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  • Received: Dec. 12, 2006

    Accepted: --

    Posted: Jun. 27, 2007

    Published Online: Jun. 27, 2007

    The Author Email: Yandong Tang (


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    Shoutao Li, Xiaomao Li, Yandong Tang. Automatic detection of the belt-like region in an image with variational PDE model[J]. Chinese Optics Letters, 2007, 5(5): 270

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Chinese Optics Letters, Vol. 5, Issue 5, 270 (2007)

Automatic detection of the belt-like region in an image with variational PDE model

Shoutao Li1,2, Xiaomao Li1,2, and Yandong Tang1,2,*

Author Affiliations

  • 1Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016
  • 2Graduate School of the Chinese Academy of Sciences, Beijing 100039


In this paper, we propose a novel method to automatically detect the belt-like object, such as highway, river, etc., in a given image based on Mumford-Shah function and the evolution of two phase curves. The method can automatically detect two curves that are the boundaries of the belt-like object. In fact, this is a partition problem and we model it as an energy minimization of a Mumford-Shah function based minimal partition problem like active contour model. With Eulerian formulation the partial differential equations (PDEs) of curve evolution are given and the two curves will stop on the desired boundary. The stop term does not depend on the gradient of the image and the initial curves can be anywhere in the image. We also give a numerical algorithm using finite differences and present various experimental results. Compared with other methods, our method can directly detect the boundaries of belt-like object as two continuous curves, even if the image is very noisy.


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