Local histogram based segmentation using the wasserstein distance

Kangyu Ni*, Xavier Bresson, Tony Chan, Selim Esedoglu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

192 Scopus citations


We propose and analyze a nonparametric region-based active contour model for segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel intensity is independently identically distributed. Our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a region-based image term that uses histograms of pixel intensity to distinguish different regions. More specifically, the region data encourages segmentation so that local histograms within each region are approximately homogeneous. An advantage of using local histograms in the data term is that histogram differentiation is not required to solve the energy minimization problem. We use Wasserstein distance with exponent 1 to determine the dissimilarity between two histograms. The Wasserstein distance is a metric and is able to faithfully measure the distance between two histograms, compared to many pointwise distances. Moreover, it is insensitive to oscillations, and therefore our model is robust to noise. A fast global minimization method based on (Chan et al. in SIAM J. Appl. Math. 66(5):1632-1648, 2006; Bresson et al. in J. Math. Imaging Vis. 28(2):151-167, 2007) is employed to solve the proposed model. The advantages of using this method are two-fold. First, the computational time is less than that of the method by gradient descent of the associated Euler-Lagrange equation (Chan et al. in Proc. of SSVM, pp. 697-708, 2007). Second, it is able to find a global minimizer. Finally, we propose a variant of our model that is able to properly segment a cluttered scene with local illumination changes.

Original languageEnglish (US)
Pages (from-to)97-111
Number of pages15
JournalInternational Journal of Computer Vision
Issue number1
StatePublished - Aug 2009
Externally publishedYes


  • Computer vision
  • Image processing
  • Image segmentation
  • Nonparametric
  • Unsupervised
  • Wasserstein distance

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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