Name
Abstract | ||
|---|---|---|
We present a generalized optimal transport model in which the mass-preserving constraint for the L-2-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 L-2-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 L-2-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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/978-3-319-58771-4_45 | Lecture Notes in Computer Science |
Keywords | Field | DocType |
Optimal transport,Texture morphing,Generalized Wasserstein distance,Proximal splitting | Discretization,Morphing,Intensity modulation,Continuity equation,Image warping,Square (algebra),Mathematical analysis,Mathematics,Geodesic,Modulation (music) | Conference |
Volume | ISSN | Citations |
10302 | 0302-9743 | 0 |
PageRank | References | Authors |
0.34 | 7 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jan Maas | 1 | 5 | 1.27 |
| Martin Rumpf | 2 | 230 | 18.97 |
| Stefan Simon | 3 | 0 | 0.34 |