A Review on Performance Analysis of PDE based Anisotropic Diffusion Approaches for Image Enhancement

Niveditta Thakur, Nafis Uddin Khan, Sunil Datt Sharma

Abstract


Partial differential equation based anisotropic diffusion techniques are used extensively in computer vision for image enhancement and edge detection.  Anisotropic Diffusion which is found to be a low computational complexity approach which has overcome the undesirable effects of linear smoothing filters and now is popular in prominent research areas of enhancing the quality of low contrast images and speckle noise reduction from geological, industrial and medical images. This paper presents a comprehensive survey on various state-of-the-art anisotropic diffusion techniques for image enhancement. The capability of anisotropic diffusion for enhancing the quality of low contrast images and speckle noise reduction from medical images are further explored. Various objective image quality measures are studied which are used to validate the performance of enhancement approaches. The major research issuesand possible future scopes in this diffusion filtering approach are also discussed.


Full Text:

PDF

References


Gonzalez, R. C. and Woods, R. E., (2018). Digital image processing (4th Ed.). Pearson Education India.

Goyal, B., Agrawal, S., &Sohi, B. S. (2018). Noise Issues Prevailing in Various Types of Medical Images. Biomedical & Pharmacology Journal, 11(3), 1227.

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.

Bird. R.B. (2002). Transport phenomena. Applied Mechanics Reviews, 55:R1.

Catté, F., Lions, P. L., Morel, J. M., &Coll, T. (1992). Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical analysis, 29(1), 182-193.

You, Y. L., &Kaveh, M. (2000). Fourth-order partial differential equations for noise removal. IEEE Transactions on Image Processing, 9(10), 1723-1730.

Chen, Y., Barcelos, C. A. Z., &Mair, B. A. (2001). Smoothing and edge detection by time-varying coupled nonlinear diffusion equations. Computer Vision and Image Understanding, 82(2), 85-100.

Weeratunga, S. K., & Kamath, C. (2002, May). PDE-based nonlinear diffusion techniques for denoising scientific and industrial images: an empirical study. In Image Processing: Algorithms and Systems (Vol. 4667, pp. 279-290). International Society for Optics and Photonics.

Gilboa, G., Sochen, N., &Zeevi, Y. Y. (2004). Image enhancement and denoising by complex diffusion processes. IEEE transactions on pattern analysis and machine intelligence, 26(8), 1020-1036.

Tschumperle, D., &Deriche, R. (2005). Vector-valued image regularization with PDEs: A common framework for different applications. IEEE transactions on pattern analysis and machine intelligence, 27(4), 506-517.

Yu, J., Wang, Y., &Shen, Y. (2008). Noise reduction and edge detection via kernel anisotropic diffusion. Pattern Recognition Letters, 29(10), 1496-1503.

Gupta, B., Tiwari, M., &Lamba, S. S. (2019). Visibility improvement and mass segmentation of mammogram images using quantile separated histogram equalisation with local contrast enhancement. CAAI Transactions on Intelligence Technology, 4(2), 73-79.

Hailong, H., Mandal, S., Buehler, A., Deán-Ben, X. L., Razansky, D., &Ntziachristos, V. (2015). Improving optoacoustic image quality via geometric pixel super-resolution approach. IEEE transactions on medical imaging, 35(3), 812-818.

Fernandez, D. C. (2005). Delineating fluid-filled region boundaries in optical coherence tomography images of the retina. IEEE transactions on medical imaging, 24(8), 929-945.

Li, W. C., & Tsai, D. M. (2009). Defect inspection in low-contrast LCD images using Hough transform-based nonstationary line detection. IEEE Transactions on industrial informatics, 7(1), 136-147.

Rashid, M. H. O., Mamun, M. A., Hossain, M. A., & Uddin, M. P. (2018, February). Brain Tumor Detection Using Anisotropic Filtering, SVM Classifier and Morphological Operation from MR Images. In 2018 International Conference on Computer, Communication, Chemical, Material and Electronic Engineering (IC4ME2) (pp. 1-4). IEEE.

Hu, Z., Alsadoon, A., Manoranjan, P., Prasad, P. W. C., Ali, S., &Elchouemic, A. (2018, January). Early stage oral cavity cancer detection: Anisotropic pre-processing and fuzzy C-means segmentation. In 2018 IEEE 8th Annual Computing and Communication Workshop and Conference (CCWC) (pp. 714-719). IEEE.

