834 research outputs found
A Sparse Multi-Scale Algorithm for Dense Optimal Transport
Discrete optimal transport solvers do not scale well on dense large problems
since they do not explicitly exploit the geometric structure of the cost
function. In analogy to continuous optimal transport we provide a framework to
verify global optimality of a discrete transport plan locally. This allows
construction of an algorithm to solve large dense problems by considering a
sequence of sparse problems instead. The algorithm lends itself to being
combined with a hierarchical multi-scale scheme. Any existing discrete solver
can be used as internal black-box.Several cost functions, including the noisy
squared Euclidean distance, are explicitly detailed. We observe a significant
reduction of run-time and memory requirements.Comment: Published "online first" in Journal of Mathematical Imaging and
Vision, see DO
Dynamic Models of Wasserstein-1-Type Unbalanced Transport
We consider a class of convex optimization problems modelling temporal mass
transport and mass change between two given mass distributions (the so-called
dynamic formulation of unbalanced transport), where we focus on those models
for which transport costs are proportional to transport distance. For those
models we derive an equivalent, computationally more efficient static
formulation, we perform a detailed analysis of the model optimizers and the
associated optimal mass change and transport, and we examine which static
models are generated by a corresponding equivalent dynamic one. Alongside we
discuss thoroughly how the employed model formulations relate to other
formulations found in the literature.Comment: to appear in ESAIM: Control, Optimisation and Calculus of Variation
Meeresstille und Wasserrohrbruch. Über Herkunft, Funktion und Nachwirkung der Gleichnisse in Ovids Erzählung von Pyramus und Thisbe (met. 4,55-166)
Non modo militiae turbine factus eques: Ovids SelbstbewuĂźtsein und die Polemik gegen Horaz in der Elegie am. 3,15
- …