Common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial distortion is to find a radial distortion model that allows easy undistortion as well as satisfactory accuracy. This paper presents a new radial distortion model with an easy analytical undistortion formula, which also belongs to the polynomial approximation category. Experimental results are presented to show that with this radial distortion model, satisfactory accuracy is achieved.
The commonly used radial distortion model for camera calibration is in fact an assumption or a restriction. In practice, camera distortion could happen in a general geometrical manner that is not limited to the radial sense. This paper proposes a simplified geometrical distortion modeling method by using two different radial distortion functions in the two image axes. A family of simplified geometric distortion models is proposed, which are either simple polynomials or the rational functions of polynomials. Analytical geometric undistortion is possible using two of the distortion functions dis…
Camera calibration plays a critical role in various computer vision tasks such as autonomous driving or augmented reality. Widely used camera calibration tools utilize plane pattern based methodology, such as using a chessboard or AprilTag board, user's calibration expertise level significantly affects calibration accuracy and consistency when without clear instruction. Furthermore, calibration is a recurring task that has to be performed each time the camera is changed or moved. It's also a great burden to calibrate huge amounts of cameras such as Driver Monitoring System (DMS) cameras in a p…
This paper presents a blind detection and compensation technique for camera lens geometric distortions. The lens distortion introduces higher-order correlations in the frequency domain and in turn it can be detected using higher-order spectral analysis tools without assuming any specific calibration target. The existing blind lens distortion removal method only considered a single-coefficient radial distortion model. In this paper, two coefficients are considered to model approximately the geometric distortion. All the models considered have analytical closed-form inverse formulae.
School of Computer Science and Engineering, Central South University（中南大学计算机科学与工程学院）
In many scenarios where cameras are applied, such as robot positioning and unmanned driving, camera calibration is one of the most important pre-work. The interactive calibration method based on the plane board is becoming popular in camera calibration field due to its repeatability and operation advantages. However, the existing methods select suggestions from a fixed dataset of pre-defined poses based on subjective experience, which leads to a certain degree of one-sidedness. Moreover, they does not give users clear instructions on how to place the board in the specified pose.
The task of camera calibration is to estimate the intrinsic and extrinsic parameters of a camera model. Though there are some restricted techniques to infer the 3-D information about the scene from uncalibrated cameras, effective camera calibration procedures will open up the possibility of using a wide range of existing algorithms for 3-D reconstruction and recognition. The applications of camera calibration include vision-based metrology, robust visual platooning and visual docking of mobile robots where the depth information is important.
Centre for Mathematical Sciences（数学科学中心）；Lund University（隆德大学）
In this paper we present a fast minimal solver for absolute camera pose estimation from four known points that lie in a plane. We assume a perspective camera model with unknown focal length and unknown radial distortion. The radial distortion is modelled using the division model with one parameter. We show that the solutions to this problem can be found from a univariate six-degree polynomial. This results in a very fast and numerically stable solver.
