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Adaptive noise-reducing anisotropic diffusion filter

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Abstract

In image processing and computer vision, the denoising process is an important step before several processing tasks. This paper presents a new adaptive noise-reducing anisotropic diffusion (ANRAD) method to improve the image quality, which can be considered as a modified version of a speckle-reducing anisotropic diffusion (SRAD) filter. The SRAD works very well for monochrome images with speckle noise. However, in the case of images corrupted with other types of noise, it cannot provide optimal image quality due to the inaccurate noise model. The ANRAD method introduces an automatic RGB noise model estimator in a partial differential equation system similar to the SRAD diffusion, which estimates at each iteration an upper bound of the real noise level function by fitting a lower envelope to the standard deviations of pre-segment image variances. Compared to the conventional SRAD filter, the proposed filter has the advantage of being adapted to the color noise produced by today’s CCD digital camera. The simulation results show that the ANRAD filter can reduce the noise while preserving image edges and fine details very well. Also, it is favorably compared to the fast non-local means filter, showing an improvement in the quality of the restored image. A quantitative comparison measure is given by the parameters like the mean structural similarity index and the peak signal-to-noise ratio.

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References

  1. Elad M (2010) Sparse and redundant representations: from theory to applications in signal and image processing. Springer Science & Business Media, New York, p 376

    Book  MATH  Google Scholar 

  2. Sendur L, Selesnick IW (2002) Bivariate shrinkage with local variance estimation. IEEE Trans Signal Process Lett 9(12):438–441. doi:10.1109/LSP.2002.806054

    Article  Google Scholar 

  3. Donoho DL (1995) De-noising by soft-thresholding. IEEE Trans Inf Theory 41(3):613–627. doi:10.1109/18.382009

    Article  MathSciNet  MATH  Google Scholar 

  4. Mallat SG (1999) A wavelet tour of signal processing. Elsevier, USA

    MATH  Google Scholar 

  5. Rank K, Lendl M, Unbehauen R (1999) Estimation of image noise variance. IEE Proc Vis Image Signal Process 146(2):8084. doi:10.1049/ip-vis:19990238

    Article  Google Scholar 

  6. Amer A, Mitiche A, Dubois E (2002) Reliable and fast structure-oriented video noise estimation. In: International conference on image processing (ICIP 2002), IEEE. Rochester, New York, pp 840–843. 22–25 Sept. doi:10.1109/TCSVT.2004.837017

  7. Tai SC, Yang SM (2008) A fast method for image noise estimation using laplacian operator and adaptive edge detection. In: 3rd international symposium on communications, control and signal processing, ISCCSP 2008. Malta, pp 1077–1081. 12–14 March. doi:10.1109/ISCCSP.2008.4537384

  8. Uss ML, Vozel B, Lukin VV, Chehdi K (2011) Local signal-dependent noise variance estimation from hyperspectral textural images. IEEE J Sel Top Signal Process 5(3):469–486. doi:10.1109/JSTSP.2010.2104312

    Article  Google Scholar 

  9. Foi A (2009) Clipped noisy images: heteroskedastic modeling and practical denoising. Signal Process 89(12):2609–2629. doi:10.1016/j.sigpro.2009.04.035

    Article  MATH  Google Scholar 

  10. Liu X, Tanaka M, Okutomi M, (2013) Estimation of signal dependent noise parameters from a single image. In: Proceedings of the 20th IEEE international conference on image processing (ICIP), 2013. Melbourne, VIC, pp 79–82. 15–18 Sept 2013. doi:10.1109/ICIP.2013.6738017

  11. Yu Y, Acton ST (2002) Speckle reducing anisotropic diffusion. IEEE Trans Image Process 11(11):1260–1270. doi:10.1109/TIP.2002.804276

    Article  MathSciNet  Google Scholar 

  12. Abramov S, Zabrodina V, Lukin V, Vozel B, Chehdi K, Astola J (2010) Improved method for blind estimation of the variance of mixed noise using weighted LMS line fitting algorithm. In: Proceedings of 2010 IEEE international symposium on circuits and systems (ISCAS). Paris, pp 2642–2645. 30 May–2 June 2010. doi:10.1109/ISCAS.2010.5537084

