Reducing Aliasing Problem in Images using Neutrosophic Set-Based Diffusion Method

Abstract

Image enhancement is a significant topic in computer vision and image processing applications. In this paper, a new neutrosophic set based diffusion method is proposed to reduce aliasing on edge regions. Based on the diffusion equation of Ziou ve Horé, the new calculation methodology for gradient and curvature in the diffusion equation is presented. In the proposed method, aliased image is converted into the neutrosophic set and defined by three membership sets: truth, indeterminacy, and falsity. Then the proposed method actively uses the truth and falsity memberships of the neutrosophic set, and reduces aliasing artifacts. In the gradient calculation, the proposed method uses the neutrosophic truth instead of the original input image. Also, the neutrosophic falsity has been used to calculate the curvature calculation. Since the neutrosophic membership sets are more immune to noise, the disadvantage of traditional diffusion equations has been resolved in terms of noise. The neutrosophic sets can suppress the noise components, and thus the smooth gradient and curvature models can be calculated. These gradient and curvature informations reflect both the edge changes and aliasing artifacts in aliased image. Thus inverse diffusivity process in the equation of Ziou ve Horé is performed efficiently. The proposed method reduces aliasing artifacts while preserving the details of edge regions through neutrosophic set. The experiment results show that the proposed method can detect the aliasing problems on edge regions. Also, Mean Square Error (MSE) metric is used to evaluate the proposed diffusion method's performance. The results are compared with results of other methods on the same images. This new method can be used as a pre-processing step for applications in image processing.

Keywords

• Image enhancement
• Neutrosophic set
• Diffusion equation

Nötrozofik Küme Temelli Difüzyon Metodu Kullanılarak Görüntülerdeki Örtüşme Problemini Azaltma

Öz

Görüntü iyileştirme bilgisayar görmesi ve görüntü işleme uygulamalarında önemli bir konudur. Bu çalışmada kenar bölgelerindeki örtüşmeyi azaltmak için nötrozofik küme temelli yeni bir difüzyon metodu önerilmiştir. Ziou ve Horé’nin difüzyon denklemi temel alınarak, difüzyon denklemindeki gradyan ve eğrilik için yeni bir hesaplama metodolojisi önerilmiştir. Önerilen metotta örtüşme içeren görüntü nötrozofik kümeye dönüştürülür ve üç üyelik kümesi tarafından tanımlanır: doğruluk, belirsizlik ve yanlışlık. Daha sonra önerilen metot nötrozofik kümenin doğruluk ve yanlışlık üyeliklerini aktif olarak kullanır ve örtüşme etkilerini azaltır. Gradyan hesaplamasında önerilen metot orijinal giriş görüntüsü yerine nötrozofik doğruluk kümesini kullanır. Ayrıca eğrilik hesaplaması için nötrozofik yanlışlık kümesi kullanılmıştır. Nötrozofik üyelik kümeleri gürültüye karşı daha dayanıklı oldukları için, geleneksel difüzyon denklemlerinin dezavantajları gürültü açısından giderilmiştir. Nötrozofik kümeler gürültü bileşenlerini baskılayabilir ve böylece yumuşak gradyan ve eğrilik modelleri hesaplanabilir. Bu gradyan ve eğrilik bilgileri örtüşme içeren görüntüdeki hem kenar değişimlerini hem de örtüşme kalıntılarını yansıtır. Böylece Ziou ve Horé’nin denklemindeki ters yayınım işlemi etkili bir şekilde gerçekleştirilmiştir. Önerilen metot örtüşme kalıntılarını azaltırken nötrozofik küme vasıtasıyla kenar bölgelerinin detaylarını korumuştur. Deneysel sonuçlar önerilen metodun kenar bölgelerinde örtüşme problemlerini tespit edebildiğini göstermiştir. Yine önerilen difüzyon metodunun performansını değerlendirmek için Ortalama Karesel Hata (OKH) metriği kullanılmıştır. Sonuçlar aynı görüntüler üzerinde diğer metotların sonuçları ile karşılaştırılmıştır. Bu yeni metot görüntü işlemedeki uygulamalar için ön işlem adımı olarak kullanılabilecektir.

