Article
Model-Independent Lens Distortion Correction Based on
Sub-Pixel Phase Encoding
Pengbo Xiong
1,2
, Shaokai Wang
1
, Weibo Wang
1,2,3,
*, Qixin Ye
1,2
and Shujiao Ye
1,2
Citation: Xiong, P.; Wang, S.; Wang,
W.; Ye, Q.; Ye, S. Model-Independent
Lens Distortion Correction Based on
Sub-Pixel Phase Encoding. Sensors
2021, 21, 7465. https://doi.org/
10.3390/s21227465
Academic Editor: Nunzio Cennamo
Received: 7 October 2021
Accepted: 7 November 2021
Published: 10 November 2021
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4.0/).
1
Institute of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology,
Harbin 150001, China; 19b901031@stu.hit.edu.cn (P.X.); wangsk@hit.edu.cn (S.W.);
19s001037@stu.hit.edu.cn (Q.Y.); yeshujiao@stu.hit.edu.cn (S.Y.)
2
Key Lab of Ultra-Precision Intelligent Instrumentation, Harbin Institute of Technology, Ministry of Industry
and Information Technology, Harbin 150001, China
3
Postdoctoral Research Station of Optical Engineering, Harbin Institute of Technology, Harbin 150001, China
* Correspondence: wwbhit@hit.edu.cn
Abstract:
Lens distortion can introduce deviations in visual measurement and positioning. The
distortion can be minimized by optimizing the lens and selecting high-quality optical glass, but it
cannot be completely eliminated. Most existing correction methods are based on accurate distortion
models and stable image characteristics. However, the distortion is usually a mixture of the radial
distortion and the tangential distortion of the lens group, which makes it difficult for the mathematical
model to accurately fit the non-uniform distortion. This paper proposes a new model-independent
lens complex distortion correction method. Taking the horizontal and vertical stripe pattern as the
calibration target, the sub-pixel value distribution visualizes the image distortion, and the correction
parameters are directly obtained from the pixel distribution. A quantitative evaluation method
suitable for model-independent methods is proposed. The method only calculates the error based
on the characteristic points of the corrected picture itself. Experiments show that this method can
accurately correct distortion with only 8 pictures, with an error of 0.39 pixels, which provides a
simple method for complex lens distortion correction.
Keywords: camera calibration; fringe pattern; phase encoding; model-independent method
1. Introduction
The optical aberration of the lens will cause the non-linear distortion of the image.
Distortion correction is necessary in digital image analysis. For example, computer vision
tasks involving geometric location, size measurement, image recognition, and accurate
distortion correction are essential [
1
–
4
]. The existing distortion correction methods can be
subdivided into three categories: traditional vision calibration, active vision calibration,
and learning-based methods [5–7].
In traditional vision measurement methods, geometric features such as corner points,
vanishing points, and straight lines are the main control targets for correction [
8
]. The
characteristic of the traditional methods is to use the known structure information of the
scene, which is usually used to calibrate the block. It can be used for any camera model with
high calibration accuracy. However, the calibration process is complicated and requires
high-precision known structural information. In many cases, the calibration block cannot
be used in actual applications. The accuracy depends on the density of geometric feature
selection and is invalid for nonlinear distortion. Therefore, Zhang [
9
,
10
] proposed a multi-
viewpoint correction method that uses the correspondence between points in different
images to measure lens distortion parameters. It does not require special operations to
realize automatic correction, but a set of images to establish a mathematical model. The
method and its improved version are more flexible calibration methods, which can calculate
the internal and external parameters of the camera by capturing 3 to 20 patterns at different
Sensors 2021, 21, 7465. https://doi.org/10.3390/s21227465 https://www.mdpi.com/journal/sensors
