An Accurate Fourier-Based Method for Three-Dimensional Reconstruction of Transparent Surfaces in the Shape-From-Polarization Method

The Fourier-based gradient field integration method can efficiently reconstruct transparent surfaces from the measured gradient data in the Shape-from-polarization method. However, for the differentiation operator having large truncation errors and lacking constraints on adjacent heights, it will in...

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Main Authors: Zhuang Sun, Yang Qiao, Zhaoguo Jiang, Xiping Xu, Jing Zhou, Xuanrui Gong
Format: Article
Language:English
Published: IEEE 2020-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/9018216/
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spelling doaj-0974c8f0c53b4237b609eaf1d19706c42021-03-30T02:04:43ZengIEEEIEEE Access2169-35362020-01-018420974211010.1109/ACCESS.2020.29770979018216An Accurate Fourier-Based Method for Three-Dimensional Reconstruction of Transparent Surfaces in the Shape-From-Polarization MethodZhuang Sun0https://orcid.org/0000-0001-8828-7939Yang Qiao1Zhaoguo Jiang2https://orcid.org/0000-0002-8223-6468Xiping Xu3https://orcid.org/0000-0002-4561-4570Jing Zhou4https://orcid.org/0000-0003-1014-3526Xuanrui Gong5https://orcid.org/0000-0002-8585-0295College of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun, ChinaCollege of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun, ChinaCollege of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun, ChinaCollege of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun, ChinaCollege of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun, ChinaCollege of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun, ChinaThe Fourier-based gradient field integration method can efficiently reconstruct transparent surfaces from the measured gradient data in the Shape-from-polarization method. However, for the differentiation operator having large truncation errors and lacking constraints on adjacent heights, it will increase the reconstructing error of the Fourier-based integration method. This paper presents an accurate Fourier-based integration approach to improve the reconstruction accuracy, in which a new differentiation operator is derived by limiting the truncation error and increasing heights and slopes in the operator. In order to modify the data obtained by the new operator to meet the requirements of both periodicity and size for the use of the discrete Fourier transform, we propose a method to extend the raw gradient data by first performing antisymmetric extension and then performing periodic extension. A series of simulations and experiments have been developed to verify the performance of the proposed method. By comparing the approach of this paper with other Fourier-based approaches, including Frankot-Chellappa, Southwell-FT and Simpson-FT, both of the simulation and experiment results show that the proposed Fourier-based integration method performs a higher accuracy than other approaches. In the reconstruction experiment, the reconstruction error can be reduced from 0.065 ~ 0.081 mm to 0.020 mm for the spherical surface, and from 0.060 ~ 0.12 mm to 0.016 mm for the free-form surface.https://ieeexplore.ieee.org/document/9018216/Differentiation operatordiscrete Fourier transformsgradient methodsshape-from-polarizationreconstruction algorithms
collection DOAJ
language English
format Article
sources DOAJ
author Zhuang Sun
Yang Qiao
Zhaoguo Jiang
Xiping Xu
Jing Zhou
Xuanrui Gong
spellingShingle Zhuang Sun
Yang Qiao
Zhaoguo Jiang
Xiping Xu
Jing Zhou
Xuanrui Gong
An Accurate Fourier-Based Method for Three-Dimensional Reconstruction of Transparent Surfaces in the Shape-From-Polarization Method
IEEE Access
Differentiation operator
discrete Fourier transforms
gradient methods
shape-from-polarization
reconstruction algorithms
author_facet Zhuang Sun
Yang Qiao
Zhaoguo Jiang
Xiping Xu
Jing Zhou
Xuanrui Gong
author_sort Zhuang Sun
title An Accurate Fourier-Based Method for Three-Dimensional Reconstruction of Transparent Surfaces in the Shape-From-Polarization Method
title_short An Accurate Fourier-Based Method for Three-Dimensional Reconstruction of Transparent Surfaces in the Shape-From-Polarization Method
title_full An Accurate Fourier-Based Method for Three-Dimensional Reconstruction of Transparent Surfaces in the Shape-From-Polarization Method
title_fullStr An Accurate Fourier-Based Method for Three-Dimensional Reconstruction of Transparent Surfaces in the Shape-From-Polarization Method
title_full_unstemmed An Accurate Fourier-Based Method for Three-Dimensional Reconstruction of Transparent Surfaces in the Shape-From-Polarization Method
title_sort accurate fourier-based method for three-dimensional reconstruction of transparent surfaces in the shape-from-polarization method
publisher IEEE
series IEEE Access
issn 2169-3536
publishDate 2020-01-01
description The Fourier-based gradient field integration method can efficiently reconstruct transparent surfaces from the measured gradient data in the Shape-from-polarization method. However, for the differentiation operator having large truncation errors and lacking constraints on adjacent heights, it will increase the reconstructing error of the Fourier-based integration method. This paper presents an accurate Fourier-based integration approach to improve the reconstruction accuracy, in which a new differentiation operator is derived by limiting the truncation error and increasing heights and slopes in the operator. In order to modify the data obtained by the new operator to meet the requirements of both periodicity and size for the use of the discrete Fourier transform, we propose a method to extend the raw gradient data by first performing antisymmetric extension and then performing periodic extension. A series of simulations and experiments have been developed to verify the performance of the proposed method. By comparing the approach of this paper with other Fourier-based approaches, including Frankot-Chellappa, Southwell-FT and Simpson-FT, both of the simulation and experiment results show that the proposed Fourier-based integration method performs a higher accuracy than other approaches. In the reconstruction experiment, the reconstruction error can be reduced from 0.065 ~ 0.081 mm to 0.020 mm for the spherical surface, and from 0.060 ~ 0.12 mm to 0.016 mm for the free-form surface.
topic Differentiation operator
discrete Fourier transforms
gradient methods
shape-from-polarization
reconstruction algorithms
url https://ieeexplore.ieee.org/document/9018216/
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