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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Bibliographic Details
Published in:IEEE access 2020, Vol.8, p.42097-42110
Main Authors: Sun, Zhuang, Qiao, Yang, Jiang, Zhaoguo, Xu, Xiping, Zhou, Jing, Gong, Xuanrui
Format: Article
Language:English
Subjects:
Azimuth
Cameras
Differentiation
Differentiation operator
Discrete Fourier transforms
Error reduction
Finite wordlength effects
Fourier transforms
Free form
gradient methods
Periodic variations
Polarization
Reconstruction
reconstruction algorithms
Shape
shape-from-polarization
Surface reconstruction
Surface waves
Truncation errors
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Summary: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.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2020.2977097