Results 61 to 70 of about 3,027 (198)
A View on Optimal Transport from Noncommutative Geometry
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.
Francesco D'Andrea, Pierre Martinetti
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On the Minimax Optimality of Estimating the Wasserstein Metric
CoRR, 2019 We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability measures, is not significantly easier than estimating the probability measures under the Wasserstein metric.
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A note on the Bures-Wasserstein metric
, 2023 In this brief note, it is shown that the Bures-Wasserstein (BW) metric on the space positive definite matrices lends itself to convex optimization. In other words, the computation of the BW metric can be posed as a convex optimization problem. In turn, this leads to efficient computations of (i) the BW distance between convex subsets of positive ...
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Real‐time by‐example texture synthesis and filtering using local statistics exchange
Computer Graphics Forum, EarlyView.Abstract Real‐time by‐example texture synthesis is used in interactive virtual worlds to generate the appearance of an unbounded surface from an exemplar texture with as few repetitions as possible. Currently, leading real‐time methods rely on a tiling and blending scheme which is known to synthesize well texture patterns with little spatial ...
Nicolas Lutz, Guillaume Gilet
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Metric Currents and Geometry of Wasserstein Spaces
Rendiconti del Seminario Matematico della Università di Padova, 2010 We investigate some geometric aspects of Wasserstein spaces through the continuity equation as worked out in mass transportation theory. By defining a suitable homology on the flat torus \mathbb T^n , we prove that the space
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Constrained steepest descent in the 2-Wasserstein metric
Annals of Mathematics, 2003 We study several constrained variational problem in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given a probability density $F_0$ on $\R^d$ and a time-step $h>0$, we seek to minimize $I(F) = hS(F) + W_2^2(F_0,F)$ over all of the probability densities $F$ that have the same
Carlen, E. A., Gangbo, W.
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Establishing Shape Correspondences: A Survey
Computer Graphics Forum, EarlyView.Abstract Shape correspondence between surfaces in 3D is a central problem in geometry processing, concerned with establishing meaningful relations between surfaces. While all correspondence problems share this goal, specific formulations can differ significantly: Downstream applications require certain properties that correspondences must satisfy ...
A. Heuschling, H. Meinhold, L. Kobbelt
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Geometry‐Aware Alignment and Comparison of Hierarchical Morse Complexes with Applications
Computer Graphics Forum, EarlyView.Abstract Scalar fields derived from 3D X‐ray CT scans of samples undergoing ex situ processes, such as thermal aging, chemical etching, or mechanical stress, pose unique challenges for characterizing similarities and differences across acquisitions. Typically, a sample A (source) is imaged, removed, and subjected to experimental conditions that alter ...
Aniketh Venkat +3 more
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Application of the Wasserstein metric to seismic signals [PDF]
Communications in Mathematical Sciences, 2014 Seismic signals are typically compared using travel time difference or $L_2$ difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology. It exhibits properties from both of the traditional measures mentioned above. The numerical computation is based on the recent development of fast numerical methods for
Engquist, Bjorn, Froese, Brittany D.
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Individualized Pathfinding in Rugged Open Terrains Using Semantic Navigation Meshes
Computer Graphics Forum, EarlyView.We introduce semantic navigation meshes for complex outdoor terrains, partitioning space into regions with coherent semantic properties like slope or vegetation density. The resulting graphs enable efficient pathfinding with agent‐specific, parameterized cost functions without precomputation, accelerating search while maintaining path quality close to ...
C. Creus, N. Pelechano, O. Argudo
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