Lens Distortion Calibration Research Articles

On-orbit calibration of space camera lens distortion using a single image

Since space cameras need to withstand the harsh mechanical and thermal conditions in the space environment for a long time, it is necessary to calibrate them in orbit. However, existing calibration methods have various disadvantages, making them impossible to use in orbit. To address this problem, we present an on-orbit calibration of space camera lens distortion with the vanishing points obtained from a single image of the solar panel. First, we propose a parallel-line-extraction method based on collinear constraints to obtain the parallel lines. Then, we train the optimal vanishing point using the common point constraint method. Using the optimal vanishing point, we establish the optimization function of lens distortion based on vanishing point consistency. Finally, we present an improved genetic algorithm to solve the optimization function. Simulations and experiments show that the proposed method is flexible and robust.

Novel Bayesian Inference-Based Approach for the Uncertainty Characterization of Zhang's Camera Calibration Method.

Camera calibration is necessary for many machine vision applications. The calibration methods are based on linear or non-linear optimization techniques that aim to find the best estimate of the camera parameters. One of the most commonly used methods in computer vision for the calibration of intrinsic camera parameters and lens distortion (interior orientation) is Zhang's method. Additionally, the uncertainty of the camera parameters is normally estimated by assuming that their variability can be explained by the images of the different poses of a checkerboard. However, the degree of reliability for both the best parameter values and their associated uncertainties has not yet been verified. Inaccurate estimates of intrinsic and extrinsic parameters during camera calibration may introduce additional biases in post-processing. This is why we propose a novel Bayesian inference-based approach that has allowed us to evaluate the degree of certainty of Zhang's camera calibration procedure. For this purpose, the a prioriprobability was assumed to be the one estimated by Zhang, and the intrinsic parameters were recalibrated by Bayesian inversion. The uncertainty of the intrinsic parameters was found to differ from the ones estimated with Zhang's method. However, the major source of inaccuracy is caused by the procedure for calculating the extrinsic parameters. The procedure used in the novel Bayesian inference-based approach significantly improves the reliability of the predictions of the image points, as it optimizes the extrinsic parameters.

Geometric Calibration for the Aerial Line Scanning Camera GFXJ

The Gao Fen Xiang Ji (GFXJ) is the first Chinese self–developed airborne three–line array charge-coupled devices (CCD) camera and is designed to meet 8 cm ground sample distance (GSD), 0.5 m planimetry accuracy, and 0.28 m elevation accuracy for ground three-dimensional (3D) points at a flight height of 2000 m. These values also meet the 1:1000 scale mapping requirements in China. However, the original direct geopositioning accuracy of the GFXJ is approximately 4 m in the planimetry direction and 6 m in the elevation direction. To meet the ground 3D point accuracy requirements and improve the direct geopositioning accuracy of the GFXJ, this paper carries out a deep investigation on the GFXJ geometric calibration. This geometric calibration includes two main parts: the Global Navigation Satellite System (GNSS) lever arms and inertial measurement unit (IMU) boresight misalignment calibration, and the camera lens and CCD line distortion calibration. First, a brief introduction is given on the imaging properties of the GFXJ camera. Then, the GNSS lever arms and IMU boresight misalignment calibration models are built for the GFXJ camera. Next, a piecewise self-calibration model based on the CCD viewing angle is established for the GFXJ lens and CCD line distortion calibration. Subsequently, an iterative two-step calibration scheme is proposed for the geometric calibration. Finally, experiments were implemented using multiple flight blocks obtained in the Songshan remote sensing comprehensive field and the Hegang area of Heilongjiang Province. Through calibration experiments, geometric calibration values were obtained for the GNSS lever arms and IMU boresight misalignment. Reliable CAM files were independently generated for the forward, nadir, and backward line arrays. The experiments showed that the proposed GNSS lever arms and IMU boresight misalignment calibration models and the piecewise self-calibration model had good applicability and effectiveness for the GFXJ camera. The proposed two-step calibration scheme can significantly enhance the geometric positioning accuracy of the GFXJ camera. The original direct geopositioning accuracy of the GFXJ is approximately 4 m in the planimetry direction and 6 m in the elevation direction. Using the GNSS lever arms and the IMU boresight misalignment calibration values and the CAM files, the positioning accuracy of the GFXJ camera can fulfill the 3D point accuracy requirements and the 1:1000 mapping accuracy requirements at a 2000 m flight height after aerial triangulation with only several ground control points. The planimetry accuracy is approximately 0.2 m, and the elevation accuracy is less than 0.28 m. In addition, the calibration models and calibration scheme established in this paper can provide a reference for calibration studies on other airborne linear array CCD cameras.

