Abstract
In this paper we propose a new variational model for image denoising and segmentation of both gray and color images. This method is inspired by the complex Ginzburg–Landau model and the weighted bounded variation model. Compared with active contour methods, our new algorithm can detect non-closed edges as well as quadruple junctions, and the initialization is completely automatic. The existence of the minimizer for our energy functional is proved. Numerical results show the effectiveness of our proposed model in image denoising and segmentation.
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Fang Li received the MSc degree in Mathematics from the South West China Normal University in 2004 and from then on she works in the South West University. Meanwhile, she studies mathematics at the East China Normal University as a doctoral student. Her research interests include anisotropic diffusion filtering, the variational methods and PDEs in image processing.
Chaomin Shen received the MSc degree in Mathematics from the National University of Singapore (NUS) in 1998. He worked in the Centre for Remote Imaging, Sensing and Processing (CRISP), NUS as an associate scientist during 1998 to 2004. Currently he is a lecturer in Joint Laboratory for Imaging Science & Technology and Department of Computer Science, East China Normal University. His research interests include remote sensing applications and variational methods in image processing.
Ling Pi received her MSc degree from the Department of Mathematics, East China Normal University in 2003. She is currently a lecturer in the Department of Applied Mathematics, Shanghai Jiaotong University. Her work involves the application of geometric and analytic methods to problems in image processing.
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Li, F., Shen, C. & Pi, L. A New Diffusion-Based Variational Model for Image Denoising and Segmentation. J Math Imaging Vis 26, 115–125 (2006). https://doi.org/10.1007/s10851-006-8303-2
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DOI: https://doi.org/10.1007/s10851-006-8303-2