  13. Aiazzi B, Alparone L, Barducci A, Baronti S, Marcoionni P, Pippi I, Selva M (2006) Noise modelling and estimation of hyperspectral data from airborne imaging spectrometers. Ann Geogr 49(1):1–9. doi:10.4401/ag-3141

    Google Scholar 

  14. Lebrun M, Colom M, Morel J (2014) The noise clinic: A universal blind denoising algorithm. In: 2014 IEEE international conference on image processing (ICIP). Paris, pp 2674–2678. 27–30 Oct 2014. doi:10.1109/ICIP.2014.7025541

  15. Liu C, Szeliski R, Kang SB, Zitnick CL, Freeman WT (2008) Automatic estimation and removal of noise from a single image. IEEE Trans Pattern Anal Mach Intell 30(2):299–314. doi:10.1109/TPAMI.2007.1176

    Article  Google Scholar 

  16. Tomasi C, Manduchi R (1998) Bilateral filtering for gray and color images. In: Proceedings of the sixth international conference on computer vision. Bombay, pp 839–846. 4–7 Jan 1998. doi:10.1109/ICCV.1998.710815

  17. Pham TQ, van Vliet, LJ (2005) Separable bilateral filtering for fast video preprocessing. In: International conference on multimedia computing and systems/international conference on multimedia and expo-ICME(ICMCS). New York, IEEE Press, pp 454–457. 6–8 July 2005. doi:10.1109/ICME.2005.1521458

  18. Weiss B (2006) Fast median and bilateral filtering. ACM Trans Graph 25(3):519–526. doi:10.1145/1179352.1141918

    Article  Google Scholar 

  19. Paris S, Durand F (2009) A fast approximation of the bilateral filter using a signal processing approach. Int J Comput Vis 81(1):24–52. doi:10.1007/s11263-007-0110-8

    Article  Google Scholar 

  20. Durand F, Dorsey J (2002) Fast bilateral filtering for the display of high-dynamic-range images. ACM Trans Graph TOG 21(3):257–266. doi:10.1145/566654.566574

    Google Scholar 

  21. Elad M (2002) On the origin of the bilateral filter and ways to improve it. IEEE Trans Image Process 11(10):1141–1151. doi:10.1109/TIP.2002.801126

    Article  MathSciNet  Google Scholar 

  22. Barash D (2002) A fundamental relationship between bilateral filtering, adaptive smoothing and the nonlinear diffusion equation. IEEE Trans Pattern Anal Mach Intell 24(6):844–847. doi:10.1109/TPAMI.2002.1008390

    Article  Google Scholar 

  23. Zhang B, Allebach JP (2008) Adaptive bilateral filter for sharpness enhancement and noise removal. IEEE Trans Image Process 17(5):664–678. doi:10.1109/TIP.2008.919949

    Article  MathSciNet  Google Scholar 

  24. Kim S, Allebach JP (2005) Optimal unsharp mask for image sharpening and noise removal. J Electron Imaging 14(2):0230071. doi:10.1117/12.538366

    Google Scholar 

  25. Hu H, de Haan G (2007) Trained bilateral filters and applications to coding artifacts reduction. In: IEEE international conference on image processing, 2007. ICIP 2007. San Antonio, TX, pp 325–328. 16 Sept–19 Oct. doi:10.1109/ICIP.2007.4378957

  26. Yang Q (2015) Recursive approximation of the bilateral filter. IEEE Trans Image Process 24(6):1919–1927. doi:10.1109/TIP.2015.2403238

    Article  MathSciNet  Google Scholar 

  27. Mayer MA, Borsdorf A, Wagner M, Hornegger J, Mardin CY, Tornow RP (2012) Wavelet denoising of multiframe optical coherence tomography data. Biomed Opt Express 3(3):572–589. doi:10.1364/BOE.3.000572

