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dc.contributor.authorGenest, Baptisteen_US
dc.contributor.authorCourty, Nicolasen_US
dc.contributor.authorCoeurjolly, Daviden_US
dc.contributor.editorBermano, Amit H.en_US
dc.contributor.editorKalogerakis, Evangelosen_US
dc.date.accessioned2024-04-16T14:39:31Z
dc.date.available2024-04-16T14:39:31Z
dc.date.issued2024
dc.identifier.issn1467-8659
dc.identifier.urihttps://doi.org/10.1111/cgf.15020
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf15020
dc.description.abstractIn machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability measures on general spaces, Optimal Transport (OT) emerges as a pivotal theoretical framework within this context. However, the associated computational burden is prohibitive in most real-world scenarios. Leveraging the simple structure of OT in 1D, Sliced Optimal Transport (SOT) has appeared as an efficient alternative to generate samples in Euclidean spaces. This paper pushes the boundaries of SOT utilization in computational geometry problems by extending its application to sample densities residing on more diverse mathematical domains, including the spherical space Sd, the hyperbolic plane Hd, and the real projective plane Pd. Moreover, it ensures the quality of these samples by achieving a blue noise characteristic, regardless of the dimensionality involved. The robustness of our approach is highlighted through its application to various geometry processing tasks, such as the intrinsic blue noise sampling of meshes, as well as the sampling of directions and rotations. These applications collectively underscore the efficacy of our methodology.en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectCCS Concepts: Computing methodologies -> Computer graphics
dc.subjectComputing methodologies
dc.subjectComputer graphics
dc.titleNon-Euclidean Sliced Optimal Transport Samplingen_US
dc.description.seriesinformationComputer Graphics Forum
dc.description.sectionheadersGeometry Processing
dc.description.volume43
dc.description.number2
dc.identifier.doi10.1111/cgf.15020
dc.identifier.pages14 pages


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