Khan, T. M., Bailey, D. G., Khan, M. A., & Kong, Y. (2017). Efficient hardware implementation for fingerprint image enhancement using anisotropic Gaussian filter. IEEE Transactions on Image processing, 26(5), 2116-2126.

Abd Halim, S., Ibrahim, A., &Manurung, Y. H. (2013). PDE-based model for weld defect detection on digital radiographic image.International Journal of Signal Processing Systems, 1(2), (pp. 146-151).

Giakoumis, I., Nikolaidis, N., & Pitas, I. (2005). Digital image processing techniques for the detection and removal of cracks in digitized paintings. IEEE Transactions on Image Processing, 15(1), 178-188.

Wang, Y., Wu, K., Yang, Y., & Chen, T. (2015). Gradient and Laplacian-Based Hyperspectral Anisotropic Diffusion. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 8(6), 3235-3249.

Zang, Y., Wang, C., Yu, Y., Luo, L., Yang, K., & Li, J. (2016). Joint enhancing filtering for road network extraction. IEEE Transactions on Geoscience and Remote Sensing, 55(3), 1511-1525.

Weickert, J. (1999). Coherence-enhancing diffusion filtering. International journal of computer vision, 31(2-3), 111-127.

Cho, S. I., Kang, S. J., Kim, H. S., & Kim, Y. H. (2014). Dictionary-based anisotropic diffusion for noise reduction. Pattern Recognition Letters, 46, 36-45.

Cho, S. I., Kang, S. J., Lee, S., & Kim, Y. H. (2016). Extended-dimensional anisotropic diffusion using diffusion paths on inter-color planes for noise reduction. Digital Signal Processing, 48, 27-39.

Tur, M., Chin, K. C., & Goodman, J. W. (1982). When is speckle noise multiplicative? Applied optics, 21(7), 1157-1159.

Wagner, R. F. (1983). Statistics of speckle in ultrasound B-scans. IEEE Trans. Sonics &Ultrason. 30(3), 156-163.

Lee, J. S. (1980). Digital image enhancement and noise filtering by use of local statistics. IEEE transactions on pattern analysis and machine intelligence, (2), 165-168.

Frost, V. S., Stiles, J. A., Shanmugan, K. S., &Holtzman, J. C. (1982). A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on pattern analysis and machine intelligence, (2), 157-166.

Kuan, D. T., Sawchuk, A. A., Strand, T. C., &Chavel, P. (1985). Adaptive noise smoothing filter for images with signal-dependent noise. IEEE transactions on pattern analysis and machine intelligence, (2), 165-177.

Lopes, A., Touzi, R., &Nezry, E. (1990). Adaptive speckle filters and scene heterogeneity. IEEE transactions on Geoscience and Remote Sensing, 28(6), 992-1000.

Yu, Y., & Acton, S. T. (2002). Speckle reducing anisotropic diffusion. IEEE Transactions on image processing, 11(11), 1260-1270.

Aja-Fernández, S., &Alberola-López, C. (2006). On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering. IEEE Transactions on Image Processing, 15(9), 2694-2701.

Krissian, K., Westin, C. F., Kikinis, R., &Vosburgh, K. G. (2007). Oriented speckle reducing anisotropic diffusion. IEEE Transactions on Image Processing, 16(5), 1412-1424.

Coupé, P., Hellier, P., Kervrann, C., &Barillot, C. (2009). Nonlocal means-based speckle filtering for ultrasound images. IEEE transactions on image processing, 18(10), 2221-2229.

Puvanathasan, P., &Bizheva, K. (2009). Interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in optical coherence tomography images. Optics express, 17(2), 733-746.

Vegas-Sanchez-Ferrero, G., Aja-Fernandez, S., Martín-Fernández, M., Frangi, A. F., & Palencia, C. (2010, September). Probabilistic-driven oriented speckle reducing anisotropic diffusion with application to cardiac ultrasonic images. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 518-525). Springer, Berlin, Heidelberg.

Wu, J., & Tang, C. (2011). PDE-based random-valued impulse noise removal based on new class of controlling functions. IEEE transactions on image processing, 20(9), 2428-2438.

