Transport based image morphing with intensity modulation

J. Maas, M. Rumpf, S. Simon, in:, F. Lauze, Y. Dong, A. Bjorholm Dahl (Eds.), Springer, 2017, pp. 563–577.

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Conference Paper | Published | English
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LNCS
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.
Publishing Year
Date Published
2017-05-18
Volume
10302
Page
563 - 577
Conference
SSVM: Scale Space and Variational Methods in Computer Vision
Conference Location
Kolding, Denmark
Conference Date
2017-06-04 – 2017-06-08
ISSN
IST-REx-ID

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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.

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