Maas, JanISTA ; Rumpf, Martin; Simon, Stefan
Lauze, François; Dong, Yiqiu; Bjorholm Dahl, Anders
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  and selected numerical test cases show the potential of the proposed approach. Furthermore, the approach is applied to the warping and blending of textures.
563 - 577
SSVM: Scale Space and Variational Methods in Computer Vision
2017-06-04 – 2017-06-08
Maas J, Rumpf M, Simon S. Transport based image morphing with intensity modulation. In: Lauze F, Dong Y, Bjorholm Dahl A, eds. Vol 10302. Springer; 2017:563-577. doi:10.1007/978-3-319-58771-4_45
Maas, J., Rumpf, M., & Simon, S. (2017). Transport based image morphing with intensity modulation. In F. Lauze, Y. Dong, & A. Bjorholm Dahl (Eds.) (Vol. 10302, pp. 563–577). Presented at the SSVM: Scale Space and Variational Methods in Computer Vision, Kolding, Denmark: Springer. https://doi.org/10.1007/978-3-319-58771-4_45
Maas, Jan, Martin Rumpf, and Stefan Simon. “Transport Based Image Morphing with Intensity Modulation.” edited by François Lauze, Yiqiu Dong, and Anders Bjorholm Dahl, 10302:563–77. Springer, 2017. https://doi.org/10.1007/978-3-319-58771-4_45.
J. Maas, M. Rumpf, and S. Simon, “Transport based image morphing with intensity modulation,” presented at the SSVM: Scale Space and Variational Methods in Computer Vision, Kolding, Denmark, 2017, vol. 10302, pp. 563–577.
Maas J, Rumpf M, Simon S. 2017. Transport based image morphing with intensity modulation. SSVM: Scale Space and Variational Methods in Computer Vision, LNCS, vol. 10302, 563–577.
Maas, Jan, et al. Transport Based Image Morphing with Intensity Modulation. Edited by François Lauze et al., vol. 10302, Springer, 2017, pp. 563–77, doi:10.1007/978-3-319-58771-4_45.