    Article  Google Scholar 

  28. Du Y, Liu G, Feng G, Chen Z (2014) Speckle reduction in optical coherence tomography images based on wave atoms. J Biomed Opt 19(5):056009. doi:10.1117/1.JBO.19.5.056009

    Article  Google Scholar 

  29. Barthel KU, Cycon HL, Marpe D (2003) Image denoising using fractal and wavelet-based methods. Proc SPIE 5266:1018

    Google Scholar 

  30. Chowdhury MMH, Khatun A (2012) Image compression using discrete wavelet transform. IJCSI Int J Comput Sci issues 9(4):1694–1814

    Google Scholar 

  31. Boopathi G (2011) Image compression: an approach using wavelet transform and modified FCM. Int J Comput Appl 28(2):7–12. doi:10.5120/3363-4643

    Google Scholar 

  32. Kamrul HT, Koichi H (2007) Haar wavelet based approach for image compression and quality assessment of compressed image. IAENG Int J Appl Math 36(1):1–8

    MathSciNet  MATH  Google Scholar 

  33. Sateesh Kumar HC, Raja KB, Venugopal KR, Patnaik LM (2009) Automatic image segmentation using wavelets. IJCSNS Int J Comput Sci Netw Secur 9(2):305–313

    Google Scholar 

  34. Lee J, Kim Y, Park C, Park Changhan, Paik Joonki (2006) Robust feature detection using 2D wavelet transform under low light environment. In: Intelligent computing in signal processing and pattern recognition lecture notes in control and information sciences, vol 345, pp 1042–1050. doi:10.1007/978-3-540-37258-5_134

  35. Ma X, Peyton AJ (2010) Feature detection and monitoring of eddy current imaging data by means of wavelet based singularity analysis. NDT & E Int 43(8):687–694. doi:10.1016/j.ndteint.2010.07.006

    Article  Google Scholar 

  36. Habib W, Siddiqui AM, Touqir I (2013) Wavelet based despeckling of multiframe optical coherence tomography data using similarity measure and anisotropic diffusion filtering. In: 2013 IEEE international conference on bioinformatics and biomedicine (BIBM). Shanghai, pp 330–333. 18–21 Dec. doi:10.1109/BIBM.2013.6732512

  37. Witkin A (1983) Scale space filtering. In: Proceedings of the 8th International Joint Con5 Artficial Zntell. Karlsruhe, pp 1019–1022. August 1983

  38. Mallat S, Hwang WL (1992) Singularity detection and processing with wavelets. IEEE Trans Inf Theory 38(2):617–643. doi:10.1109/18.119727

    Article  MathSciNet  MATH  Google Scholar 

  39. Yansun X, John BW, Dennis MH Jr, Jian L (1994) Wavelet transform domain filters: a spatially selective noise filtration technique. IEEE Trans Image Process 3(6):747–758. doi:10.1109/83.336245

    Article  Google Scholar 

  40. Donoho D (1995) Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc 90(432):1200–1224. doi:10.1080/01621459.1995.10476626

    Article  MathSciNet  MATH  Google Scholar 

  41. Donoho D (1995b) De-noising by soft-thresholding. IEEE Trans Inf Theory 41(3):613–627. doi:10.1109/18.382009

    Article  MathSciNet  MATH  Google Scholar 

  42. Chang SG, Yu B, Vetterli M (2000) Spatially adaptive wavelet thresholding with context modeling for image denoising. IEEE Trans Image Process 9(9):1522–1531. doi:10.1109/83.862630

    Article  MathSciNet  MATH  Google Scholar 

  43. Li H, Wang S (2009) A new image denoising method using wavelet transform. In: International forum on information technology and applications, 2009. IFITA ’09. In Chengdu, pp 111–114. 15–17 May. doi:10.1109/IFITA.2009.47

  44. Buades A, Coll B, Morel JM (2005) A non-local algorithm for image denoising. In: IEEE computer society conference on computer vision and pattern recognition, 2005. CVPR 2005. San Diego, CA, pp 260–65. 20–25 June. doi:10.1109/CVPR.2005.38

