Abstract
In this paper we illustrate and compare the use of explicit and semi-implicit finite difference schemes for nonlinear complex diffusion with different boundary conditions in the context of medical imaging despeckling, namely for Optical Coherence Tomography images of the eye fundus. Performance metrics are shown to illustrate the feasibility and performance of these numerical schemes.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Araújo, A., Barbeiro, S., Serranho, P.: Stability of finite difference schemes for complex diffusion processes. SIAM J. Numer. Anal. 50(3), 1284–1296 (2012)
Bernardes, R., Maduro, C., Serranho, P., Araújo, A., Barbeiro, S., Cunha-Vaz, J.: Improved adaptive complex diffusion despeckling filter. Optics Express 18(23), 24048–24059 (2010)
Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High accuracy optical flow estimation based on a theory for warping. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 25–36. Springer, Heidelberg (2004)
Gilboa, G., Sochen, N., Zeeni, Y.: Image enhancement and denoising by complex diffusion processes. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 1020–1036 (2004)
Grossauer, H., Scherzer, O.: Using the Complex Ginzburg-Landau Equation for Digital Inpainting in 2D and 3D. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, Springer, Heidelberg (2003)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)
Salinas, H., Fernández, D.: Comparison of pde-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography. IEEE Trans. Med. Imaging 26(6), 761–771 (2007)
Serranho, P., Maduro, C., Santos, T., Cunha-Vaz, J., Bernardes, R.: Synthetic data for image processing performance testing. In: International Conference in Image Processing (ICIP 2011), pp. 401–404 (2011)
Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 1–14 (2004)
Weickert, J.: Anisotropic diffusion filters for image processing based quality control. In: Proc. 7th Eur. Conf. Mathematics in Industry, vol. 1252, pp. 355–362 (1994)
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)
Zimmer, H., Bruhn, A., Valgaerts, L., Breuß, M., Weickert, J., Rosenhahn, B., Seidel, H.P.: PDE-based anisotropic disparity-driven stereo vision. In: Vision, Modeling, and Visualization, pp. 263–272. AKA, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rodrigues, P., Guimarães, P., Araújo, A., Barbeiro, S., Bernardes, R., Serranho, P. (2013). Explicit and Semi-implicit Complex-Diffusion Schemes for Optical Coherence Tomography Despeckling. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2013. Lecture Notes in Computer Science, vol 7950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39094-4_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-39094-4_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39093-7
Online ISBN: 978-3-642-39094-4
eBook Packages: Computer ScienceComputer Science (R0)