Radial Distortion Parameters Research Articles

Research on the Optimization Method of Visual Sensor Calibration Combining Convex Lens Imaging with the Bionic Algorithm of Wolf Pack Predation.

To improve the accuracy of camera calibration, a novel optimization method is proposed in this paper, which combines convex lens imaging with the bionic algorithm of Wolf Pack Predation (CLI-WPP). During the optimization process, the internal parameters and radial distortion parameters of the camera are regarded as the search targets of the bionic algorithm of Wolf Pack Predation, and the reprojection error of the calibration results is used as the fitness evaluation criterion of the bionic algorithm of Wolf Pack Predation. The goal of optimizing camera calibration parameters is achieved by iteratively searching for a solution that minimizes the fitness value. To overcome the drawback that the bionic algorithm of Wolf Pack Predation is prone to fall into local optimal, a reverse learning strategy based on convex lens imaging is introduced to transform the current optimal individual and generate a series of new individuals with potential better solutions that are different from the original individual, helping the algorithm out of the local optimum dilemma. The comparative experimental results show that the average reprojection errors of the simulated annealing algorithm, Zhang's calibration method, the sparrow search algorithm, the particle swarm optimization algorithm, bionic algorithm of Wolf Pack Predation, and the algorithm proposed in this paper (CLI-WPP) are 0.42986500, 0.28847656, 0.23543161, 0.219342495, 0.10637477, and 0.06615037, respectively. The results indicate that calibration accuracy, stability, and robustness are significantly improved with the optimization method based on the CLI-WPP, in comparison to the existing commonly used optimization algorithms.

Measurement and correction of TEM image distortion using arbitrary samples.

We have developed a method to quantitatively measure image distortion, one of the five Seidel aberrations, in transmission electron microscopes without using a standard sample with a known structure. Displacements of small local segments in an image due to image distortion of the intermediate and projection lens system are first measured by comparing images taken before and after a given shift at the first image plane of the objective lens. Then, the sum of the second partial derivatives, or the Laplacian, of the displacement field is measured, and the radial and azimuthal distortion parameters are determined from the measured results. We confirmed using numerically distorted images that the proposed method can measure the image distortion within a relative error ratio of 0.04 for a wide range of distortion amount from 0.1% to 5.0%. The distortion measurement and correction were confirmed to work correctly by using the experimental images, and the iterative measurement and correction procedure could reduce the distortion to a level where the average image displacement was < 0.05 pixels.

Improved high-resolution EBSD analyses by correcting radial distortion of electron diffraction patterns

• An integrated DIC method is proposed to measure the radial optical distortion of electron diffraction cameras. • The method has a comparable accuracy with previous studies using chessboard samples. • Various high-resolution EBSD analyses benefit from the radial distortion corrections. Registering experimental and simulated electron diffraction patterns is increasingly used for advanced electron backscatter diffraction indexation (EBSD) analysis, yet the accuracy of registration is limited by several effects not accounted for in pattern simulation, such as the Kikuchi band (K-band) asymmetry, gray level reversal and (mainly radial) optical distortion. Radial distortion parameters have previously been measured with chessboard-type standard samples. Simulated patterns have been adopted to demonstrate the necessity of optical distortion removal in EBSD analyses. However there still lacks an efficient and precise radial distortion assessment and correction method. Here a simple radial distortion model, including barrel and pincushion distortions, is proposed to rectify the diffraction patterns during EBSD analyses. The correlation between experimental pattern and the simulated master pattern permits to index the diffraction pattern and assess the radial distortion simultaneously. The method is applied to three high-definition experimental electron diffraction datasets acquired with different cameras. The radial distortion parameter is identified with a relative uncertainty below 4%. The consideration of radial distortion improves the correlation between experimental and simulated patterns. Gray level profiles of the K-bands are analyzed to verify the correctness of image registration. The current method provides a fast, economic yet precise correction of the radial distortion for advanced EBSD analyses.