  45. Dauwe A, Goossens B, Luong H, Philips W (2008) A fast non-local image denoising algorithm. In: Proceedings of SPIE electronic imaging. San Diego, CA, pp 681210–681210. 16–21 Feb. doi:10.1117/12.765505

  46. Deledalle C, Denisy L, Poggiz G, Tupinx F, Verdoliva L (2014) Exploiting patch similarity for SAR image processing: the nonlocal paradigm. IEEE Signal Process Mag 31(4):69–78. doi:10.1109/MSP.2014.2311305

    Article  Google Scholar 

  47. Tolga T (2009) Principal neighborhood dictionaries for nonlocal means image denoising. IEEE Trans Image Process 18(12):2649–2660. doi:10.1109/TIP.2009.2028259

    Article  MathSciNet  Google Scholar 

  48. Wua K, Zhanga X, Dinga M (2013) Curvelet based nonlocal means algorithm for image denoising. Int J Electron Commun 68(1):3743. doi:10.1016/j.aeue.2013.07.011

    Google Scholar 

  49. Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639. doi:10.1109/34.56205

    Article  Google Scholar 

  50. Samson C, Blanc-Féraud L, Aubert G, Zerubia J (2000) A variational model for image classification and restoration. IEEE Trans Pattern Anal Mach Intell 22(5):460–472. doi:10.1109/34.857003

    Article  MATH  Google Scholar 

  51. Grazzini J, Turiel A, Yahia H (2005) Presegmentation of high-resolution satellite images with a multifractal reconstruction scheme based on an entropy criterium. In: IEEE international conference on image processing, 2005. ICIP 2005. Italy, pp I-649–652. 11–14 Sept. doi:10.1109/ICIP.2005.1529834

  52. Blanc-Féraud L, Barlaud M (1996) Edge preserving restoration of astrophysical images. Vistas Astron 40(4):531–538. doi:10.1016/S0083-6656(96)00038-4

    Article  Google Scholar 

  53. Chao SM, Tsai DM (2006) Astronomical image restoration using an improved anisotropic diffusion. Pattern Recognit Lett 27(5):335–344. doi:10.1016/j.patrec.2005.08.021

    Article  Google Scholar 

  54. Bao P, Zhang D (2003) Noise reduction for magnetic resonance images via adaptive multiscale products thresholding. IEEE Trans Med Imaging 22(9):1089–1099. doi:10.1109/TMI.2003.816958

    Article  Google Scholar 

  55. Villain N, Goussard Y, Idier J, Allain M (2003) Three-dimensional edge-preserving image enhancement for computed tomography. IEEE Trans Med Imaging 22(10):1275–1287. doi:10.1109/TMI.2003.817767

    Article  Google Scholar 

  56. Hsiao IT, Rangarajan A, Gindi G (2003) A new convex edge-preserving median prior with applications to tomography. IEEE Trans Med Imaging 22(5):580–585. doi:10.1109/TMI.2003.812249

    Article  Google Scholar 

  57. Almansa A, Lindeberg T (2000) Fingerprint enhancement by shape adaptation of scale-space operators with automatic scale selection. IEEE Trans Image Process 9(12):2027–2042. doi:10.1109/83.887971

    Article  MathSciNet  MATH  Google Scholar 

  58. Meihua X, Zhengming W (2004) Fingerprint enhancement based on edge-directed diffusion. In: International conference on image and graphics—ICIG, IEEE computer society 2004. Hong Kong, pp 274–277. 18–20 Dec. doi:10.1109/ICIG.2004.68

  59. Weickert J (1994) Scale-space properties of nonlinear diffusion filtering with a diffusion tensor. Citeseer report 110, University of Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern

  60. Krissian K (2002) Flux-based anisotropic diffusion applied to enhancement of 3-D angiogram. IEEE Trans Med Imaging 21(11):1440–1442. doi:10.1109/TMI.2002.806403