鱼眼镜头的畸变纠正分析

鱼眼镜头的畸变纠正分析

Calibration of radial lens distortion using a Gaussian model

We present a lens distortion model based on the Gaussian function. The model is a potential source function of the popular Brown distortion model and requires the practical estimation of one Boolean and one real parameter. We also present a general technique for lens distortion identification, which consists of three steps: image data acquisition, localization and indexation/matching of image features, and the estimation of distortion parameters. The method uses a structured light technique, in which bar patterns are indexed by a Gray code. Acquired images are automatically processed using a multistep approach that localizes and indexes calibration points. An iterative analysis of differences between localizations of distorted points and their undistorted counterparts is proposed to estimate distortion model parameters. To compute undistorted localizations, the method estimates a homography matrix that is based on both undistorted data and iterative processing of distorted coordinates, which improves compensation accuracy. Experiments with three cameras show that the indexing strategy significantly decreases compensation error (from 0.26 to 0.09 pixels). The newly introduced Gaussian model is shown to be slightly more accurate and considerably more stable than the popular Brown model.

SYSTEMATIC CALIBRATION FOR A BACKPACKED SPHERICAL PHOTOGRAMMETRY IMAGING SYSTEM

A spherical camera can observe the environment for almost 720 degrees’ field of view in one shoot, which is useful for augmented reality, environment documentation, or mobile mapping applications. This paper aims to develop a spherical photogrammetry imaging system for the purpose of 3D measurement through a backpacked mobile mapping system (MMS). The used equipment contains a Ladybug-5 spherical camera, a tactical grade positioning and orientation system (POS), i.e. SPAN-CPT, and an odometer, etc. This research aims to directly apply photogrammetric space intersection technique for 3D mapping from a spherical image stereo-pair. For this purpose, several systematic calibration procedures are required, including lens distortion calibration, relative orientation calibration, boresight calibration for direct georeferencing, and spherical image calibration. The lens distortion is serious on the ladybug-5 camera’s original 6 images. Meanwhile, for spherical image mosaicking from these original 6 images, we propose the use of their relative orientation and correct their lens distortion at the same time. However, the constructed spherical image still contains systematic error, which will reduce the 3D measurement accuracy. Later for direct georeferencing purpose, we need to establish a ground control field for boresight/lever-arm calibration. Then, we can apply the calibrated parameters to obtain the exterior orientation parameters (EOPs) of all spherical images. In the end, the 3D positioning accuracy after space intersection will be evaluated, including EOPs obtained by structure from motion method.

SYSTEMATIC CALIBRATION FOR A BACKPACKED SPHERICAL PHOTOGRAMMETRY IMAGING SYSTEM

Abstract. A spherical camera can observe the environment for almost 720 degrees’ field of view in one shoot, which is useful for augmented reality, environment documentation, or mobile mapping applications. This paper aims to develop a spherical photogrammetry imaging system for the purpose of 3D measurement through a backpacked mobile mapping system (MMS). The used equipment contains a Ladybug-5 spherical camera, a tactical grade positioning and orientation system (POS), i.e. SPAN-CPT, and an odometer, etc. This research aims to directly apply photogrammetric space intersection technique for 3D mapping from a spherical image stereo-pair. For this purpose, several systematic calibration procedures are required, including lens distortion calibration, relative orientation calibration, boresight calibration for direct georeferencing, and spherical image calibration. The lens distortion is serious on the ladybug-5 camera’s original 6 images. Meanwhile, for spherical image mosaicking from these original 6 images, we propose the use of their relative orientation and correct their lens distortion at the same time. However, the constructed spherical image still contains systematic error, which will reduce the 3D measurement accuracy. Later for direct georeferencing purpose, we need to establish a ground control field for boresight/lever-arm calibration. Then, we can apply the calibrated parameters to obtain the exterior orientation parameters (EOPs) of all spherical images. In the end, the 3D positioning accuracy after space intersection will be evaluated, including EOPs obtained by structure from motion method.

Mathematical Analysis of Stereo Vision Camera with Lens Distortion Calibration

In this paper is to control the high presision camera mapping for robotic vision system purposes. The benchmark approach models the camera mapping as a camera with distortion. Moreover in this article presents mathamatical solution of disparity produced in case of stereo calibration due to non-linearity of images obtained from two cameras. Due to the change in the angle between the two cameras, image position changes and rectification procedures are required to correct calibration. Using fundamental matrix and minimizing disparity matrix error is removed. Paper involves finding the fundamental matrix of the camera and then using it to find depth of image. Next follows disparity correction using correlation methods. Microsoft visual studio is used as programming environment. Chessboard is taken as test image.

