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Deep Compositing Using Lie Algebras

Author:

Tom DuffAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 36, Issue 3

Article No.: 26, Pages 1 - 12

https://doi.org/10.1145/3023386

Published: 01 June 2017 Publication History

Abstract

Deep compositing is an important practical tool in creating digital imagery, but there has been little theoretical analysis of the underlying mathematical operators. Motivated by finding a simple formulation of the merging operation on OpenEXR-style deep images, we show that the Porter-Duff over function is the operator of a Lie group. In its corresponding Lie algebra, the splitting and mixing functions that OpenEXR deep merging requires have a particularly simple form. Working in the Lie algebra, we present a novel, simple proof of the uniqueness of the mixing function.

The Lie group structure has many more applications, including new, correct resampling algorithms for volumetric images with alpha channels, and a deep image compression technique that outperforms that of OpenEXR.

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Cited By

Zhang XRöthlin GZhu SAydın TSalehi FGross MPapas M(2024)Neural Denoising for Deep‐Z Monte Carlo RenderingsComputer Graphics Forum10.1111/cgf.1505043:2Online publication date: 15-May-2024
https://doi.org/10.1111/cgf.15050
Chen ZHua YZuo PSun YGuo Y(2024)Approximate Similarity-Aware Compression for Non-Volatile Main MemoryJournal of Computer Science and Technology10.1007/s11390-023-2565-739:1(63-81)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s11390-023-2565-7
Kim DKye H(2021) Z ‐Thickness Blending: Effective Fragment Merging for Multi‐Fragment Rendering Computer Graphics Forum10.1111/cgf.1440940:7(149-160)Online publication date: 27-Nov-2021
https://doi.org/10.1111/cgf.14409
Show More Cited By

Index Terms

Deep Compositing Using Lie Algebras
1. Computing methodologies
  1. Computer graphics
    1. Image manipulation
      1. Antialiasing
      2. Image processing
    2. Rendering
      1. Visibility

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Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 36, Issue 3

June 2017

165 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3087678

Editor:
Kavita Bala
Cornell University

Issue’s Table of Contents

Copyright © 2017 Owner/Author.

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 2017

Accepted: 01 December 2016

Received: 01 September 2016

Published in TOG Volume 36, Issue 3

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Cited By

Zhang XRöthlin GZhu SAydın TSalehi FGross MPapas M(2024)Neural Denoising for Deep‐Z Monte Carlo RenderingsComputer Graphics Forum10.1111/cgf.1505043:2Online publication date: 15-May-2024
https://doi.org/10.1111/cgf.15050
Chen ZHua YZuo PSun YGuo Y(2024)Approximate Similarity-Aware Compression for Non-Volatile Main MemoryJournal of Computer Science and Technology10.1007/s11390-023-2565-739:1(63-81)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s11390-023-2565-7
Kim DKye H(2021) Z ‐Thickness Blending: Effective Fragment Merging for Multi‐Fragment Rendering Computer Graphics Forum10.1111/cgf.1440940:7(149-160)Online publication date: 27-Nov-2021
https://doi.org/10.1111/cgf.14409
Ohkawara MFujishiro I(2021)Illumination-aware Digital Image Compositing for Full-length Human Figures2021 International Conference on Cyberworlds (CW)10.1109/CW52790.2021.00011(17-24)Online publication date: Sep-2021
https://doi.org/10.1109/CW52790.2021.00011
Vasilakis AVardis KPapaioannou G(2020)A Survey of Multifragment RenderingComputer Graphics Forum10.1111/cgf.1401939:2(623-642)Online publication date: 13-Jul-2020
https://doi.org/10.1111/cgf.14019
Hillman PBalents BGossett CPhillips CRose R(2018)A scheme for storing object ID manifests in openEXR imagesProceedings of the 8th Annual Digital Production Symposium10.1145/3233085.3233086(1-8)Online publication date: 11-Aug-2018
https://dl.acm.org/doi/10.1145/3233085.3233086
Archer JLeach Gvan Schyndel RGutierrez DHuang H(2017)GPU based techniques for deep image mergingSIGGRAPH Asia 2017 Technical Briefs10.1145/3145749.3149448(1-4)Online publication date: 27-Nov-2017
https://dl.acm.org/doi/10.1145/3145749.3149448

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