Riemann Anlamında Eğri Evrim Modeli İncelemesi: Görüntü Segmentasyonu Uygulaması

Abstract

Görüntü bölütlemesinde görüntü üzerinde bir başlangıç eğrisi vererek, eğrinin hareketi ile görüntü üzerindeki objeleri sarması sağlanabilir. Burada eğri hareketine neden olan bir kısmi türevli yapı olduğu için, bu sınıfta bir bölütlemeye kısmi diferensiyel tabanlı bölütleme denilmektedir. Bu çalışmada, kısmi türevlerden oluşturulan bir matematik modelle görüntü segmentasyonu ile ilgili derin bir matematiksel analiz ve sayısal hesaplamalar bulunmaktadır. Sayısal hesaplamalarda, modele kullanıcı tarafından girilen parametrelerin incelemesi yapılmış, ayrıca bu parametrelerin yapay zeka algoritmaları ile optimizasyonu üzerinde durulmuştur. Ayrıca tüm nümerik hesapları yapan kullanıcı dostu bir arayüz uygulaması geliştirilmiştir. Uygulamadaki hesaplamalar yapay zeka algoritmaları ile yapılabilir, veya kullanıcı isterse arayüze gireceği değerlerle manuel bir hesaplamada yapabilir.

Keywords

• Görüntü Bölütleme
• Optimizasyon
• Eğri Evrimi
• Yapay Zekâ
• Matematik Model

Riemannian Curve Model Analysis: Image Segmentation Application

Abstract

By giving an initial curve on the image in image segmentation, it can be provided to wrap the objects on the image with the movement of the curve. A segmentation in this class is called partial differential-based segmentation, since there is a partial differential structure that causes the curve motion here. In this study, there is a deep mathematical analysis and numerical calculations related to image segmentation with a mathematical model created from partial derivatives. In numerical calculations, the parameters entered into the model by the user were examined, and the optimization of these parameters with artificial intelligence algorithms was emphasized. In addition, a user-friendly interface application that performs all numerical calculations has been developed. Calculations in the user interface can be made with artificial intelligence algorithms, or if the user wishes, user can make a manual calculation with the values entered into the interface.

Keywords

• Image Segmentation
• Optimization
• Curve Evolution
• Artificial Intelligence
• Mathematical Model

References

1. Pal, N. R. & Pal, S. K. (1993). A review on image segmentation techniques. Pattern recognition, 26, 1277–1294.
2. Jaglan, P., Dass, R., & Duhan, M. (2019). A comparative analysis of various image segmentation techniques. Proceedings of 2nd International Conference on Communication, Computingand Networking, Springer, 359–374.
3. Javadpour, A., & Mohammadi, A. (2016). Improving brain magnetic resonance image (mri) segmentation via a novel algorithm based on genetic and regional growth. Journal of biomedical physics & engineering, 6, 95.
4. Ziou, D., & Tabbone, S. (1998). Edge detection techniques-an overview. Pattern Recognition and Image Analysis C/C of Raspoznavaniye Obrazov I Analiz Izobrazhenii, 8, 537–559.
5. Al-Amri, S. S., & Kalyankar, N. V. (2010). Image segmentation by using threshold techniques. arXiv:1005. 4020.
6. Senthilkumaran, N., & Rajesh, R. (2008). Edge detection techniques for image segmentation-a survey. Proceedings of the International Conference on Managing Next Generation Software Applications (MNGSA-08), 749–760.
7. Norouzi, A., Rahim, M. S. M., Altameem, A., Saba, T., Rad, A. E., Rehman, A., & Uddin, M. (2014). Medical image segmentation methods, algorithms, and applications. IETE TechnicalReview, 31, 199–213
8. Chebbout, S., & Merouani, H. F. (2012). Comparative study of clustering-based colour image segmentation techniques. 2012 Eighth International Conference on Signal Image Technology and Internet Based Systems, IEEE, 839–844.

