Fast ADMM ℓ1 minimization by applying SMW formula and multi-row simultaneous estimation for Light Transport Matrix acquisition

Naoya Chiba, Akira Imakura, Koichi Hashimoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The Light Transport Matrix (LTM) is a fundamental expression of the light propagation of the projector-camera system. The matrix includes all the characteristics of light rays transferred from the projector to the camera, and it is used for scene relighting, understanding the light path, and 3D measurement. Especially, LTM enables robust 3D measurement even if the scene includes metallic or semi-transparent objects; thus it is already used for robot vision. The LTM is often estimated by ℓ1 minimization because the LTM has a huge number of elements. ℓ1 minimization methods, which utilize the Alternating Direction Method of Multipliers (ADMM), can reduce the number of observations. In addition, a powerful extended ADMM ℓ1 minimization method named Saturation ADMM, which can estimate the LTM under saturated conditions, also exists. In the study presented in this paper, we reduce the computational cost of ADMM ℓ1 minimization by applying the Sherman-Morrison-Woodbury (SMW) formula. Furthermore, we propose "multi-row simultaneous LTM estimation, " which is a new method to improve the computational efficiency. The contribution of this paper is to propose the use of these two methods to speed up LTM estimation and demonstrate that our methods reduce the computational cost in theory and the calculation time in practice. Experiments indicate that our method accelerates ADMM ℓ1 minimization by up to 4.64 times, and Saturation ADMM ℓ1 minimization by up to 2.54 times compared to the original methods.

Original languageEnglish
Title of host publicationIEEE International Conference on Robotics and Biomimetics, ROBIO 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages14-21
Number of pages8
ISBN (Electronic)9781728163215
DOIs
Publication statusPublished - 2019 Dec
Event2019 IEEE International Conference on Robotics and Biomimetics, ROBIO 2019 - Dali, China
Duration: 2019 Dec 62019 Dec 8

Publication series

NameIEEE International Conference on Robotics and Biomimetics, ROBIO 2019

Conference

Conference2019 IEEE International Conference on Robotics and Biomimetics, ROBIO 2019
CountryChina
CityDali
Period19/12/619/12/8

Keywords

  • 3D Measurement
  • Alternating Direction Method of Multipliers (ADMM)
  • Light Transport Matrix

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Science Applications
  • Hardware and Architecture
  • Mechanical Engineering
  • Control and Optimization

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