Learning-Based Distortion Correction and Feature Detection for High Precision and Robust Camera Calibration

Camera calibration is a crucial technique which significantly influences the performance of many robotic systems. Robustness and high precision have always been the pursuit of diverse calibration methods. State-of-the-art calibration techniques, however, still suffer from inexact corner detection, radial lens distortion and unstable parameter estimation. Therefore, in this paper, we improve the precision and robustness of calibration by widening these bottlenecks. In particular, effective distortion correction is performed by a learning-based method. Then, accurate sub-pixel feature location is achieved by the combination of robust learning detection, exact refinement and complete post-processing. To obtain stable parameter estimation, an image-level RANSAC-based calibration procedure is proposed. Ultimately, we assemble these methods into a novel and practical calibration framework. Compared with state-of-art methods, experiment results on both real and synthetic datasets under noise, bad lighting and distortion manifest the better robustness and higher precision of the proposed framework.

An In-Orbit Stereo Navigation Camera Self-Calibration Method for Planetary Rovers with Multiple Constraints

In order to complete the high-precision calibration of the planetary rover navigation camera using limited initial data in-orbit, we proposed a joint adjustment model with additional multiple constraints. Specifically, a base model was first established based on the bundle adjustment model, second-order radial and tangential distortion parameters. Then, combining the constraints of collinearity, coplanarity, known distance and relative pose invariance, a joint adjustment model was constructed to realize the in orbit self-calibration of the navigation camera. Given the problem of directionality in line extraction of the solar panel due to large differences in the gradient amplitude, an adaptive brightness-weighted line extraction method was proposed. Lastly, the Levenberg-Marquardt algorithm for nonlinear least squares was used to obtain the optimal results. To verify the proposed method, field experiments and in-orbit experiments were carried out. The results suggested that the proposed method was more accurate than the self-calibration bundle adjustment method, CAHVOR method (a camera model used in machine vision for three-dimensional measurements), and vanishing points method. The average error for the flag of China and the optical solar reflector was only 1 mm and 0.7 mm, respectively. In addition, the proposed method has been implemented in China’s deep space exploration missions.

Assessing Stability Performance of Non-Metric Camera’s Lens Distortion Model during UAV Flight Missions

The process and definition of camera calibration have change greatly over recent years. Aerial metric cameras calibration, for which laboratory and field calibration procedures were a separate process, was performed before and independent of any actual mapping data collection using precise calibration fixtures with an assumption that the camera parameters determined would remain valid for a significant period. In contrast, non-metric cameras are characterized by unstable intrinsic parameters over the times and they are vulnerable to the engine and other vibrations during flight data acquisitions. Moreover, there is no standard calibration procedures exist for these cameras. But, since non-metric camera self-calibration augments the concept of calibration as a part of the measurement process, it can determine the camera intrinsic parameters at the time of the data acquisition as long as highly-convergent geometry and the use of multiple exposures are employed. Therefore, this paper investigates variations of the lens distortion components with object distance within the photographic field by using the self-calibration method. The use of redundant flight paths and tilted camera is also incorporated to ascertain the stability of the principal distance and the principal points during the flight mission. During the experiments, a series of flight mission is conducted to photograph test field areas from over a relatively flat area to highly mountainous one. It is revealed that the radial, decentering, and affinity distortion parameters are more stable than that of the principal distance and principal points against vibrations.

Unfocused plenoptic metric modeling and calibration.

For unfocused plenoptic imaging systems, metric calibration is generally mandatory to achieve high-quality imaging and metrology. In this paper, we present an explicit derivation of an unfocused plenoptic metric model associating a measured light field in the object space with a recorded light field in the image space to conform physically to the imaging properties of unfocused plenoptic cameras. In addition, the impact of unfocused plenoptic imaging distortion on depth computation was experimentally explored, revealing that radial distortion parameters contain depth-dependent common factors, which were then modeled as depth distortions. Consequently, a complete unfocused plenoptic metric model was established by combining the explicit metric model with the imaging distortion model. A three-step unfocused plenoptic metric calibration strategy, in which the Levenberg-Marquardt algorithm is used for parameter optimization, is correspondingly proposed to determine 12 internal parameters for each microlens unit. Based on the proposed modeling and calibration, the depth measurement precision can be increased to 0.25 mm in a depth range of 300 mm, ensuring the potential applicability of consumer unfocused plenoptic cameras in high-accuracy three-dimensional measurement.

