Abstract
Shock filter represents an important family in the field of nonlinear Partial Differential Equations (PDEs) models for image restoration and enhancement. Commonly, the smoothed second order derivative of the image assists this type of method in the deblurring mechanism. This paper presents the advantages to insert information issued of oriented half Gaussian kernels in a shock filter process. Edge directions assist to preserve contours whereas the gradient direction allow to enhance and deblur images. For this purpose, the two edge directions are extracted by the oriented half kernels, preserving and enhancing well corner points and object contours as well as small objects. The proposed approach is compared to 7 other PDE techniques, presenting its robustness and reliability, without creating a grainy effect around edges.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Abdulrahman, H., Magnier, B., Montesinos, P.: Oriented asymmetric kernels for corner detection. In: IEEE EUSIPCO, pp. 778–782 (2017)
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, vol. 147. Springer, New York (2006).https://doi.org/10.1007/978-0-387-44588-5
Alvarez, L., Mazorra, L.: Signal and image restoration using shock filters and anisotropic diffusion. SIAM J. Numer. Anal. 31(2), 590–605 (1994)
Bettahar, S., Lambert, P., Stambouli, A.B.: Anisotropic color image denoising and sharpening. In: IEEE ICIP, pp. 2669–2673 (2014)
Fu, S., Ruan, Q., Wang, W., Chen, J.: Region-based shock-diffusion equation for adaptive image enhancement. In: Huang, D.S., Li, K., Irwin, G.W. (eds.) Advances in Machine Vision, Image Processing, and Pattern Analysis. Lecture Notes in Control and Information Sciences, vol. 345, pp. 387–395. Springer, Heidelberg (2006). https://doi.org/10.1007/978-3-540-37258-5_133
Gilboa, G., Sochen, N.A., Zeevi, Y.Y.: Regularized shock filters and complex diffusion. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 399–413. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-47969-4_27
Guichard, F., Moisan, L., Morel, J.-M.: A review of PDE models in image processing and image analysis. J. Phys. IV 12(1), 137–154 (2002)
Kornprobst, P., Deriche, R., Aubert, G.: Image coupling, restoration and enhancement via PDE’s. In: IEEE ICIP, pp. 458–46 (1997)
Ludusan, C., Lavialle, O., Terebes, R., Borda, M.: Morphological sharpening and denoising using a novel shock filter model. In: Elmoataz, A., Lezoray, O., Nouboud, F., Mammass, D., Meunier, J. (eds.) ICISP 2010. LNCS, vol. 6134, pp. 19–27. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13681-8_3
Magnier, B.: An objective evaluation of edge detection methods based on oriented half kernels. In: Mansouri, A., El Moataz, A., Nouboud, F., Mammass, D. (eds.) ICISP 2018. LNCS, vol. 10884, pp. 80–89. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94211-7_10
Magnier, B.: Matlab code of “Edge detection methods based on oriented half kernels”. https://fr.mathworks.com/matlabcentral/fileexchange/66853-edge-detection-methods-based-on-oriented-half-kernels?s_tid=srchtitle
Magnier, B., Montesinos, P., Diep, D.: Texture removal by pixel classification using a rotating filter. In: IEEE ICASSP, pp. 1097–1100 (2011)
Magnier, B., Montesinos, P.: Evolution of image regularization with PDEs toward a new anisotropic smoothing based on half kernels. In: IS&T/SPIE Electrical Imaging, International Society for Optics and Photonics, p. 86550M (2013)
Montesinos, P., Magnier, B.: A new perceptual edge detector in color images. In: Blanc-Talon, J., Bone, D., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2010. LNCS, vol. 6474, pp. 209–220. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17688-3_21
Montesinos, P., Magnier, B.: Des filtres anisotropes causaux pour une diffusion non contrôlées. In: GRETSI (2017)
Osher, S., Rudin, L.I.: Feature-oriented image enhancement using shock filters. SIAM J. Numer. Anal. 27(4), 919–940 (1990). ISSN 0036–1429
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE TPAMI 12, 629–639 (1990)
Püspöki, Z., Martin, S., Sage, D., Unser, M.: Transforms and operators for directional bioimage analysis: a survey. In: De Vos, W., Munck, S., Timmermans, J.P. (eds.) Focus on Bio-Image Informatics, vol. 219, pp. 69–93. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-28549-8_3
Tschumperlé, D., Deriche, R.: Diffusion PDE’s on vector-valued images: local approach and geometric viewpoint. IEEE Signal Process. Mag. 19(5), 16–25 (2002)
Venkatrayappa, D., Montesinos, P., Diep, D., Magnier, B.: A novel image descriptor based on anisotropic filtering. In: Azzopardi, G., Petkov, N. (eds.) CAIP 2015. LNCS, vol. 9256, pp. 161–173. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23192-1_14
Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE TIP 13(4), 600–612 (2004)
Weickert, J.: Coherence-enhancing shock filters. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 1–8. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45243-0_1
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Magnier, B., Noblet, V., Voisin, A., Legouestre, D. (2018). Derivative Half Gaussian Kernels and Shock Filter. In: Blanc-Talon, J., Helbert, D., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2018. Lecture Notes in Computer Science(), vol 11182. Springer, Cham. https://doi.org/10.1007/978-3-030-01449-0_49
Download citation
DOI: https://doi.org/10.1007/978-3-030-01449-0_49
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01448-3
Online ISBN: 978-3-030-01449-0
eBook Packages: Computer ScienceComputer Science (R0)