Robert Bosch GmbH（罗伯特·博世有限公司）；Karlsruher Institute of Technology (KIT)（卡尔斯鲁厄理工学院（KIT））
Accurate camera calibration is a precondition for many computer vision applications. Calibration errors, such as wrong model assumptions or imprecise parameter estimation, can deteriorate a system's overall performance, making the reliable detection and quantification of these errors critical. In this work, we introduce an evaluation scheme to capture the fundamental error sources in camera calibration: systematic errors (biases) and uncertainty (variance). The proposed bias detection method uncovers smallest systematic errors and thereby reveals imperfections of the calibration setup and prov…
Fish-eye cameras are becoming increasingly popular in computer vision, but their use for 3D measurement is limited partly due to the lack of an accurate, efficient and user-friendly calibration procedure. For such a purpose, we 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 camera…
Most algorithms in 3D computer vision rely on the pinhole camera model because of its simplicity, whereas virtually all imaging devices introduce certain amount of nonlinear distortion, where the radial distortion is the most severe part. Common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial distortion is to find a radial distortion model that allows easy undistortion as well as satisfactory accuracy. This paper …
Although recent learning-based calibration methods can predict extrinsic and intrinsic camera parameters from a single image, the accuracy of these methods is degraded in fisheye images. This degradation is caused by mismatching between the actual projection and expected projection. To address this problem, we propose a generic camera model that has the potential to address various types of distortion. Our generic camera model is utilized for learning-based methods through a closed-form numerical calculation of the camera projection. Simultaneously to recover rotation and fisheye distortion, w…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial distortion is to find a radial distortion model that allows easy undistortion as well as satisfactory accuracy. This paper presents a new piecewise radial distortion model with easy analytical undistortion formula. The motivation for seeking a piecewise radial distortion model is that, when a camera is resulted in a low quality during manufacturing, the no…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Institute for Infocomm Research（信息通信研究院）；National University of Singapore（新加坡国立大学）
Depth sensing devices have created various new applications in scientific and commercial research with the advent of Microsoft Kinect and PMD (Photon Mixing Device) cameras. Most of these applications require the depth cameras to be pre-calibrated. However, traditional calibration methods using a checkerboard do not work very well for depth cameras due to the low image resolution. In this paper, we propose a depth calibration scheme which excels in estimating camera calibration parameters when only a handful of corners and calibration images are available. We exploit the noise properties of PM…
Faculty of Electrical Engineering, Czech Technical University in Prague（捷克理工大学电气工程学院）；ETH Zurich（苏黎世联邦理工学院）；National Institute of Informatics（国立信息学研究所）；Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague（捷克理工大学捷克信息学、机器人与控制论研究所）
The internal geometry of most modern consumer cameras is not adequately described by the perspective projection. Almost all cameras exhibit some radial lens distortion and are equipped with an electronic rolling shutter that induces distortions when the camera moves during the image capture. When focal length has not been calibrated offline, the parameters that describe the radial and rolling shutter distortions are usually unknown. While for global shutter cameras, minimal solvers for the absolute camera pose and unknown focal length and radial distortion are available, solvers for the rollin…
We propose an easy-to-use non-overlapping camera calibration method. First, successive images are fed to a PoseNet-based network to obtain ego-motion of cameras between frames. Next, the pose between cameras are estimated. Instead of using a batch method, we propose an on-line method of the inter-camera pose estimation. Furthermore, we implement the entire procedure on a computation graph. Experiments with simulations and the KITTI dataset show the proposed method to be effective in simulation.
National Yang Ming Chiao Tung University（国立阳明交通大学）
Preparing appropriate images for camera calibration is crucial to obtain accurate results. In this paper, new suggestions for preparing such data to alleviate the adverse effect of radial distortion for a calibration procedure using principal lines are developed through the investigations of: (i) identifying directions of checkerboard movements in an image which will result in maximum (and minimum) influence on the calibration results, and (ii) inspecting symmetry and monotonicity of such effect in (i) using the above principal lines. Accordingly, it is suggested that the estimation of princip…
Most current single image camera calibration methods rely on specific image features or user input, and cannot be applied to natural images captured in uncontrolled settings. We propose directly inferring camera calibration parameters from a single image using a deep convolutional neural network. This network is trained using automatically generated samples from a large-scale panorama dataset, and considerably outperforms other methods, including recent deep learning-based approaches, in terms of standard L2 error. However, we argue that in many cases it is more important to consider how human…