Shanmugam, K., &Wahidabanu, R. S. D. (2012). Condensed anisotropic diffusion for speckle reducton and enhancement in ultrasonography. EURASIP Journal on Image and Video Processing, 2012(1), 12.

Fabbrini, L., Greco, M., Messina, M., &Pinelli, G. (2014). Improved edge enhancing diffusion filter for speckle-corrupted images. IEEE Geoscience and Remote Sensing Letters, 11(1), 99-103.

Ramos-Llordén, G., Vegas-Sánchez-Ferrero, G., Martin-Fernandez, M., Alberola-López, C., & Aja-Fernández, S. (2014). Anisotropic diffusion filter with memory based on speckle statistics for ultrasound images. IEEE transactions on Image Processing, 24(1), 345-358.

Cottet, G. H., &Ayyadi, M. E. (1998). A Volterra type model for image processing. IEEE transactions on image processing, 7(3), 292-303.

Zhou, Z., Guo, Z., Dong, G., Sun, J., Zhang, D., & Wu, B. (2015b). A doubly degenerate diffusion model based on the gray level indicator for multiplicative noise removal. IEEE Transactions on Image Processing, 24(1), 249-260.

Hu, Z., & Tang, J. (2016, September). Cluster driven anisotropic diffusion for speckle reduction in ultrasound images. In 2016 IEEE International Conference on Image Processing (ICIP) (pp. 2325-2329). IEEE.

Mishra, D., Chaudhury, S., Sarkar, M., Soin, A. S., & Sharma, V. (2017). Edge probability and pixel relativity-based speckle reducing anisotropic diffusion. IEEE Transactions on Image Processing, 27(2), 649-664.

Zhou, Z., Guo, Z., Zhang, D., & Wu, B. (2018). A nonlinear diffusion equation-based model for ultrasound speckle noise removal. Journal of Nonlinear Science, 28(2), 443-470.

Gao, M., Kang, B., Feng, X., Zhang, W., & Zhang, W. (2019). Anisotropic Diffusion Based Multiplicative Speckle Noise Removal. Sensors, 19(14), 3164.

Xu, H. H., Gong, Y. C., Xia, X. Y., Li, D., Yan, Z. Z., Shi, J., & Zhang, Q. (2019). Gabor-based anisotropic diffusion with lattice Boltzmann method for medical ultrasound despeckling. Mathematical biosciences and engineering: MBE, 16(6), 7546-7561.

Goyal, S., Rani, A., Yadav, N., & Singh, V. (2019, March). SGS-SRAD Filter for Denoising and Edge Preservation of Ultrasound Images. In 2019 6th International Conference on Signal Processing and Integrated Networks (SPIN) (pp. 676-682). IEEE.

Wang, Y., Zhang, L., & Li, P. (2007). Local variance-controlled forward-and-backward diffusion for image enhancement and noise reduction. IEEE Transactions on Image Processing, 16(7), 1854-1864.

Chao, S. M., & Tsai, D. M. (2008). An anisotropic diffusion-based defect detection for low-contrast glass substrates. Image and Vision Computing, 26(2), 187-200.

Chao, S. M., & Tsai, D. M. (2010). An improved anisotropic diffusion model for detail-and edge-preserving smoothing. Pattern Recognition Letters, 31(13), 2012-2023.

Chao, S. M., & Tsai, D. M. (2010). Anisotropic diffusion with generalized diffusion coefficient function for defect detection in low-contrast surface images. Pattern Recognition, 43(5), 1917-1931.

Khan, U. N., Arya, K. V., &Pattanaik, M. (2013). Histogram statistics based variance controlled adaptive threshold in anisotropic diffusion for low contrast image enhancement. Signal Processing, 93(6), 1684-1693.

Ham, B., Min, D., &Sohn, K. (2013). Revisiting the relationship between adaptive smoothing and anisotropic diffusion with modified filters. IEEE transactions on image processing, 22(3), 1096-1107.

Weickert, J. (1995, September). Multiscale texture enhancement. In International Conference on Computer Analysis of Images and Patterns (pp. 230-237). Springer, Berlin, Heidelberg.

Zhou, Q., Gao, J., Wang, Z., & Li, K. (2015a). Adaptive variable time fractional anisotropic diffusion filtering for seismic data noise attenuation. IEEE Transactions on Geoscience and Remote Sensing, 54(4), 1905-1917.