9. Amza, C. (2012). A review on neural network-based image segmentation techniques. De Montfort University, Mechanical and Manufacturing Engg., The Gateway Leicester, LE1 9BH, United Kingdom, 1–23.
10. Bebis, G., & Georgiopoulos, M. (1994). Feed-forward neural networks. IEEE Potentials, 13, 27–31.
11. Montana, D. J., & Davis, L. (1989). Training feedforward neural networks using genetic algorithms. IJCAI, 89, 762–767.
12. Erb, R. J. (1993). Introduction to backpropagation neural network computation. Pharmaceutical research, 10, 165–170.
13. Fahlman, C. L. (1990). The cascade-correlation learning architecture. Advances in Neural Information Processing Systems, 2.
14. Lin, W. C., Tsao, E. C. K., & Chen, C. T. (1992). Constraint satisfaction neural networks for image segmentation. Pattern Recognition, 25, 679–693.
15. Ranganath, H., Kuntimad, G., & Johnson, J. (1995). Pulse coupled neural networks for image processing. Proceedings IEEE Southeastcon’95. Visualize the Future, 37–43.
16. Selverston, A. I., & Moulins, M. (1985). Oscillatory neural networks. Annual review of physiology, 47, 29-48.
17. Sulehria, H. K., & Zhang, Y. (2007). Hopfield neural networks: A survey. Proceedings of the 6thConference on 6th WSEAS Int. Conf. on Artificial Intelligence, Knowledge Engineering and Data Bases, Citeseer, 6, 125–130.
18. Dekker, A. H. (1994). Kohonen neural networks for optimal colour quantization. Network: Computation in Neural Systems, 5, 351–367.
19. Alirezaie, J., Jernigan, M., & Nahmias, C. (1997). Neural network-based segmentation of magnetic resonance images of the brain. IEEE Transactions on Nuclear Science, 44,194–198.
20. Azmi, R., & Norozi, N. (2011). A new markov random field segmentation method for breast lesion segmentation in mr images. Journal of medical signals and sensors, 1, 156.
21. Barker, S. A., & Rayner, P. J. (2000). Unsupervised image segmentation using markov random field models. Pattern Recognition, 33, 587–602.
22. Yang, F., & Jiang, T. (2003). Pixon-based image segmentation with markov random fields. IEEE Transactions on Image Processing, 12, 1552–1559.
23. Kass, M., Witkin, A., & Terzopoulos, D. (1988). Snakes: Active contour models. International Journal of Computer Vision, 1, 321–331.
24. Li, C., Huang, R., Ding, Z., Gatenby, J. C., Metaxas, D. N., & J. C., Gore. (2011). A level set method for image segmentation in the presence of intensity inhomogeneities with application to mri. IEEE transactions on image processing, 20, 2007–2016.
25. Jiang, X., Zhang, R., & Nie, S. (2009). Image segmentation based on pdes model: A survey.2009 3rd International Conference on Bioinformatics and Biomedical Engineering, IEEE, 1–4.
26. Xu, C., Yezzi, A., & Prince, J. L. (2000). On the relationship between parametric and geometric active contours. Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No. 00CH37154), IEEE, 1, 483–489.
27. Caselles, V., Catté, F., Coll, T., & Dibos, F. (1993). A geometric model for active contours in image processing. Numerische mathematik, 66, 1–31.
28. Caselles, V., Kimmel, R., & Sapiro, G. (1997). Geodesic active contours. International journal of computer vision, 22, 61–79.
29. Bolsinov, A., V., Kozlov, V. V. E., & Fomenko, A. T. (1995). The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body. Russian Mathematical Surveys, 50, 473.
30. Javaloyes, M. A. (2012). Conformally standard stationary spacetimes and fermat metrics. Recent Trends in Lorentzian Geometry, Springer, 207–230.
31. Perlick, V. (1990). On fermat’s principle in general relativity. i. the general case. Classical and Quantum Gravity, 7, 1319.
32. Torromé, R. G., Piccione P., & Vitório, H. (2012). On fermat’s principle for causal curves in time oriented finsler spacetimes. Journal of mathematical physics, 53, 123.
33. Zhao, D., & Luo, M. (2017). General conformable fractional derivative and its physical interpretation. Calcolo, 54, 903–917.
34. Petrova, S. S., & Solov’ev, A. D. (1997). The origin of the method of steepest descent. Historia Mathematica, 24, 361–375.
35. Chen, Y. G., Giga, Y., Goto, S. (1991). Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. Journal of differential geometry, 33, 749–786.
36. Malladi, R., Sethian, J. A., & Vemuri, B. C. (1995). Shape modeling with front propagation: A level set approach. IEEE transactions on pattern analysis and machine intelligence, 17, 158–175.
37. Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on pattern analysis and machine intelligence, 12, 629–639.
38. Osher, S., & Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on hamilton-jacobi formulations. Journal of computational physics, 79, 12–49.
39. Hussain, K., Salleh, M. N. M., Cheng, S., & Shi, Y. (2019). Metaheuristic research: A comprehensive survey. Artificial Intelligence Review, 52, 2191–2233.
40. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. Proceedings of ICNN’95-International Conference on Neural Networks, IEEE, 4, 1942–1948.
41. Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes university, engineering faculty, computer engineering department, 200, 1-10
42. Dorigo, M., Birattari, M., & Stutzle, T. (2006). Ant colony optimization. IEEE computational intelligence magazine, 1, 28–39.
43. Holland, J. H. (1992). Genetic algorithms. Scientific American, 267, 66–73.
44. Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: Harmony search. Simulation, 76, 60–68.
45. Rao, R. V., Savsani, V. J., & Vakharia, D. (2011). Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems. Computer-Aided Design, 43, 303–315.
46. Simon, D. (2008). Biogeography-based optimization. IEEE transactions on evolutionary computation, 12, 702–713.
47. Potter, K., Hagen, H., Kerren, A., & Dannenmann, P. (2006). Methods for presenting statistical information: The box plot. Visualization of large and unstructured data sets, 4, 97–106.