    Article  Google Scholar 

  61. Aja-Fernández S, Alberola-López C (2006) On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering. IEEE Trans Image Process 15(9):2694–2701. doi:10.1109/TIP.2006.877360

    Article  Google Scholar 

  62. Aja-Fernández S, Vegas-Sánchez-Ferrero G, Martín-Fernández M, Alberola-López C (2009) Automatic noise estimation in images using local statistics. Addit Mult Cases 27(6):756–770. doi:10.1016/j.imavis.2008.08.002

    Google Scholar 

  63. Chen Q, Montesinos P, Sun QS, Xia DS (2010) Ramp preserving Perona–Malik model. Signal Process 90(6):19631975. doi:10.1016/j.sigpro.2009.12.015

    Article  MATH  Google Scholar 

  64. Mittal D, Kumar V, Saxena SC, Khandelwal N, Kalra N (2010) Enhancement of the ultrasound images by modified anisotropic diffusion method. Med Biol Eng Comput 48(12):1281–1291. doi:10.1007/s11517-010-0650-x

    Article  Google Scholar 

  65. Yu J, Tan J, Wang Y (2010) Ultrasound speckle reduction by a SUSAN-controlled anisotropic diffusion method. Pattern Recognit 43(9):3083–3092. doi:10.1016/j.patcog.2010.04.006

    Article  Google Scholar 

  66. Bai J, Feng XC (2007) Fractional-order anisotropic diffusion for image denoising. IEEE Trans Image Process 16(10):2492–2502. doi:10.1109/TIP.2007.904971

    Article  MathSciNet  Google Scholar 

  67. Xie MH, Wang ZM (2006) Edge-directed enhancing based anisotropic diffusion. Chin J Electron 34(1):59–64

    Google Scholar 

  68. Liu X, Liu J, Xu X, Chun L, Tang J, Deng Y (2011) A robust detail preserving anisotropic diffusion for speckle reduction in ultrasound images. BMC Genomics 12(Suppl 5):1–10. doi:10.1186/1471-2164-12-S5-S14

    Article  Google Scholar 

  69. Tsiotsios C, Petrou M (2012) On the choice of the parameters for anisotropic diffusion in image processing. Pattern Recognit 46(5):1369–1381. doi:10.1016/j.patcog.2012.11.012

    Article  Google Scholar 

  70. Gilboa G, Sochen N, Zeevi YY (2006) Estimation of optimal PDE-based denoising in the SNR sense. IEEE Trans Image Process 15(8):2269–2280. doi:10.1109/TIP.2006.875248

    Article  Google Scholar 

  71. Papandreou G, Maragos P (2005) A cross-validatory statistical approach to scale selection for image denoising by non linear diffusion. In: IEEE conference on computer vision and pattern recognition. San Diego, CA, pp 625–630. 20–25 June. doi:10.1109/CVPR.2005.21

  72. Cohen E, Cohen LD, Zeevi YY (2014) Texture enhancement using diffusion process with potential. In: 2014 IEEE 28th convention of electrical and electronics engineers in Israel (IEEEI). Eilat, pp 1–5. 3–5 Dec. doi:10.1109/EEEI.2014.7005778

  73. Healey GE, Kondepudy R (1994) Radiometric CCD camera calibration and noise estimation. IEEE Trans Pattern Anal Mach Intell 16(3):267–276. doi:10.1109/34.276126

    Article  Google Scholar 

  74. Irie K, McKinnon AE, Unsworth K, Woodhead IM (2008) A model for measurement of noise in CCD digital-video cameras. Meas Sci Technol 19(4):045207–045211. doi:10.1088/0957-0233/19/4/045207

    Article  Google Scholar 

  75. Grossberg MD, Nayar SK (2003) What is the space of camera response functions. In: Proceedings 2003 IEEE computer society conference on computer vision and pattern recognition, 2003, pp 602–609. 18–20 June 2003. doi:10.1109/CVPR.2003.1211522

