author = {Maas, Jan and Rumpf, Martin and Sch{\"o}nlieb, Carola and Simon,
  title = {A generalized Model for Optimal Transport of Images including Dissipation
	and Density Modulation},
  journal = {ESAIM Math. Model. Numer. Anal.},
  year = {2015},
  volume = {49},
  pages = {1745--1769},
  number = {6},
  abstract = {In this paper the optimal transport and the metamorphosis perspectives
	are combined. For a pair of given input images geodesic paths in
	the space of images are defined as minimizers of a resulting path
	energy. To this end, the underlying Riemannian metric measures the
	rate of transport cost and the rate of viscous dissipation. Furthermore,
	the model is capable to deal with strongly varying image contrast
	and explicitly allows for sources and sinks in the transport equations
	which are incorporated in the metric related to the metamorphosis
	approach by Trouv\'e and Younes. In the non-viscous case with source
	term existence of geodesic paths is proven in the space of measures.
	The proposed model is explored on the range from merely optimal transport
	to strongly dissipative dynamics. For this model a robust and effective
	variational time discretization of geodesic paths is proposed. This
	requires to minimize a discrete path energy consisting of a sum of
	consecutive image matching functionals. These functionals are defined
	on corresponding pairs of intensity functions and on associated pairwise
	matching deformations. Existence of time discrete geodesics is demonstrated.
	Furthermore, a finite element implementation is proposed and applied
	to instructive test cases and to real images. In the non-viscous
	case this is compared to the algorithm proposed by Benamou and Brenier
	including a discretization of the source term. Finally, the model
	is generalized to define discrete weighted barycentres with applications
	to textures and objects.},
  doi = {10.1051/m2an/2015043},
  eprint = {1504.01988},
  fjournal = {ESAIM. Mathematical Modelling and Numerical Analysis}