A survey of Optimal Transport for Computer Graphics and Computer Vision

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...

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Published in:	Computer graphics forum Vol. 42; no. 2; pp. 439 - 460
Main Authors:	Bonneel, Nicolas, Digne, Julie
Format:	Journal Article
Language:	English
Published:	Oxford Blackwell Publishing Ltd 01.05.2023 Wiley
Subjects:	Algorithms Artificial Intelligence CCS Concepts Computational Geometry Computer graphics Computer Science Computer vision Computer Vision and Pattern Recognition Computing methodologies → Computer graphics Graphics Image processing Operations research Computer vision CCS Concepts • Computing methodologies → Computer graphics
ISSN:	0167-7055, 1467-8659
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Abstract	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.
AbstractList	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.
Author	Bonneel, Nicolas Digne, Julie
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Snippet	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... 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...
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SubjectTerms	Algorithms Artificial Intelligence CCS Concepts Computational Geometry Computer graphics Computer Science Computer vision Computer Vision and Pattern Recognition Computing methodologies → Computer graphics Graphics Image processing Operations research
Title	A survey of Optimal Transport for Computer Graphics and Computer Vision
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