  76. Mitsunaga T, Nayar SK (1999) Radiometric self calibration. In: Proceedings IEEE conference on computer vision and pattern recognition CVPR’99. Fort Collins, CO, pp 374–380. 23–25 June 1999. doi:10.1109/CVPR.1999.786966

  77. Ortiz A, Oliver G (2004) Radiometric calibration of CCD sensors: dark current and fixed pattern noise estimation. In: International conference on robotics and automation, ICRA, 2004. New Orleans, pp 4730–4735. 26 April–1 May 2004. doi:10.1109/ROBOT.2004.1302465

  78. Adams Jr, James E (1997) Design of practical color filter array interpolation algorithms for digital cameras. In: Electronic imaging’97. San Jose, CA, pp 117–125. 8–14 Feb 1997. doi:10.1117/12.270338

  79. Takamatsu J, Matsushita Y, Ogasawara T, Ikeuchi K (2010) Estimating demosaicing algorithms using image noise variance. In: 2010 IEEE conference on computer vision and pattern recognition (CVPR). pp 279–286. 13–18 June. doi:10.1109/CVPR.2010.5540200

  80. Ramanath R, Snyder WE, Bilbro GL, Sander WA (2002) Demosaicking methods for Bayer color arrays. J Electron imaging 11(3):306–315. doi:10.1117/1.1484495

    Article  Google Scholar 

  81. Gravel P, Beaudoin G, De Guise JA (2004) A method for modeling noise in medical images. IEEE Trans Med Imaging 23(10):1221–1232. doi:10.1109/TMI.2004.832656

    Article  Google Scholar 

  82. Shree KN (2001) The CAVE databases. www.cs.columbia.edu/CAVE Colombia

  83. Liu X, Tanaka M, Okutomi M (2012) Noise level estimation using weak textured patches of a single noisy image. In: Proceedings of the 19th IEEE international conference on image processing (ICIP), 2012. Orlando, FL, pp 665–668. 30 Sept–3 Oct. doi:10.1109/ICIP.2012.6466947

  84. Arthur D, Vassilvitskii S (2007) k-means++: The advantages of careful seeding. In: Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms. New Orleans, pp 1027–1035. 7–9 Jan. doi:10.1145/1283383.1283494

  85. Abramov S, Zabrodina V, Lukin V, Vozel B, Chehdi K, Astola J (2011) Methods for blind estimation of the variance of mixed noise and their performance analysis. In: Awrejcewicz J (ed) Numerical analysis-theory and applications. InTech, Poland, pp 49–70. doi:10.5772/24596

    Google Scholar 

  86. Cottet GH, Germain L (1993) Image processing through reaction combined with nonlinear diffusion. Math Comput 16(204):659–673. doi:10.1090/S0025-5718-1993-1195422-2

    Article  MathSciNet  MATH  Google Scholar 

  87. Ben Abdallah M, Malek J, Azar AT, Montesinos P, Belmabrouk H, Esclarin Monreal J, Krissian K (2015a) Automatic extraction of blood vessels in the retinal vascular tree using multiscale medialness. Int J Biomed Imaging 2015, Article ID 519024, 16 pages. doi:10.1155/2015/519024

  88. Krissian K, Aja-Fernández S (2009) Noise-driven anisotropic diffusion filtering of MRI. IEEE Trans Image Process 18(10):2265–2274. doi:10.1109/TIP.2009.2025553

    Article  MathSciNet  Google Scholar 

  89. Martin D, Fowlkes C, Tal D, Malik J (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings eighth IEEE international conference on computer vision, 2001. ICCV 2001. Vancouver, BC, pp 416–423. 07–14 July. doi:10.1109/ICCV.2001.937655

  90. Yang SM, Tai SC (2010) Fast and reliable image-noise estimation using a hybrid approach. J Electron Imaging 19(3):033007-1–033007-15. doi:10.1117/1.3476329