Fisheye Lens Distortion Calibration Based on the Lens Charactetic Curves

The fisheye lens is a kind of ultra wide angle lens, which can produce a big super-wide-angle lens distortion. In order to cover a large scope of light, barrel distortion is artificially added to the optical system. However, in some cases this distortion is not allowed, then it requires calibrations of those distortions. Most of the traditional distortion calibration method uses target plane calibration to do it. This paper discusses the way of design fisheye lens, through which we can know the forming process of distortion clearly. Based on this paper, a simple and effective calibration method can be understood. Different from common camera calibration method, the proposed calibration method can avoid the error occurring in the process of calibrating test, that directly use the lens’ characteristic curve. Through multiple sets of experimental verifications, this method is effective and feasible.

Fisheye Lens Distortion Calibration Based on the Lens Charactetic Curves

The fisheye lens is a kind of ultra wide angle lens, which can produce a big super-wide-angle lens distortion. In order to cover a large scope of light, barrel distortion is artificially added to the optical system. However, in some cases this distortion is not allowed, then it requires calibrations of those distortions. Most of the traditional distortion calibration method uses target plane calibration to do it. This paper discusses the way of design fisheye lens, through which we can know the forming process of distortion clearly. Based on this paper, a simple and effective calibration method can be understood. Different from common camera calibration method, the proposed calibration method can avoid the error occurring in the process of calibrating test, that directly use the lens’ characteristic curve. Through multiple sets of experimental verifications, this method is effective and feasible.

基于共线向量的非量测镜头畸变校正

基于共线向量的非量测镜头畸变校正

Calibration and correction of lens distortion for two-dimensional digital speckle correlation measurement

Lens distortion practically presents in optical imaging system using in two-dimensional digital speckle correlation measurement (2D-DSCM) system, and gives rise to additional errors in the displacement and strain measurement. Camera calibration procedure is performed to obtain the coefficients of radial distortion and tangential distortion. The corrected displacement fields can be calculated using the distortion coefficient. The influence of distortion on displacement and strain measurement errors in experiment is further discussed. The three-point bending test result shows that the camera lens calibration method can effectively eliminate the effect of lens distortion and improve displacement and strain measurement accuracy.

Radial Lens Distortion Calibration from Spheres: Theory and Method

This paper addresses the problem of lens distortion calibration from a single image of a sphere. Almost all calibration methods based on spheres have focused on estimating all the camera parameters except the lens distortion ones which are left for another independent calibration process not using spheres. The paper presents for the first time a radial lens distortion calibration method based on the analysis of local shading measures in the sphere image. Several properties of these measures are pointed out and validated. While these measures are robust to noise, they are shown to vary nonlinearly as a function of lens distortion. As such, they can work as a basis for lens distortion calibration. The proposed method is easy to use and requires no specific feature extraction from the images. Experiments on simulated and real data are reported with comparisons to well-known techniques.

Using the camera pin-hole model restrictions to calibrate the lens distortion model

Camera calibration required the computation of camera pin-hole and lens distortion models. The lens distortion is estimated alone or together with the pin-hole model, by using some existing lens distortion non-metric or self-calibration methods. If both models are computed together, then the models are adjusted to training data, but not to real camera. This is because both pin-hole and lens distortion models are coupled. If they are computed separately, difficulties arise since calibration of lens distortion alone is an unstable process. To improve existing camera calibration methods, this paper proposes a metric calibration method to compute lens distortion separately from the pin-hole model. This method is solved under stable conditions, independently of the computed lens distortion model, since pin-hole and distortion models are computed separately. Images of a planar template are used. First, using distorted control points extracted from images, a set of undistorted points which fits in the pin-hole model are computed. Second, with distorted and undistorted control points, lens distortion is calibrated by using a metric calibration process.

Single Pan and Tilt Camera Indoor Positioning and Tracking System

An inexpensive single pan and tilt camera based indoor positioning and tracking system is proposed, supported on a functional architecture where three main modules can be identified: one related to the interface with the camera, tackled with parameter estimation techniques; other, responsible for isolating and identifying the target, based on advanced image processing techniques, and a third, that resorting to nonlinear dynamic system suboptimal state estimation techniques, performs the tracking of the target and estimates its position, and linear and angular velocities. The contributions of this work are fourfold: i) a new indoor positioning and tracking system architecture; ii) a new lens distortion calibration method, that preserves generic straight lines in images; iii) suboptimal nonlinear multiple-model adaptive estimation techniques, for the adopted target model, to tackle the positioning and trackingtasks, andiv) theimplementationandvalidationin real time of a complex tracking system, based on a low cost single camera. To assess the performance of the proposed system, a series of indoor experimental tests for a range of operation of up to ten meter were carried out. Acentimetric accuracy was obtained under realistic conditions.

