Harmonic Flow for Histogram Matching

  • Thomas Batard
  • Marcelo Bertalmío
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8334)


We present a method to perform histogram matching between two color images based on the concept of harmonic mapping between Riemannian manifolds. The key idea is to associate the histogram of a color image to a Riemannian manifold. In this context, the energy of the matching between the two images is measured by the Dirichlet energy of the mapping between the Riemannian manifolds. Then, we assimilate optimal matchings to critical points of the Dirichlet energy. Such points are called harmonic maps. As there is no explicit expression for harmonic maps in general, we use a gradient descent flow with boundary condition to reach them, that we call harmonic flow. We present an application to color transfer, however many others applications can be envisaged using this general framework.


Histogram matching Variational method Riemannian geometry Dirichlet energy Color transfer 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Thomas Batard
    • 1
  • Marcelo Bertalmío
    • 1
  1. 1.Department of Information and Communication TechnologiesUniversity Pompeu FabraBarcelonaSpain

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