{"abstract":[{"lang":"eng","text":"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."}],"department":[{"_id":"JaMa"}],"publication_status":"published","date_published":"2017-05-18T00:00:00Z","date_updated":"2023-09-22T09:55:50Z","month":"05","article_processing_charge":"No","day":"18","type":"conference","alternative_title":["LNCS"],"status":"public","quality_controlled":"1","title":"Transport based image morphing with intensity modulation","scopus_import":"1","publisher":"Springer","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2018-12-11T11:49:34Z","oa_version":"None","_id":"989","language":[{"iso":"eng"}],"editor":[{"full_name":"Lauze, François","first_name":"François","last_name":"Lauze"},{"first_name":"Yiqiu","last_name":"Dong","full_name":"Dong, Yiqiu"},{"full_name":"Bjorholm Dahl, Anders","first_name":"Anders","last_name":"Bjorholm Dahl"}],"citation":{"ama":"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:<a href=\"https://doi.org/10.1007/978-3-319-58771-4_45\">10.1007/978-3-319-58771-4_45</a>","apa":"Maas, J., Rumpf, M., &#38; Simon, S. (2017). Transport based image morphing with intensity modulation. In F. Lauze, Y. Dong, &#38; A. Bjorholm Dahl (Eds.) (Vol. 10302, pp. 563–577). Presented at the SSVM:  Scale Space and Variational Methods in Computer Vision, Kolding, Denmark: Springer. <a href=\"https://doi.org/10.1007/978-3-319-58771-4_45\">https://doi.org/10.1007/978-3-319-58771-4_45</a>","ista":"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.","chicago":"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. <a href=\"https://doi.org/10.1007/978-3-319-58771-4_45\">https://doi.org/10.1007/978-3-319-58771-4_45</a>.","short":"J. Maas, M. Rumpf, S. Simon, in:, F. Lauze, Y. Dong, A. Bjorholm Dahl (Eds.), Springer, 2017, pp. 563–577.","mla":"Maas, Jan, et al. <i>Transport Based Image Morphing with Intensity Modulation</i>. Edited by François Lauze et al., vol. 10302, Springer, 2017, pp. 563–77, doi:<a href=\"https://doi.org/10.1007/978-3-319-58771-4_45\">10.1007/978-3-319-58771-4_45</a>.","ieee":"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."},"conference":{"location":"Kolding, Denmark","end_date":"2017-06-08","name":"SSVM:  Scale Space and Variational Methods in Computer Vision","start_date":"2017-06-04"},"publication_identifier":{"issn":["03029743"]},"external_id":{"isi":["000432210900045"]},"author":[{"orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Rumpf, Martin","last_name":"Rumpf","first_name":"Martin"},{"full_name":"Simon, Stefan","last_name":"Simon","first_name":"Stefan"}],"page":"563 - 577","doi":"10.1007/978-3-319-58771-4_45","isi":1,"year":"2017","publist_id":"6410","volume":10302,"intvolume":"     10302"}