the difference of and was zero.
5. Summary and Some Further Remarks
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
ANN | Artificial Neural Network |
ANFIS | Adaptive Neuro-Fuzzy Inference System |
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Lines of data matrix 1 used as testing samples | |||||||||
---|---|---|---|---|---|---|---|---|---|
2 | 5 | 7 | 11 | 14 | 18 | 20 | 21 | 25 | 33 |
34 | 35 | 36 | 41 | 43 | 50 | 63 | 65 | 87 | 89 |
101 | 111 | 115 | 123 | 124 | 128 | 132 | 137 | 142 | 152 |
155 | 177 | 178 | 184 | 190 | 193 | 201 | 204 | 209 | 210 |
213 | 220 | 222 | 229 | 231 | 238 | 239 | 240 | 247 | 251 |
Sample | Difference | Sample | Difference | ||||
---|---|---|---|---|---|---|---|
292066 | 0.87 | 0.11 | 0.76 | 90076 | 0.83 | 0.09 | 0.74 |
21077 | 0.81 | 0.14 | 0.67 | 135037 | 0.91 | 0.29 | 0.62 |
27059 | 0.72 | 0.13 | 0.59 | 108041 | 0.86 | 0.30 | 0.56 |
188063 | 0.90 | 0.39 | 0.51 | 106020 | 0.68 | 0.18 | 0.50 |
101087 | 0.82 | 0.33 | 0.49 | 109053 | 0.75 | 0.26 | 0.49 |
69020 | 0.88 | 0.39 | 0.48 | 46076 | 0.84 | 0.37 | 0.47 |
20008 | 0.67 | 0.21 | 0.46 | 385028 | 0.71 | 0.25 | 0.46 |
216066 | 0.81 | 0.36 | 0.45 | 100075 | 0.76 | 0.30 | 0.46 |
368078 | 0.68 | 0.25 | 0.43 | 103070 | 0.70 | 0.28 | 0.42 |
274007 | 0.74 | 0.33 | 0.41 | 55075 | 0.83 | 0.42 | 0.41 |
155060 | 0.72 | 0.31 | 0.41 | 216053 | 0.72 | 0.31 | 0.41 |
38082 | 0.86 | 0.47 | 0.39 | 187003 | 0.64 | 0.25 | 0.39 |
163085 | 0.77 | 0.38 | 0.39 | 23080 | 0.76 | 0.37 | 0.39 |
229036 | 0.68 | 0.30 | 0.38 | 138078 | 0.73 | 0.35 | 0.38 |
22013 | 0.62 | 0.25 | 0.37 | 183055 | 0.74 | 0.38 | 0.36 |
227046 | 0.70 | 0.33 | 0.37 | 216081 | 0.63 | 0.27 | 0.36 |
65132 | 0.72 | 0.36 | 0.36 | 41069 | 0.81 | 0.46 | 0.35 |
45077 | 0.72 | 0.36 | 0.36 | 105025 | 0.86 | 0.51 | 0.35 |
159008 | 0.72 | 0.37 | 0.35 | 178054 | 0.88 | 0.54 | 0.34 |
376043 | 0.60 | 0.26 | 0.34 | 69040 | 0.75 | 0.42 | 0.33 |
… | … | … | … | … | … | … | … |
227092 | 0.54 | 0.69 | −0.15 | 198023 | 0.12 | 0.29 | −0.17 |
Sample | Difference | Sample | Difference | ||||
---|---|---|---|---|---|---|---|
108041 | 0.59 | 0.06 | 0.53 | 90076 | 0.58 | 0.06 | 0.52 |
135037 | 0.65 | 0.18 | 0.47 | 188063 | 0.61 | 0.16 | 0.45 |
61060 | 0.82 | 0.42 | 0.40 | 21077 | 0.43 | 0.06 | 0.37 |
27059 | 0.39 | 0.04 | 0.35 | 100075 | 0.44 | 0.09 | 0.35 |
69020 | 0.41 | 0.07 | 0.34 | 292066 | 0.40 | 0.07 | 0.33 |
101087 | 0.57 | 0.25 | 0.32 | 65132 | 0.42 | 0.10 | 0.32 |
38082 | 0.42 | 0.10 | 0.32 | 46076 | 0.56 | 0.25 | 0.31 |
105025 | 0.53 | 0.22 | 0.31 | 55075 | 0.53 | 0.24 | 0.29 |
94079 | 0.42 | 0.15 | 0.27 | 138032 | 0.33 | 0.06 | 0.27 |
156065 | 0.40 | 0.13 | 0.27 | 368078 | 0.35 | 0.08 | 0.27 |
163085 | 0.37 | 0.11 | 0.26 | 239096 | 0.42 | 0.15 | 0.27 |
106020 | 0.32 | 0.06 | 0.26 | 385028 | 0.33 | 0.08 | 0.25 |
159008 | 0.42 | 0.16 | 0.26 | 48055 | 0.57 | 0.32 | 0.25 |
109053 | 0.30 | 0.05 | 0.25 | 130026 | 0.31 | 0.06 | 0.25 |
41069 | 0.29 | 0.05 | 0.24 | 103070 | 0.35 | 0.10 | 0.25 |
176039 | 0.40 | 0.16 | 0.24 | 187003 | 0.30 | 0.07 | 0.23 |
225017 | 0.29 | 0.06 | 0.23 | 254054 | 0.30 | 0.07 | 0.23 |
143090 | 0.46 | 0.23 | 0.23 | 216053 | 0.38 | 0.16 | 0.22 |
62096 | 0.44 | 0.23 | 0.21 | 183055 | 0.40 | 0.18 | 0.22 |
178054 | 0.49 | 0.28 | 0.21 | 24063 | 0.55 | 0.35 | 0.20 |
… | … | … | … | … | … | … | … |
227092 | 0.27 | 0.38 | −0.11 | 151087 | 0.39 | 0.50 | −0.11 |
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Bogiatzis, A.; Papadopoulos, B. Global Image Thresholding Adaptive Neuro-Fuzzy Inference System Trained with Fuzzy Inclusion and Entropy Measures. Symmetry 2019, 11, 286. https://doi.org/10.3390/sym11020286
Bogiatzis A, Papadopoulos B. Global Image Thresholding Adaptive Neuro-Fuzzy Inference System Trained with Fuzzy Inclusion and Entropy Measures. Symmetry. 2019; 11(2):286. https://doi.org/10.3390/sym11020286
Chicago/Turabian StyleBogiatzis, Athanasios, and Basil Papadopoulos. 2019. "Global Image Thresholding Adaptive Neuro-Fuzzy Inference System Trained with Fuzzy Inclusion and Entropy Measures" Symmetry 11, no. 2: 286. https://doi.org/10.3390/sym11020286
APA StyleBogiatzis, A., & Papadopoulos, B. (2019). Global Image Thresholding Adaptive Neuro-Fuzzy Inference System Trained with Fuzzy Inclusion and Entropy Measures. Symmetry, 11(2), 286. https://doi.org/10.3390/sym11020286