Transport based image morphing with intensity modulation Conference Paper

Author(s): Maas, Jan; Rumpf, Martin; Simon, Stefan
Title: Transport based image morphing with intensity modulation
Title Series: LNCS
Affiliation IST Austria
Abstract: We present a generalized optimal transport model in which the mass-preserving constraint for the L2-Wasserstein distance is relaxed by introducing a source term in the continuity equation. The source term is also incorporated in the path energy by means of its squared L2-norm in time of a functional with linear growth in space. This extension of the original transport model enables local density modulations, which is a desirable feature in applications such as image warping and blending. A key advantage of the use of a functional with linear growth in space is that it allows for singular sources and sinks, which can be supported on points or lines. On a technical level, the L2-norm in time ensures a disintegration of the source in time, which we use to obtain the well-posedness of the model and the existence of geodesic paths. The numerical discretization is based on the proximal splitting approach [18] and selected numerical test cases show the potential of the proposed approach. Furthermore, the approach is applied to the warping and blending of textures.
Keywords: Optimal transport; texture morphing; generalized Wasserstein distance; proximal splitting
Conference Title: SSVM: Scale Space and Variational Methods in Computer Vision
Volume: 10302
Conference Dates: June 4-8, 2017
Conference Location: Kolding, Denmark
ISBN: 978-3-319-58771-4
Publisher: Springer  
Date Published: 2017-05-18
Start Page: 563
End Page: 577
DOI: 10.1007/978-3-319-58771-4_45
Open access: no
IST Austria Authors
  1. Jan Maas
    28 Maas
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