  91. Martens JB, Meesters L (1998) Image dissimilarity. Signal Process 70(3):155–176. doi:10.1016/S0165-1684(98)00123-6

    Article  MATH  Google Scholar 

  92. Darbon J, Cunha A, Chan TF, Osher S, Jensen GJ (2008) Fast nonlocal filtering applied to electron cryomicroscopy. In: Proceedings of the 5th IEEE international symposium on biomedical imaging: from nano to macro, 2008. ISBI 2008. Paris, pp 1331–1334, 14–17 May. doi:10.1109/ISBI.2008.4541250

  93. Buades A, Coll B, Morel J-M (2005) A non-local algorithm for image denoising. In: IEEE computer society conference on computer vision and pattern recognition, 2005. CVPR 2005, vol 2. San Diego, pp 60–65. 20–25 June. doi:10.1109/CVPR.2005.38

  94. Mahmoudi M, Sapiro G (2005) Fast image and video denoising via nonlocal means of similar neighborhoods. IEEE Signal Process Lett 12(12):839–842. doi:10.1109/LSP.2005.859509

    Article  Google Scholar 

  95. Coupé P, Yger P, Barillot C (2006) Fast non local means denoising for 3D MR images. In: Proceedings of the 9th international conference, medical image computing and computer-assisted intervention-MICCAI 2006. Springer, Copenhagen, pp 33–40. 1–6 Oct. doi:10.1007/11866763_5

  96. Malek J, Azar AT, Nasralli B, Tekari M, Kamoun H, Tourki R (2015) Computational analysis of blood flow in the retinal arteries and veins using fundus image. Comput Math Appl 69(2):101–116

    Article  Google Scholar 

  97. Asad AH, Azar AT, Hassanien AE (2013a) Ant colony-based system for retinal blood vessels segmentation. In: Proceedings of seventh international conference on bio-inspired computing: theories and applications (BIC-TA 2012) advances in intelligent systems and computing, vol 201, 2013, pp 441–452. doi:10.1007/978-81-322-1038-2_37

  98. Asad AH, Azar AT, Hassanien AE (2013b). An improved ant colony system for retinal vessel segmentation. In: 2013 federated conference on computer science and information systems (FedCSIS). Kraków. 8–11 Sept 2013

  99. Asad AH, Azar AT, Hassanien AE (2014) A comparative study on feature selection for retinal vessel segmentation using ant colony system. In: Recent advances in intelligent informatics advances in intelligent systems and computing vol 235, pp 1–11. doi:10.1007/978-3-319-01778-5_1

  100. Malek J, Tourki R (2013) Blood vessels extraction and classification into arteries and veins in retinal images. In: 2013 10th international multi-conference on systems, signals and devices (SSD). Hammamet, pp 1–6. 18–21 March. doi:10.1109/SSD.2013.6564037

  101. Malek J, Azar AT, Tourki R (2014) Impact of retinal vascular tortuosity on retinal circulation. Neural Comput Appl 26(1):25–40. doi:10.1007/s00521-014-1657-2

    Article  Google Scholar 

  102. Emary E, Zawbaa H, Hassanien AE, Schaefer G, Azar AT (2014a) Retinal blood vessel segmentation using bee colony optimization and pattern search. In: IEEE 2014 international joint conference on neural networks (IJCNN 2014). Beijing International Convention Center, Beijing. 6–11 July

  103. Emary E, Zawbaa H, Hassanien AE, Schaefer G, Azar AT (2014b) Retinal vessel segmentation based on possibilistic fuzzy c-means clustering optimised with cuckoo search. In: IEEE 2014 international joint conference on neural networks (IJCNN 2014). Beijing International Convention Center, Beijing. 6–11 July

  104. Malek J, Tourki R (2013) Inertia-based vessel centerline extraction in retinal image. In: 2013 international conference on control, decision and information technologies (CoDIT). Hammamet. p 378381. 6–8 May. doi:10.1109/CoDIT.2013.6689574

  105. Malek J, Ben Abdallah M, Mansour A, Tourki R (2012) Automated optic disc detection in retinal images by applying region-based active aontour model in a variational level set formulation. In: 2012 international conference on computer vision in remote sensing (CVRS). Xiamen, p 3944. 6–18 Dec. doi:10.1109/CVRS.2012.6421230