Lens distortion models evaluation

Many lens distortion models exist with several variations, and each distortion model is calibrated by using a different technique. If someone wants to correct lens distortion, choosing the right model could represent a very difficult task. Calibration depends on the chosen model, and some methods have unstable results. Normally, the distortion model containing radial, tangential, and prism distortion is used, but it does not represent high distortion accurately. The aim of this paper is to compare different lens distortion models to define the one that obtains better results under some conditions and to explore if some model can represent high and low distortion adequately. Also, we propose a calibration technique to calibrate several models under stable conditions. Since performance is hard conditioned with the calibration technique, the metric lens distortion calibration method is used to calibrate all the evaluated models.

Correcting non-linear lens distortion in cameras without using a model

Camera lens distortion calibration is the first step in resolving any metric application with a camera. To date, lens distortion was corrected using some existing lens distortion non-metric or self-calibration methods. Using a lens distortion model means defining a global rule to correct the entire image. This global rule does not take into account particular lens distortion effects not represented by the model. Moreover, to calibrate the model, only some features of the scene such as straight lines, circles or vanishing points are used. Since only the feature of the scene used to calibrate the model is guaranteed by the distortion rectification, it is certain that the model will not be precise. The result is an approximation of the real image distortion. To improve the lens distortion rectification, a method without using a model is proposed. Using a set of control points distributed across the entire image, they are corrected to assure all the restrictions of the scene. With both sets of points, the points detected in the image and the undistorted ones, image local transformations are defined considering only nearby control points. Rather than calibrating a global model, local functions are characterized. The distortion correction is defined by a rectification surface composed of local surface patches each influenced by nearby control points. This method is more sensitive to local deformations and allows the image to be corrected in accordance with its distortion.

Robust metric calibration of non-linear camera lens distortion

Camera lens distortion is crucial to obtain the best performance cameral model. Up to now, different techniques exist, which try to minimize the calibration error using different lens distortion models or computing them in different ways. Some compute lens distortion camera parameters in the camera calibration process together with the intrinsic and extrinsic ones. Others isolate the lens distortion calibration without using any template and basing the calibration on the deformation in the image of some features of the objects in the scene, like straight lines or circles. These lens distortion techniques which do not use any calibration template can be unstable if a complete camera lens distortion model is computed. They are named non-metric calibration or self-calibration methods. Traditionally a camera has been always best calibrated if metric calibration is done instead of self-calibration. This paper proposes a metric calibration technique which computes the camera lens distortion isolated from the camera calibration process under stable conditions, independently of the computed lens distortion model or the number of parameters. To make it easier to resolve, this metric technique uses the same calibration template that will be used afterwards for the calibration process. Therefore, the best performance of the camera lens distortion calibration process is achieved, which is transferred directly to the camera calibration process.

Photogrammetric calibration and colorization of the SwissRanger SR-3100 3-D range imaging sensor

Many robotic and industrial systems require 3-D range-sensing capabilities for mapping, localization, navigation, and obstacle avoidance. Laser-scanning systems that mechanically trace a range-sensing beam over a raster or similar pattern can produce highly accurate models but tend to be bulky and slow when acquiring a significant field of view at useful resolutions. Stereo cameras can provide video-rate range images over significant fields of view but tend to have difficulty with scenes containing low or confusing textures. A new generation of active light, time-of-flight range sensors use a 2-D array of sensor elements to produce a 3-D range image at video rates. These sensors pose unique calibration challenges, requiring both the usual calibration of lens distortion (intrinsic calibration) and calibration of the time-of-flight range measurement (3-D calibration). We present our application of a photogrammetric calibration approach using inexpensive printed optical targets and off-the-shelf software to solve both intrinsic and range calibrations for the MESA Imaging SwissRanger SR-3100 range imaging sensor. Specific calibration issues stemming from this sensor's correlation of reflectivity with measured range are identified. We further present the integration of this otherwise grayscale 3-D sensor with an optical camera, providing a full-color, video-rate 3-D sensing solution.

摄像机镜头畸变的一种非量测校正方法

摄像机镜头畸变的一种非量测校正方法