Ben Gharsallah, M., Ben Mohammed, I., & Ben Braiek, E. (2016). Improved Geometric Anisotropic Diffusion Filter for Radiography Image Enhancement. Intelligent Automation & Soft Computing, 1-9.

Chen, Y., Bai, Y., Zhang, Q., Wang, Y., &Gui, Z. (2017). Self-Adaptive Anisotropic Image Enhancement Algorithm Based on Local Variance. Journal of Engineering Science & Technology Review, 10(3).

Liu, H., & Zhang, J. (2017, December). Filtering combined dynamic stochastic resonance for enhancement of dark and low-contrast images. In 2017 International Conference on Progress in Informatics and Computing (PIC) (pp. 133-137). IEEE.

Cho, S. I., & Kang, S. J. (2018). Geodesic path-based diffusion acceleration for image denoising. IEEE Transactions on Multimedia, 20(7), 1738-1750.

Chen, C. S., Weng, C. M., & Tseng, C. C. (2018). An efficient detection algorithm based on anisotropic diffusion for low-contrast defect. The International Journal of Advanced Manufacturing Technology, 94(9-12), 4427-4449.

Nair, R. R., David, E., &Rajagopal, S. (2019). A robust anisotropic diffusion filter with low arithmetic complexity for images. EURASIP Journal on Image and Video Processing, 2019(1), 48.

Chen, Q., Liu, B., & Zhou, F. (2019). Anisotropy-based image smoothing via deep neural network training. Electronics Letters, 55(24), 1279-1281.

Eskicioglu, A. M., & Fisher, P. S. (1995). Image quality measures and their performance. IEEE Transactions on communications, 43(12), 2959-2965.

Larson, E. C., & Chandler, D. M. (2010). Most apparent distortion: full-reference image quality assessment and the role of strategy. Journal of electronic imaging, 19(1), 011006.

Lin, W., &Kuo, C. C. J. (2011). Perceptual visual quality metrics: A survey. Journal of visual communication and image representation, 22(4), 297-312.

Pratt, W. K., & Wiley, J. (1978). A Wiley-Interscience publication. In Digital Image Processing.

Narvekar, N. D., &Karam, L. J. (2011). A no-reference image blur metric based on the cumulative probability of blur detection (CPBD). IEEE Transactions on Image Processing, 20(9), 2678-2683.

Choi, L. K., You, J., &Bovik, A. C. (2015). Referenceless prediction of perceptual fog density and perceptual image defogging. IEEE Transactions on Image Processing, 24(11), 3888-3901.

Wang, Z., &Bovik, A. C. (2002). A universal image quality index. IEEE signal processing letters, 9(3), 81-84.

Wang, Z., Bovik, A. C., Sheikh, H. R., &Simoncelli, E. P. (2004). Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4), 600-612.

Brooks, A. C., Zhao, X., & Pappas, T. N. (2008). Structural similarity quality metrics in a coding context: Exploring the space of realistic distortions. IEEE Transactions on image processing, 17(8), 1261-1273.

Wang, Z., &Bovik, A. C. (2009). Mean squared error: Love it or leave it? A new look at signal fidelity measures. IEEE signal processing magazine, 26(1), 98-117.

Ding, L., Huang, H., &Zang, Y. (2017). Image quality assessment using directional anisotropy structure measurement. IEEE Transactions on Image Processing, 26(4), 1799-1809.

Sheikh, H. R. (2005). LIVE image quality assessment database release 2. http://live. ece.utexas. edu/research/quality.

Ponomarenko, N., Lukin, V., Zelensky, A., Egiazarian, K., Carli, M., &Battisti, F. (2009). TID2008-a database for evaluation of full-reference visual quality assessment metrics. Advances of Modern Radioelectronics, 10(4), 30-45.

Wernick, M. N., Yang, Y., Brankov, J. G., Yourganov, G., &Strother, S. C. (2010). Machine learning in medical imaging. IEEE signal processing magazine, 27(4), 25-38.

Talebi, H., &Milanfar, P. (2018). NIMA: Neural image assessment. IEEE Transactions on Image Processing, 27(8), 3998-4011.




DOI: https://doi.org/10.31449/inf.v45i6.3333

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.