We propose a variational model with diffeomorphic optimal transportation for joint image reconstruction and motion estimation. The proposed is production of assembling the Wasserstein distance Benamou--Brenier formula in flow diffeomorphisms involved large deformation metric mapping, which suitable scenario spatiotemporal imaging mass-preserving deformations. Specifically, we first use to chara...

We consider algorithms for finding the optimal location of a simple transportation device, that we call a moving walkway, consisting of a pair of points in the plane between which the travel speed is high. More specifically, one can travel from one endpoint of the walkway to the other at speed v > 1, but can only travel at unit speed between any other pair of points. The travel time between any...

We give a model for the description of an urban transportation network and we consider the related optimization problem which consists in finding the desing of the network which has the best transportation performances. This will be done by introducing, for every admissible network, a suitable metric space with a distance that inserted into the Monge-Kantorovich cost functional provides the cri...

In this document, I outline a few challenging algorithmic problems arising in my research on optimal transportation. I have attempted to pose these problems in “discrete” language. It easily could be the case that they admit straightforward solutions— which is great news!—or that you can do little more than the obvious algorithm. Any and all guidance from members of the theory community is welc...

Our meeting took place during a week of many flight cancellations, due to the eruption of a volcano in Iceland. This caused a number of European participants to arrive late and prevented several more — 10 total, including one organizer — from attending at all. Nevertheless, by rearranging the planned activities, a lively and stimulating program was achieved involving the 32 odd participants who...

We report here two recent developments in the theory of optimal transportation. The first is a proof for the existence of optimal mappings to the Monge mass transportation problem [16]. The other is an application of optimal transportation in geometric optics [19]. The optimal transportation problem, in general, deals with the redistribution of materials in the most economical way. The original...

Here c is a given lower semicontinuous cost function, and πi are the marginals of π . In the typical case c(x, y) = ‖x − y‖, p > 1, and the pth root of the minimum in (1.1) is then called the p-Wasserstein distance Wp(μ, μ) between μ and μ. Brancolini and Buttazzo [6], Buttazzo and Stepanov [8], and Buttazzo et al. [7], among other works, consider a variant of the problem with two different med...

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function. Here we consider a natural but largely unexplored variant of this problem by imposing a pointwise constraint on the joint (absolutely continuous) measures: ...