A STUDY ON THE VARIATIONS OF INNER ORIENTATION PARAMETERS OF A HYPERSPECTRAL FRAME CAMERA

Abstract. New low-cost hyperspectral frame sensors have created a new perspective for remote sensing applications. In this work, we investigate some issues related to the geometric calibration of a hyperspectral frame camera based of FPI (Fabry-Pérot Interferometer), the Rikola camera. The approach proposed in paper is to study the changes in internal optical path caused by the FPI and by the splitting prism. The aim is to model the changes in the IOPs with an analytical function and also to estimate the misalignments between sensors. Several experiments were performed. The changes in position of a specific point were analasyzed to confirm that the bundle of rays is deviated. A self-calibrating bundle adjustment was performed and the Interior Orientation Parameters (IOP) of each band were estimated. The IOPs were analysed and it was concluded that a single set of symmetrical radial distortion parameters can be used for all band. Also, the estimated parameters for each image band were analysed as a function of the air gap of the FPI interferometer. It was noticed some correlation between the focal length and the air gap, and an air-gap dependent model was estimated. Thus, instead of considering an IOP set for each band or for each sensor, a single set of distortion parameters and another set of parameters that is “air-gap dependent”, was assessed. Another important issue was the determination of the misalignment angles between the two sensors, which can explain some differences in the recovered camera trajectory when performing the bundle adjustment.

Improved Cross-Ratio Invariant-Based Intrinsic Calibration of A Hyperspectral Line-Scan Camera.

Hyperspectral line-scan cameras are increasingly being deployed on mobile platforms operating in unstructured environments. To generate geometrically accurate hyperspectral composites, the intrinsic parameters of these cameras must be resolved. This article describes a method for determining the intrinsic parameters of a hyperspectral line-scan camera. The proposed method is based on a cross-ratio invariant calibration routine and is able to estimate the focal length, principal point, and radial distortion parameters in a hyperspectral line-scan camera. Compared to previous methods that use similar calibration targets, our approach extends the camera model to include radial distortion. It is able to utilize calibration data recorded from multiple camera view angles by optimizing the re-projection error of all calibration data jointly. The proposed method also includes an additional signal processing step that automatically detects calibration points in hyperspectral imagery of the calibration target. These contributions result in accurate estimates of the intrinsic parameters with minimal supervision. The proposed method is validated through comprehensive simulation and demonstrated on real hyperspectral line-scans.

Planar self-calibration for stereo cameras with radial distortion.

In this paper, we present a robust technique of stereo calibration using homography constraints. Our method is novel as stereo calibration is performed by solving a polynomial equation system including two radial distortion parameters, using a minimal number of five image point correspondences. This enables us to calibrate from only a pair of stereo images of a planar scene, and to provide the exact algebraic solution to the stereo calibration problem. The minimal case solution is useful to reduce the computation time and increase the calibration robustness when using random sample consensus (RANSAC) from the correspondences of the stereo image pair. Further, a non-linear parameter optimization for the intrinsic and extrinsic parameters of stereo cameras is performed using the inliers, which are determined after RANSAC. In addition, our method can achieve more robust calibration results with multiple stereo image pairs by performing joint optimization. In contrast to the previous stereo calibration methods, our method works without requiring any special hardware and has no problems with one stereo image pair, even corrupted by severe radial distortions. Finally, by evaluating our method on both synthetic and real scene data, we demonstrate that our method is both efficient and accurate for stereo calibration.

Experimental Study of Suction Flow Control Effectiveness in a Serpentine Intake

The intakes of modern aircraft are subjected to ever-increasing demands in their performance. Particularly, they are expected to carry out diffusion with the highest isentropic efficiency while subjected to aggressive geometry requirements arising from stealth considerations. To avoid a penalty in engine performance, the flow through intake needs to be controlled using various methods of flow control. In this study, a serpentine intake is studied experimentally and its performance compared with and without boundary layer suction. The performance parameters used are nondimensional total pressure loss coefficient and standard total pressure distortion descriptors. The effect is observed on surface pressure distributions, and inferences are made regarding separation location and extent. A detailed measurement at the exit plane shows flow structures that draw attention to secondary flows within the duct. Suction is applied at three different locations, spanning different number of ports along each location, comprising of ten unique configurations. The mass flow rate of suction employed ranges from 1.1% to 6.7% of mass flow rate at the inlet of the intake. The effect is seen on exit total pressure recovery as well as circumferential and radial distortion parameters. This is examined in the context of the location of the suction ports and amount of suction mass flow, by the deviation in surface pressure distributions, as well as the separation characteristics from the baseline case. The results show that applying suction far upstream of the separation point together with a modest amount of suction downstream results in the best performance.

