Abstract
Image processing algorithms are being intensively researched in the last decades. One of the most influential filtering tendencies is based on partial differential equations (PDE). Different kinds of modifications of classical linear process were already proposed. Most of them are based on non-linear or anisotropic process taking into consideration local descriptor of image structure. Main goal is to remove noise and simultaneously to decrease level of blurring important features (like edges). In this paper a new approach is presented, which introduces, into non-linear diffusion process, extra knowledge about geometric structures existing on an image. Algorithm scheme is proposed and results of numerical experiments are presented. Moreover, possibilities of algorithm application within cellular neural networks paradigm will be analysed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ballard, D.: Generalized Hough transform to detect arbitrary patterns. Pattern Recognition 13(2), 111–122 (1981)
Black, M., Sapiro, G., Marimont, D., Heeger, D.: Robust Anisotropic Diffusion. IEEE Trans. On Image Processing 7(1), 421–432 (1998)
Catt, F., Lions, P.L., Morel, J.M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal of Numerical Analysis 29, 182–193 (1992)
Chua, L.O., Roska, T.: The CNN Paradigm. IEEE Trans. on Circuits and Systems 40(1), 147–156 (1993)
Chua, L.O., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. on Circuits and Systems 35(10), 1257–1272 (1998)
Chua, L.O., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. on Circuits and Systems 35(10), 1273–1290 (1998)
Cottet, G.H., El Ayyadi, M.: Nonlinear PDE operators with memory terms for image processing. In: Proc. IEEE International Conference on Image Processing, vol. 1, pp. 481–483 (1996)
Crounse, K.R., Chua, L.O.: Methods for Image Processing and Pattern Formation in Cellular Neural Networks: A Tutorial. IEEE Trans. on Circuits and Systems 42(10), 583–601 (1995)
Didas, S., Weickert, J., Burgeth, B.: Stability and Local Feature Enhancement of Higher Order Nonlinear Diffusion Filtering. In: Kropatsch, W.G., Sablatnig, R., Hanbury, A. (eds.) DAGM 2005. LNCS, vol. 3663, pp. 451–458. Springer, Heidelberg (2005)
Duda, R., Hart, P.: Use of the Hough transformation to detect lines and curves in the pictures. Communications of the ACM 15(1), 11–15 (1972)
Gacsdi, A., Szolgay, P.: A Variational Method for Image Denoising, by using Cellular Neural Networks. In: Proc. of The 8th IEEE International Biannual Workshop on Cellular Neural Networks and their Applications, Budapest, Hungary (2004)
Gerig, G., Kikinis, R., Kbler, O., Jolesz, F.A.: Nonlinear Anisotropic Filtering of MRI Data. IEEE Trans. on Medical Imaging 11(2), 221–231 (1992)
Guil, N., Villalba, J., Zapata, E.: A Fast Hough Transform for Segment Detection. IEEE Trans. on Image Processing 4(11), 1541–1548 (1995)
Kesidis, A.L., Papamarkos, N.: On the Inverse Hough Transform. IEEE Trans. on Pattern Analysis and Machine Intelligence 21(12), 1329–1343 (1999)
Perona, P., Malik, J.: Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Trans. On Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)
Snchez-Ortiz, G.I., Rueckert, D., Burger, P.: Knowledge-based tensor anisotropic diffusion of cardiac magnetic resonance images. Medical Image Analysis 3(1), 77–101 (1999)
Sapiro, G., Ringach, L.: Anisotropic Diffusion of Multivalued Images with Applications to Color Filtering. IEEE Trans. on Image Processing 5(11), 1582–1586 (1996)
Taraglio, S., Zanela, A.: A practical use of cellular neural networks: the stereo-vision problem as an optimisation. Machine Vision and Applications (11), 242–251 (2000)
Weickert, J.: Theoretical Foundations of Anisotropic Diffusion in Image Processing. Computing Supplement 11, 221–236 (1996)
Weickert, J.: A Review of Nonlinear Diffusion Filtering. In: ter Haar Romeny, B.M., Florack, L.M.J., Viergever, M.A. (eds.) Scale-Space 1997. LNCS, vol. 1252, pp. 3–28. Springer, Heidelberg (1997)
Weickert, J.: Anisotropic Diffusion in Image Processing. B.G. Teubner, Stuttgart (1998)
Wu, C.W., Chua, L.O., Roska, T.: A two-layer Radon transform cellular neural network. IEEE Trans. On Circuits and Systems 39(7), 488–489 (1992)
You, Y.L., Kaveh, M.: Image Enhancement Using Fourth Order Partial Differential Equations. IEEE Trans. on Image Processing 9(10), 1723–1730 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jablonski, B. (2008). Geometric Structure Filtering Using Coupled Diffusion Process and CNN-Based Approach. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2008. ICAISC 2008. Lecture Notes in Computer Science(), vol 5097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69731-2_76
Download citation
DOI: https://doi.org/10.1007/978-3-540-69731-2_76
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69572-1
Online ISBN: 978-3-540-69731-2
eBook Packages: Computer ScienceComputer Science (R0)