Görüntü Bölütleme için Fourier Dönüşümü, Hessian Matris ve Özdeğerler Kullanılarak Yeni bir Aktif Kontur Modeli

Abstract

Aktif kontur model nesne sınırlarını bölütleyebilir ve bu yüzden görüntü analizinde ve bölütlemesinde kullanılmaktadır. Frekans bilgisi ve yüksek mertebe diferansiyel hesaplamalar içermeyen mevcut aktif kontur modelleri yoğunluk eşitsizliği ve gürültü içeren bazı görüntüleri bölütlerken başarısızdır. Bu çalışmada mevcut Hessian matris ve özdeğer temelli metot içerisine Fourier dönüşümü entegre edilerek yeni bir aktif kontur modeli geliştirilmiştir. Giriş görüntüsünün Fourier dönüşümü hesaplanmış ve düzey küme fonksiyonunda aktif bir şekilde kullanılmıştır. Sonuçta frekans alanında elde edilen piksel yoğunluk bilgisinin diferansiyel analizi gerçekleştirilmiştir. Ayrıca piksel analizinin uzaysal bilgi içerdiği mevcut Hessian matris ve özdeğer temelli metottan farklı olarak, bu yeni model değişmez Fourier alanında sınır piksel bileşenlerini tespit etmeyi amaçlamaktadır. Geliştirilen model mevcut Hessian matris ve özdeğer temelli metot ve LIF metodu ile karşılaştırılmıştır. Deneysel sonuçlar önerilen metodun düşük iterasyon ve yüksek bölütleme doğruluğu ile daha iyi bölütleme performansını elde edebildiğini göstermiştir.

Keywords

• Aktif kontur modeli
• Görüntü bölütleme
• Fourier dönüşümü
• Hessian matrisi

A New Active Contour Model Using Fourier Transform, Hessian Matrix And Eigenvalues For Image Segmentation

Abstract

Active contour model can segment object boundaries and thus it has been used in image analysis and segmentation. Current active contour models without frequency information and high-order differential computations fail when segmenting some images containing intensity inhomogeneity and noise. In this paper, a new active contour model has been developed by integrating the Fourier transform into the existing Hessian matrix and eigenvalue-based method. The Fourier transform of the input image is calculated and used actively in the level set function. As a result, differential analysis of the pixel density information obtained in the frequency domain has also performed. Also, unlike the current Hessian matrix and eigenvalue-based method where the pixel analysis contains the spatial information, this new model aim to detect the boundary pixel components in the invariant Fourier domain. The developed method is compared with existing Hessian matrix and eigenvalue-based method and LIF method. Experimental results show that the proposed method can achieve a better segmentation performance with less iterations and high segmentation accuracy.

Keywords

• Active contour model
• Image segmentation
• Fourier transform
• Hessian matrix

References

1. 1. Kass M, Witkin A, Terzopoulos D. Snakes: Active contour models. Int J Comput Vis. 1988;1(4):321–31.
2. 2. Caselles V, Kimmel R, Sapiro G. Geodesic Active Contours. Int J Comput Vis. 1997;22(1):61–79.
3. 3. Hanbay K, Talu MF. A novel active contour model for medical images via the Hessian matrix and eigenvalues. Comput Math with Appl. 2018;75(9):3081–104.
4. 4. Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy. Pattern Recognit. 2010;43(4):1199–206.
5. 5. Zhang K, Zhang L, Song H, Zhou W. Active contours with selective local or global segmentation: A new formulation and level set method. Image Vis Comput. 2010;28(4):668–76.
6. 6. Chan TF, Vese LA. Active contours without edges. IEEE Trans Image Process. 2001;10(2):266–77.
7. 7. Paragios N. Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Trans Pattern Anal Mach Intell. 2000;22(3):266–80.
8. 8. Min H, Xia L, Pan Q, Fu H, Wang H, Li H. Local features based level set method for segmentation of images with intensity inhomogeneity. Commun Comput Inf Sci. 2017;772:498–508.

9. 9. Duan Y, Peng T, Qi X. Active contour model based on LIF model and optimal DoG operator energy for image segmentation. Optik. 2020;202:163667.
10. 10. Li C, Kao CY, Gore JC, Ding Z. Implicit active contours driven by local binary fitting energy. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Minneapolis; 2007. p. 1–7.
11. 11. Brown ES, Chan TF, Bresson X. Completely convex formulation of the Chan-Vese image segmentation model. Int J Comput Vis. 2012;98(1):103–21.
12. 12. Vese LA, Chan TF. A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model. Int J Comput Vis 2002 503. 2002;50(3):271–93.
13. 13. Menon R V., Kalipatnapu S, Chakrabarti I. High speed VLSI architecture for improved region based active contour segmentation technique. Integration. 2021;77:25–37.
14. 14. Niu S, Chen Q, de Sisternes L, Ji Z, Zhou Z, Rubin DL. Robust noise region-based active contour model via local similarity factor for image segmentation. Pattern Recognit. 2017;61:104–19.
15. 15. Abdelsamea MM, Pitiot A, Grineviciute RB, Besusparis J, Laurinavicius A, Ilyas M. A cascade-learning approach for automated segmentation of tumour epithelium in colorectal cancer. Expert Syst Appl. 2019;118:539–52.
16. 16. Carmo M Do. Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, NJ; 1976.
17. 17. Cooley JW, Tukey JW. An algorithm for the machine calculation of complex Fourier series. Math Comput. 1965;19(90):297–301.
18. 18. Duhamel P, Vetterli M. Fast fourier transforms: A tutorial review and a state of the art. Signal Processing. 1990;19(4):259–99.
19. 19. Abdou IE, Pratt WK. Quantitative design and evaluation of enhancement/thresholding edge detectors. Proc IEEE. 1979;67(5):753–63.