Cost‐effective non‐metric photogrammetry from consumer‐grade sUAS: implications for direct georeferencing of structure from motion photogrammetry

AbstractThe declining costs of small Unmanned Aerial Systems (sUAS), in combination with Structure‐from‐Motion (SfM) photogrammetry have triggered renewed interest in image‐based topography reconstruction. However, the potential uptake of sUAS‐based topography is limited by the need for ground control acquired with expensive survey equipment. Direct georeferencing (DG) is a workflow that obviates ground control and uses only the camera positions to georeference the SfM results. However, the absence of ground control poses significant challenges in terms of the data quality of the final geospatial outputs. Notably, it is generally accepted that ground control is required to georeference, refine the camera calibration parameters, and remove any artefacts of optical distortion from the topographic model. Here, we present an examination of DG carried out with low‐cost consumer‐grade sUAS. We begin with a study of surface deformations resulting from systematic perturbations of the radial lens distortion parameters. We then test a number of flight patterns and develop a novel error quantification method to assess the outcomes. Our perturbation analysis shows that there exists families of predictable equifinal solutions of K1‐K2 which minimize doming in the output model. The equifinal solutions can be expressed as K2 = f (K1) and they have been observed for both the DJI Inspire 1 and Phantom 3 sUAS platforms. This equifinality relationship can be used as an external reliability check of the self‐calibration and allow a DG workflow to produce topography exempt of non‐affine deformations and with random errors of 0.1% of the flying height, linear offsets below 10 m and off‐vertical tilts below 1°. Whilst not yet of survey‐grade quality, these results demonstrate that low‐cost sUAS are capable of producing reliable topography products without recourse to expensive survey equipment and we argue that direct georeferencing and low‐cost sUAS could transform survey practices in both academic and commercial disciplines. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Blind radial distortion compensation in a single image using fast Hough transform

In this paper, we present an automatic technique for compensation of radial distortion, which is characteristic of wide-angle lenses. The proposed method estimates distortion parameters using a single image from unknown source. No calibration objects are required, but it is assumed that the original scene contains straight lines. The method is based on finding such radial distortion parameters, that maximize total length of linear segments. We employ a fast Hough transform to estimate the overall curvature of lines without selecting any. The proposed algorithm is tested on real images obtained using calibrated camera lenses with different radial distortion. For the formal evaluation of the algorithm, we propose a quality measure for geometric distortion compensation, which works correctly even in the case when the problem of determining the coefficients is ill-conditioned.

Calibration of multiple fish‐eye cameras using a wand

Fish‐eye cameras are becoming increasingly popular in computer vision, but their use for three‐dimensional measurement is limited partly because of the lack of an accurate, efficient and user‐friendly calibration procedure. For such a purpose, the authors propose a method to calibrate the intrinsic and extrinsic parameters (including radial distortion parameters) of two/multiple fish‐eye cameras simultaneously by using a wand under general motions. Thanks to the generic camera model used, the proposed calibration method is also suitable for two/multiple conventional cameras and mixed cameras (e.g. two conventional cameras and a fish‐eye camera). Simulation and real experiments demonstrate the effectiveness of the proposed method. Moreover, the authors develop the camera calibration toolbox, which is available online.

