Scalable Multi-Class Sampling via Filtered Sliced Optimal Transport

Salaün, Corentin; Georgiev, Iliyan; Seidel, Hans‐Peter; Singh, Gurprit

doi:10.1145/3550454.3555484

Cited by 9 publications

(3 citation statements)

References 47 publications

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“…Optimal transport has been used as a measure of uniformity to minimize [De Goes et al 2012] but this has remained limited to 2 or 3-dimensions. A sliced optimal transport variant allows to reach about 20 dimensions [Paulin et al 2020;Salaün et al 2022]. By instead optimizing the variance of the function obtained by summing Gaussians centered at each sample, Ahmed et al [Ahmed et al 2022] reach excellent uniformity, demonstrated up to 8 dimensions.…”

Section: Related Workmentioning

confidence: 99%

Quad-Optimized Low-Discrepancy Sequences

Ostromoukhov,

Bonneel,

Coeurjolly

et al. 2024

Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers '24

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The convergence of Monte Carlo integration is given by the uniformity of samples as well as the regularity of the integrand. Despite much effort dedicated to producing excellent, extremely uniform, sampling patterns, the Sobol' sampler remains unchallenged in production rendering systems. This is not only due to its reasonable quality, but also because it allows for integration in (almost) arbitrary dimension, with arbitrary sample count, while actually producing sequences thus allowing for progressive rendering, with fast sample generation and small memory footprint. We improve over Sobol' sequences in terms of sample uniformity in consecutive 2-d and 4-d projections, while providing similar practical benefitssequences, high dimensionality, speed and compactness. We base our contribution on a base-3 Sobol' construction, involving a search over irreducible polynomials and generator matrices, that produce (1, 4)-sequences or (2,4

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Section: Related Workmentioning

confidence: 99%

Quad-Optimized Low-Discrepancy Sequences

Ostromoukhov,

Bonneel,

Coeurjolly

et al. 2024

Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers '24

View full text Add to dashboard Cite

show abstract

“…Their algorithm should be general but is demonstrated in two dimensions (or on surfaces embedded in 3-d). A sliced approach also allows for multi-class color stippling [SGSS22]. An interesting generalization relates to the optimal transport approximation of a density by other non punctual measures [MM99], such as a single (long) continuous curve [LdGKW19] (Fig.…”

Section: Image Stippling and Samplingmentioning

confidence: 99%

“…This approach also works for the task of multi-class blue noise sampling. Sliced multi-class sampling has also been proposed by Salaün et al [SGSS22] with a custom energy that tends to produce blue noise spatial error distribution in the image plane, by producing one point set per pixel such that neighboring pixel samples are well interleaved in a blue noise fashion.…”

Section: Image Stippling and Samplingmentioning

confidence: 99%

A survey of Optimal Transport for Computer Graphics and Computer Vision

Bonneel

Digne

2023

Computer Graphics Forum

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Optimal transport is a long‐standing theory that has been studied in depth from both theoretical and numerical point of views. Starting from the 50s this theory has also found a lot of applications in operational research. Over the last 30 years it has spread to computer vision and computer graphics and is now becoming hard to ignore. Still, its mathematical complexity can make it difficult to comprehend, and as such, computer vision and computer graphics researchers may find it hard to follow recent developments in their field related to optimal transport. This survey first briefly introduces the theory of optimal transport in layman's terms as well as most common numerical techniques to solve it. More importantly, it presents applications of these numerical techniques to solve various computer graphics and vision related problems. This involves applications ranging from image processing, geometry processing, rendering, fluid simulation, to computational optics, and many more. It is aimed at computer graphics researchers desiring to follow optimal transport research in their field as well as optimal transport researchers willing to find applications for their numerical algorithms.

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Non‐Euclidean Sliced Optimal Transport Sampling

Genest,

Courty,

Coeurjolly

2024

Computer Graphics Forum

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In 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.

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Scalable Multi-Class Sampling via Filtered Sliced Optimal Transport

Cited by 9 publications

References 47 publications

Quad-Optimized Low-Discrepancy Sequences

Quad-Optimized Low-Discrepancy Sequences

A survey of Optimal Transport for Computer Graphics and Computer Vision

Non‐Euclidean Sliced Optimal Transport Sampling

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