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Variational Image Binarization and its Multi-Scale Realizations

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Abstract

A variational approach for image binarization is discussed in this paper. The approach is based on the interpolation of surface. This interpolation is computed using edge points as interpolating points and minimizing an energy functional which interpolates a smooth threshold surface. A globally convergent Sequential Relaxation Algorithm (SRA) is proposed for solving the optimization problem. Moreover, our algorithm is also formulated in a multi-scale framework. The performance of our method is demonstrated on a variety of real and synthetic images and compared with traditional techniques. Examples show that our method gives promising results.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Chong Sze Tong

  2. The Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an, 710049, China

    Yongping Zhang

  3. Department of Mathematics, Shaanxi Normal University, Xi’an, 710062, China

    Yongping Zhang

  4. The Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an, 710049, China

    Nanning Zheng

  5. Now at Bioengineering Institute, University of Auckland, Level 6, 70 Symonds Street, Auckland, New Zealand

    Yongping Zhang

Authors
  1. Chong Sze Tong
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  2. Yongping Zhang
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  3. Nanning Zheng
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Corresponding author

Correspondence to Yongping Zhang.

Additional information

This research is partially supported by HKBU Faculty Research Grant FRG/02-03/II-04 and NSF of China Grant.

C.S. Tong received a BA degree in Mathematics and a Ph.D. degree (on Mathematical Modelling of Intermolecular Forces) both from Cambridge University. After graduation, he joined the Signal and Image Processing division of GEC-Marconi’s Hirst Research Centre as a Research Scientist, working on image restoration and fractal image compression. He then moved to the Department of Mathematics at Hong Kong Baptist University in 1992, becoming Associate Professor since 2002.

He is a member of the IEEE, a Fellow of the Institute of Mathematics and Its Application, and a Chartered Mathematician. His current research interests include image processing, fractal image compression, and neural networks.

Yongping Zhang received the M. S. degree from Department of Mathematics at Shaanxi Normal University, Xi’an, China, in 1988 and received the Ph.D. degree from The Institute of Artificial Intelligence and Robotics at Xi’an Jiaotong University, Xi’an, China, in 1998.

In 1988 he joined Department of Mathematics at Shaanxi Normal University, where he became Associate Professor in July 1987. He held postdoctoral position at Northwestern Polytechnic University during the 1999–2000 academic years. Currently he is a research associate in the Bioengineering Institute at the University of Auckland, New Zealand. His research interests are in Computer Vision and Pattern Recognition, and include Wavelets, Neural Networks, PDE methods and variational methods for image processing.

Nanning Zheng received the M.S. degree from Xi’an Jiaotong University, Xi’an, China, in 1981 and the Ph.D. degree from Keio University, Japan, in 1985. He is an academician of Chinese Engineer Academy, and currently a Professor at Xi’an Jiaotong University. His research interest includes Signal Processing, Machine Vision and Image Processing, Pattern Recognition and Virtual Reality.

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Tong, C.S., Zhang, Y. & Zheng, N. Variational Image Binarization and its Multi-Scale Realizations. J Math Imaging Vis 23, 185–198 (2005). https://doi.org/10.1007/s10851-005-6466-x

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