Invertibility and Estimation of Two-Parameter Polynomial and Division Lens Distortion Models

In this paper, we study lens distortion for still images considering two well-known distortion models: the two-parameter polynomial model and the two-parameter division model. We study the invertibility of these models, and we mathematically characterize the conditions for the distortion parameters under which the distortion model defines a one-to-one transformation. This ensures that the inverse transformation is well defined and the distortion-free image can be properly computed, which provides robustness to the distortion models. A new automatic method to correct the radial distortion is proposed, and a comparative analysis for this method is extensively performed using the polynomial and the division models. With the aim of obtaining an accurate estimation of the model, we propose an optimization scheme which iteratively improves the parameters to achieve a better matching between the distorted lines and the edge points. The proposed method estimates two-parameter radial distortion models by detecting the longest distorted lines within the image. This is done by applying the Hough transform extended with a radial distortion parameter. Next, a two-parameter model is estimated using an iterative nonlinear optimization scheme. This scheme aims at minimizing the distance from the edge points to their associated lines by adjusting the two distortion parameters as well as the coordinates of the center of distortion. We present some experiments on real images with significant distortion to show the ability of the proposed approach to correct the radial distortion. A visual and quantitative comparison between both automatic two-parameter model estimations indicates that the division model is more efficient for those images showing strong distortion.

A Linear Camera Calibration Applying in Servo Mechanical Arm System with One Camera

An easy method for camera intrinsic parameters and one order radial distortion parameter is studied by the mathematical model of camera on the basis of projective theory. It is not necessary to translate or rotate camera in this method, but it only uses several specially points to derive the equations and get the parameters. The results show that this method could quickly and conveniently calibrate camera intrinsic parameters and one-degree radial distortion parameter with good stability and precision, which can be used in servo mechanical arm system.

Zoom Dependent Lens Distortion Mathematical Models

We propose new mathematical models to study the variation of lens distortion models when modifying zoom setting in the case of zoom lenses. The new models are based on a polynomial approximation to account for the variation of the radial distortion parameters through the range of zoom lens settings and, on the minimization of a global error energy measuring the distance between sequences of distorted aligned points and straight lines after lens distortion correction. To validate the performance of the method we present experimental results on calibration pattern images and on sport event scenarios using broadcast video cameras. We obtain, experimentally, that using just a second order polynomial approximation of lens distortion parameter zoom variation, the quality of lens distortion correction is as good as the one obtained individually frame by frame using independent lens distortion model for each frame.

Automatic radial distortion correction in zoom lens video camera

We present a novel method for automatically correcting the radial lens distortion in a zoom lens video camera system. We first define the zoom lens distortion model using an inherent characteristic of the zoom lens. Next, we sample some video frames with different focal lengths and estimate their radial distortion parameters and focal lengths. We then optimize the zoom lens distortion model with preestimated parameter pairs using the least-squares method. For more robust optimization, we divide the sample images into two groups according to distortion types (i.e., barrel and pincushion) and then separately optimize the zoom lens distortion models with respect to divided groups. Our results show that the zoom lens distortion model can accurately represent the radial distortion of a zoom lens.

Fast and robust numerical solutions to minimal problems for cameras with radial distortion

A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gröbner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate that these two problems can be efficiently solved in floating point arithmetic in simulated and real experiments. For comparison we have also invented a new non-minimal algorithm for estimating fundamental matrix and two different radial distortion parameters for two uncalibrated views and twelve image point correspondences based on a generalized eigenvalue problem.

Pan–tilt–zoom camera calibration and high-resolution mosaic generation

In this paper, we discuss the problem of estimating parameters of a calibration model for active pan–tilt–zoom cameras. The variation of the intrinsic parameters of each camera over its full range of zoom settings is estimated through a two step procedure. We first determine the intrinsic parameters at the camera’s lowest zoom setting very accurately by capturing an extended panorama. The camera intrinsics and radial distortion parameters are then determined at discrete steps in a monotonically increasing zoom sequence that spans the full zoom range of the camera. Our model incorporates the variation of radial distortion with camera zoom. Both calibration phases are fully automatic and do not assume any knowledge of the scene structure. High-resolution calibrated panoramic mosaics are also computed during this process. These fully calibrated panoramas are represented as multi-resolution pyramids of cube-maps. We describe a hierarchical approach for building multiple levels of detail in panoramas, by aligning hundreds of images captured within a 1–12× zoom range. Results are shown from datasets captured from two types of pan–tilt–zoom cameras placed in an uncontrolled outdoor environment. The estimated camera intrinsics model along with the cube-maps provides a calibration reference for images captured on the fly by the active pan–tilt–zoom camera under operation making our approach promising for active camera network calibration.