Abstract
Anisotropic diffusion (AD) become a prominent image enhancement and de-noising method after its introduction in 1987. However, anisotropic diffusion requires selection of a diffusion function whose definition remained ad hoc. Additionally, AD requires determining a scale parameter on which the final result is intimately related. Typically this parameter is chosen in ad hoc basis which makes difficult to compare the final output. In literature, Median absolute deviation (MAD) is proposed as a heterogeneity scale for using with robust anisotropic diffusion (RAD). Despite its strong statistical foundation, diffusing an image by RAD results in undesirable staircasing effect and artefacts are created in presence of noise. In this paper, we propose a robust L-estimator scale that correctly demarcates the homogenous and heterogeneous regions of an image and smoothens the image with minimal staircasing effect. Experimental results show that this scale remains effective in presence of heavy noise.
This is a preview of subscription content, log in via an institution to check access.
References
Perona, P., Malik, J.:Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7) (1990)
Weickert, J.: Anisotropic diffusion in image processing. B.G. Teubner Stuttgart (1998)
Aboulaicha, R., Meskinea, D., Souissi, A.: New diffusion models in image processing. J. Comput. Math. Appl. 56, 874–882 (2008)
Acton, S.: Multigrid anisotropic diffusion. IEEE Trans. Image Proc. 7, 280–291 (1998)
Weickert, J., Scharr, H.: A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance. J. Visual Comm. and Image Repr., Spec. Issue On PDEs Img. Proc., Comp. Vis. and Comp. Grap. 13(1/2), 103–118 (2002)
Chen, Q., Montesinos, P., Sun, Q.S., Xia, D.S.: Ramp preserving perona-malik model. Signal Process. 90, 1963–1975 (2010)
You, Y., Xu, W., Tannenbaum, A., Kaveh, M.: Behavioral analysis of anisotropic in image processing. IEEE Trans. Image Proc. 5(11), 1539–1553 (1996)
Catt´e, F., Lions, P.L., Morel, J.M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29, 182–193 (1992)
Black, M.J., Sapiro, G., Marimont D.H., Heeger, D.: Robust Anisotropic Diffus. IEEE Trans. Image Proc. 7(3) (1998)
Chao, S., Tsai, D.: An improved anisotropic diffusion model for detail- and edge-preserving smoothing, Patt. Recognit. Lett. 31, 2012–2023 (2010)
Rousseeuw, P.J., Croux, C.: Alternatives to the Median Absolute Deviation. J. Am. Stat. Assoc. 88(424) (1993)
Huber, P., Ronchetti, E.: Robust Statistics, 2nd edn. Wiley
Jureckova, J., Picek, J.: Robust Statistical Methods with R. Taylor & Francis Group, LLC (2006)
Aja-Fernández, S., Ferrero, G., MartĂn-Fernández, M., Alberola-LĂłpez, C.: Automatic noise estimation in images using local statistics. Additive and multiplicative cases. Image Vis. Comput. 27, 756–770 (2009)
Pratt, W.K.: Digital Image Processing, 4th edn. Wiley
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Chatterjee, R.K., Kar, A. (2018). Estimation of Heterogeneity to Improve Robust Anisotropic Diffusion. In: Yang, XS., Nagar, A., Joshi, A. (eds) Smart Trends in Systems, Security and Sustainability. Lecture Notes in Networks and Systems, vol 18. Springer, Singapore. https://doi.org/10.1007/978-981-10-6916-1_28
Download citation
DOI: https://doi.org/10.1007/978-981-10-6916-1_28
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6915-4
Online ISBN: 978-981-10-6916-1
eBook Packages: EngineeringEngineering (R0)