NDLI: Dynamic optimal transport with mixed boundary condition for color image processing

Content Provider	IEEE Xplore Digital Library
Author	Fitschen, J.H. Laus, F. Steidl, G.
Copyright Year	2015
Description	Author affiliation: Dept. of Math., Univ. of Kaiserslautern, Kaiserslautern, Germany (Fitschen, J.H.; Laus, F.; Steidl, G.)
Abstract	Recently, Papadakis et al. [11] proposed an efficient primal-dual algorithm for solving the dynamic optimal transport problem with quadratic ground cost and measures having densities with respect to the Lebesgue measure. It is based on the fluid mechanics formulation by Benamou and Brenier [1] and proximal splitting schemes. In this paper we extend the framework to color image processing. We show how the transportation problem for RGB color images can be tackled by prescribing periodic boundary conditions in the color dimension. This requires the solution of a 4D Poisson equation with mixed Neumann and periodic boundary conditions in each iteration step of the algorithm. This 4D Poisson equation can be efficiently handled by fast Fourier and Cosine transforms. Furthermore, we sketch how the same idea can be used in a modified way to transport periodic 1D data such as the histogram of cyclic hue components of images. We discuss the existence and uniqueness of a minimizer of the associated energy functional. Numerical examples illustrate the meaningfulness of our approach.
Starting Page	558
Ending Page	562
File Size	10730453
Page Count	5
File Format	PDF
ISBN	9781467373531
DOI	10.1109/SAMPTA.2015.7148953
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-05-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Histograms Poisson equations Image color analysis Density measurement Imaging Transportation Boundary conditions
Content Type	Text
Resource Type	Article

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