International Journal of Computer Vision

, Volume 68, Issue 2, pp 145–162

A Variational Model for Object Segmentation Using Boundary Information and Shape Prior Driven by the Mumford-Shah Functional


    • Signal Processing InstituteSwiss Federal Institute of Technology
  • Pierre Vandergheynst
    • Signal Processing InstituteSwiss Federal Institute of Technology
  • Jean-Philippe Thiran
    • Signal Processing InstituteSwiss Federal Institute of Technology

DOI: 10.1007/s11263-006-6658-x

Cite this article as:
Bresson, X., Vandergheynst, P. & Thiran, J. Int J Comput Vision (2006) 68: 145. doi:10.1007/s11263-006-6658-x


In this paper, we propose a new variational model to segment an object belonging to a given shape space using the active contour method, a geometric shape prior and the Mumford-Shah functional. The core of our model is an energy functional composed by three complementary terms. The first one is based on a shape model which constrains the active contour to get a shape of interest. The second term detects object boundaries from image gradients. And the third term drives globally the shape prior and the active contour towards a homogeneous intensity region. The segmentation of the object of interest is given by the minimum of our energy functional. This minimum is computed with the calculus of variations and the gradient descent method that provide a system of evolution equations solved with the well-known level set method. We also prove the existence of this minimum in the space of functions with bounded variation. Applications of the proposed model are presented on synthetic and medical images.


image segmentationvariational modelactive contourlevel set methodshape priorshape registrationprincipal components analysisMumford-Shah model
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© Springer Science + Business Media, LLC 2006