  106. Yin Y, Adel M, Guillaume M, Bourennane S (2010) Bayesian tracking for blood vessel detection in retinal images. In: 18th European signal processing conference (EUSIPCO 2010). Aalborg. 23–27 Aug. Id: hal-00483834, version 1

  107. Hani AFM, Soomro TA, Faye I, Kamel N, Yahya N (2014) Denoising methods for retinal fundus images. In: 2014 IEEE international conference on intelligent and advanced systems (ICIAS). Kuala Lumpur, pp 1–6. 3–5 June 2014. doi:10.1109/ICIAS.2014.6869534

  108. Sun J, Luan F, Wu H (2015) Optic disc segmentation by balloon snake with texture from color fundus image. Int J Biomed Imaging. ID 528626. 2015:14. doi:10.1155/2015/528626

  109. Hoover A (1975) STARE database. http://www.ces.clemson.edu/ahoover/stare

  110. Ben Abdallah M, Malek J, Azar AT, Belmabrouk H, Esclarin Monreal J (2015b) Performance evaluation of several anisotropic diffusion filters for fundus imaging. Int J Intell Eng Inform 3(1):66–90. doi:10.1504/IJIEI.2015.069100

    Article  Google Scholar 

  111. Asad AH, Azar AT, Hassaanien AE (2012) Integrated features based on gray-level and hu moment-invariants with ant colony system for retinal blood vessels segmentation. Int J Syst Biol Biomed Technol IJSBBT 1(4):60–73

    Google Scholar 

  112. Asad AH, Azar AT, Hassanien AE (2014a) A comparative study on feature selection for retinal vessel segmentation using ant colony system. In: Recent advances in intelligent informatics advances in intelligent systems and computing, vol 235, pp 1–11. doi:10.1007/978-3-319-01778-5_1

  113. Asad AH, Azar AT, Hassanien AE (2014b) A new heuristic function of ant colony system for retinal vessel segmentation. Int J Rough Sets Data Anal 1(2):15–30

    Article  Google Scholar 

  114. Hadj Fredj A, Ben Abdallah M, Malek J, Azar AT (2015) Fundus image denoising using fpga hardware architecture. Int J Comput Appl Technol (in press)

  115. Ricci E, Perfetti R (2007) Retinal blood vessel segmentation using line operators and support vector classification. IEEE Trans Med Imaging 26(10):1357–1365. doi:10.1109/TMI.2007.898551

    Article  Google Scholar 

  116. Marin D, Aquino A, Gegúndez-Arias ME, Bravo JM (2011) A new supervised method for blood vessel segmentation in retinal images by using gray-level and moment invariants-based features. IEEE Trans Med Imaging 30(1):146–158. doi:10.1109/TMI.2010.2064333

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Sciences, Electronics and Micro-Electronic Laboratory (EMEL), Monastir University, Monastir, Tunisia

    Mariem Ben Abdallah, Jihene Malek & Hafedh Belmabrouk

  2. Faculty of Computers and Information, Benha University, Benha, Egypt

    Ahmad Taher Azar

  3. Center for Image Technologies (CTIM), Las Palmas-Gran Canaria University, Las Palmas, Spain

    Julio Esclarín Monreal & Karl Krissian

Authors
  1. Mariem Ben Abdallah
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  2. Jihene Malek
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  3. Ahmad Taher Azar
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  4. Hafedh Belmabrouk
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  5. Julio Esclarín Monreal
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  6. Karl Krissian
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Correspondence to Ahmad Taher Azar.

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Ben Abdallah, M., Malek, J., Azar, A.T. et al. Adaptive noise-reducing anisotropic diffusion filter. Neural Comput & Applic 27, 1273–1300 (2016). https://doi.org/10.1007/s00521-015-1933-9

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  • DOI: https://doi.org/10.1007/s00521-015-1933-9

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