Anahtar Kelimeler

• Görüntü iyileştirme
• Nötrozofik küme
• Difüzyon denklemi

References

1. Abdallah, A., & Zineb, A. (2018). Adaptive Non-linear Diffusion Based Local Binary Pattern for Image Denoising. In Proceedings of the 2018 International Conference on Applied Smart Systems, ICASS 2018, 1–5.
2. Casciola, G., Montefusco, L. B., & Morigi, S. (2010). Edge-driven image interpolation using adaptive anisotropic radial basis functions. Journal of Mathematical Imaging and Vision, 36(2), 125–139.
3. Chae, E., Lee, E., Kang, W., Lim, Y., Jung, J., Kim, T., … Paik, J. (2013). Frequency-domain analysis of discrete wavelet transform coefficients and their adaptive shrinkage for anti-aliasing. In 2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings,1071–1074.
4. Gan, J., & Taubman, D. (2007). Non-separable wavelet-like lifting structure for image and video compression with aliasing suppression. In IEEE International Conference in Image Processing, 65-68.
5. Jia, J., Barnard, K. J., & Hirakawa, K. (2016). Fourier Spectral Filter Array for Optimal Multispectral Imaging. IEEE Transactions on Image Processing, 25(4), 1530–1543.
6. Jiang, X., Chen, X., He, L., & Jeon, G. (2015). Improved directional weighted interpolation method combination with anti-aliasing FIR filter. In IST 2015 - 2015 IEEE International Conference on Imaging Systems and Techniques, Proceedings,1–6.
7. Jidesh, P., & George, S. (2012). Shock coupled fourth-order diffusion for image enhancement. Computers and Electrical Engineering, 38(5), 1262–1277.
8. Kawase, M., Shinoda, K., & Hasegawa, M. (2019). Demosaicking using a spatial reference image for an anti-aliasing multispectral filter array. IEEE Transactions on Image Processing, 28(10), 4984–4996.

9. Khan, T. M., Khan, M. A. U., & Kong, Y. (2014). Fingerprint image enhancement using multi-scale DDFB based diffusion filters and modified Hong filters. Optik, 125(16), 4206–4214.
10. Kulberg, N. S., & Yakovleva, T. V. (2012). Isotropic kernels for two-dimensional image interpolation. Journal of Mathematical Imaging and Vision, 44(3), 399–410.
11. Li, B., & Meng, M. Q. H. (2012). Wireless capsule endoscopy images enhancement via adaptive contrast diffusion. Journal of Visual Communication and Image Representation, 23(1), 222–228.
12. Liu, C., Yan, X., & Yang, B. (2017). An adaptive anisotropic thermal diffusion filter for image smoothing. In Proceedings - 2017 10th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics, 1–5.
13. Mohan, J., Krishnaveni, V., & Guo, Y. (2013). MRI denoising using nonlocal neutrosophic set approach of Wiener filtering. Biomedical Signal Processing and Control, 8(6), 779–791.
14. Nadernejad, E., Koohi, H., & Hassanpour, H. (2008). PDEs-Based Method for Image Enhancement. Applied Mathematical Sciences, 2(20), 981–993.
15. Perona, P., & Malik, J. (1990). Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7), 629–639.
16. Smarandache, F., Broumi, S., Singh, P. K., Liu, C., Venkateswara Rao, V., Yang, H.-L., … Elhassouny, A. (2019). Introduction to neutrosophy and neutrosophic environment. In Neutrosophic Set in Medical Image Analysis,3–29.
17. Smarandache, & Florentin. (2003). A Unifying Field in Logics Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (third). American Research Press.
18. Sung, M., & Choi, S. (2017). Selective Anti-Aliasing for Virtual Reality Based on Saliency Map. In Proceedings - 2017 International Symposium on Ubiquitous Virtual Reality, 16–19.
19. Wang, Z., & Qi, F. (2005). Analysis of multiframe super-resolution reconstruction for image anti-aliasing and deblurring. Image and Vision Computing, 23(4), 393–404.
20. Winger, L. L. (1999). Low-aliasing wavelets for pyramidal image coding. In IEEE International Conference on Image Processing Vol. 2, 255–259.
21. Yang, H., Gao, J., & Wu, Z. (2007). An efficient approach for registration and super-resolution of aliased images. In 2007 International Symposium on Intelligent Signal Processing and Communications Systems, ISPACS 2007 - Proceedings,694–697.
22. Yang, L., Pedro V., S., Jason, L., & Hugues, H. (2011). Antialiasing recovery. ACM Transactions on Graphics, 30(3), 1–9.
23. Yang, Y., Liu, F., Jin, Z., & Crozier, S. (2015). Aliasing Artefact Suppression in Compressed Sensing MRI for Random Phase-Encode Undersampling. IEEE Transactions on Biomedical Engineering, 62(9), 2215–2223.
24. Zhao, C., Shao, M., Carass, A., Li, H., Dewey, B. E., Ellingsen, L. M., … Prince, J. L. (2019). Applications of a deep learning method for anti-aliasing and super-resolution in MRI. Magnetic Resonance Imaging, 64, 132–141.
25. Zhao, Y., Xu, J., Li, H., & Zhang, P. (2018). Edge information diffusion-based reconstruction for cone beam computed laminography. IEEE Transactions on Image Processing, 27(9), 4663–4675.
26. Ziou, D., & Horé, A. (2011). Reducing aliasing in images: A simple diffusion equation based on the inverse diffusivity. In Proceedings - International Conference on Image Processing, 3389–3392.
27. Ziou, D., & Horé, A. (2012). Reducing aliasing in images: A PDE-based diffusion revisited. Pattern Recognition, 45(3), 1180–1194.