Breast Abnormality Boundary Extraction in Mammography Image Using Variational Level Set and Self-Organizing Map (SOM)
Abstract
:1. Introduction
2. Review of the Existing Models
2.1. Chan and Vese (CV) Model
2.2. SOM-Based Chan–Vese (SOMCV) Model
2.3. Primal-Dual Selective Segmentation 2 (PD2) Model
3. The Proposed Models
3.1. Derivation of Euler Lagrange (EL) Equation
3.2. A New Variant of the SSOM Model
3.3. Steps of the Algorithm for the Proposed SSOM and SSOMH Models
Algorithm 1: Algorithm for the SSOM Model. |
|
Algorithm 2: Algorithm for SSOMH Model. |
|
3.4. Convergence Analysis
- is a closed mapping;
- is continuous;
- is closed at ;
- is a decent function of and ;
- The sequence is contained in a compact set, .
4. Experimental Results
4.1. Segmentation Results of Test Images from the INbreast Database
4.2. Segmentation Results of Test Images from the CBIS-DDSM Database
4.3. Results of SSOMH Model with Different Values of Area Parameter θ
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Model | JSC | DSC | Accuracy | Error |
---|---|---|---|---|
SOMCV | 0.434 | 0.584 | 0.735 | 0.265 |
IIS | 0.801 | 0.887 | 0.961 | 0.040 |
U-NET | 0.519 | 0.674 | 0.847 | 0.153 |
PD2 | 0.819 | 0.899 | 0.962 | 0.038 |
SSOM | 0.883 | 0.937 | 0.976 | 0.024 |
SSOMH | 0.884 | 0.938 | 0.977 | 0.023 |
Model | Computation Time (Seconds) | |
---|---|---|
Training | Testing | |
SOMCV | 0.05 | 1.67 |
U-NET | 327.00 | 0.76 |
PD2 | Not Related | 71.03 |
SSOM | 0.05 | 1.42 |
SSOMH | 0.05 | 1.39 |
Model | JSC | DSC | Accuracy | Error |
---|---|---|---|---|
SOMCV | 0.425 | 0.576 | 0.695 | 0.304 |
IIS | 0.449 | 0.616 | 0.778 | 0.222 |
U-NET | 0.569 | 0.712 | 0.893 | 0.107 |
PD2 | 0.768 | 0.867 | 0.945 | 0.055 |
SSOMH | 0.856 | 0.920 | 0.964 | 0.036 |
Model | Computation Time (Seconds) | |
---|---|---|
Training | Testing | |
SOMCV | 0.05 | 1.79 |
U-NET | 307.00 | 0.73 |
PD2 | Not Related | 98.54 |
SSOMH | 0.05 | 0.8 |
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Ghani, N.A.S.M.; Jumaat, A.K.; Mahmud, R.; Maasar, M.A.; Zulkifle, F.A.; Jasin, A.M. Breast Abnormality Boundary Extraction in Mammography Image Using Variational Level Set and Self-Organizing Map (SOM). Mathematics 2023, 11, 976. https://doi.org/10.3390/math11040976
Ghani NASM, Jumaat AK, Mahmud R, Maasar MA, Zulkifle FA, Jasin AM. Breast Abnormality Boundary Extraction in Mammography Image Using Variational Level Set and Self-Organizing Map (SOM). Mathematics. 2023; 11(4):976. https://doi.org/10.3390/math11040976
Chicago/Turabian StyleGhani, Noor Ain Syazwani Mohd, Abdul Kadir Jumaat, Rozi Mahmud, Mohd Azdi Maasar, Farizuwana Akma Zulkifle, and Aisyah Mat Jasin. 2023. "Breast Abnormality Boundary Extraction in Mammography Image Using Variational Level Set and Self-Organizing Map (SOM)" Mathematics 11, no. 4: 976. https://doi.org/10.3390/math11040976
APA StyleGhani, N. A. S. M., Jumaat, A. K., Mahmud, R., Maasar, M. A., Zulkifle, F. A., & Jasin, A. M. (2023). Breast Abnormality Boundary Extraction in Mammography Image Using Variational Level Set and Self-Organizing Map (SOM). Mathematics, 11(4), 976. https://doi.org/10.3390/math11040976