The choice of poses for camera calibration with planar patterns is only rarely considered - yet the calibration precision heavily depends on it. This work presents a pose selection method that finds a compact and robust set of calibration poses and is suitable for interactive calibration. Consequently, singular poses that would lead to an unreliable solution are avoided explicitly, while poses reducing the uncertainty of the calibration are favoured. For this, we use uncertainty propagation. Our method takes advantage of a self-identifying calibration pattern to track the camera pose in real-t…
The light field camera is useful for computer graphics and vision applications. Calibration is an essential step for these applications. After calibration, we can rectify the captured image by using the calibrated camera parameters. However, the large camera array calibration method, which assumes that all cameras are on the same plane, ignores the orientation and intrinsic parameters. The multi-camera calibration technique usually assumes that the working volume and viewpoints are fixed. In this paper, we describe a calibration algorithm suitable for a mobile camera array based light field ac…
Existing camera-projector calibration methods typically warp feature points from a camera image to a projector image using estimated homographies, and often suffer from errors in camera parameters and noise due to imperfect planarity of the calibration target. In this paper we propose a simple yet robust solution that explicitly deals with these challenges. Following the structured light (SL) camera-project calibration framework, a carefully designed correspondence algorithm is built on top of the De Bruijn patterns. Such correspondence is then used for initial camera-projector calibration. Th…
ETH Zurich（苏黎世联邦理工学院）；INRIA Grenoble – Rhône-Alpes（法国国立信息学与自动化研究院格勒诺布尔-罗讷-阿尔卑斯分院）
It is well known that the accuracy of a calibration depends strongly on the choice of camera poses from which images of a calibration object are acquired. We present a system -- Calibration Wizard -- that interactively guides a user towards taking optimal calibration images. For each new image to be taken, the system computes, from all previously acquired images, the pose that leads to the globally maximum reduction of expected uncertainty on intrinsic parameters and then guides the user towards that pose. We also show how to incorporate uncertainty in corner point position in a novel principl…
In view of contemporary panoramic camera-laser scanner system, the traditional calibration method is not suitable for panoramic cameras whose imaging model is extremely nonlinear. The method based on statistical optimization has the disadvantage that the requirement of the number of laser scanner's channels is relatively high. Calibration equipments with extreme accuracy for panoramic camera-laser scanner system are costly. Facing all these in the calibration of panoramic camera-laser scanner system, a method based on supervised learning is proposed. Firstly, corresponding feature points of pa…
Single image camera calibration is the task of estimating the camera parameters from a single input image, such as the vanishing points, focal length, and horizon line. In this work, we propose Camera calibration TRansformer with Line-Classification (CTRL-C), an end-to-end neural network-based approach to single image camera calibration, which directly estimates the camera parameters from an image and a set of line segments. Our network adopts the transformer architecture to capture the global structure of an image with multi-modal inputs in an end-to-end manner. We also propose an auxiliary t…
Technical University of Denmark（丹麦技术大学）；University of Southern Denmark（南丹麦大学）
The most prevalent routine for camera calibration is based on the detection of well-defined feature points on a purpose-made calibration artifact. These could be checkerboard saddle points, circles, rings or triangles, often printed on a planar structure. The feature points are first detected and then used in a nonlinear optimization to estimate the internal camera parameters.We propose a new method for camera calibration using the principle of inverse rendering. Instead of relying solely on detected feature points, we use an estimate of the internal parameters and the pose of the calibration …
ETH Zürich（苏黎世联邦理工学院）；Microsoft Mixed Reality & AI Zurich Lab（微软混合现实与人工智能苏黎世实验室）；Chalmers University of Technology（查尔姆斯理工大学）
Camera calibration is an essential first step in setting up 3D Computer Vision systems. Commonly used parametric camera models are limited to a few degrees of freedom and thus often do not optimally fit to complex real lens distortion. In contrast, generic camera models allow for very accurate calibration due to their flexibility. Despite this, they have seen little use in practice. In this paper, we argue that this should change. We propose a calibration pipeline for generic models that is fully automated, easy to use, and can act as a drop-in replacement for parametric calibration, with a fo…
A Note on Geometric Calibration of Multiple Cameras and Projectors
University of Zagreb, Faculty of Electrical Engineering and Computing（萨格勒布大学电气工程与计算学院）；University of Toulouse, Toulouse INP – IRIT（图卢兹大学，图卢兹国立理工学院 – 图卢兹计算机研究所）
The plenoptic camera can capture both angular and spatial information of the rays, enabling 3D reconstruction by single exposure. The geometry of the recovered scene structure is affected by the calibration of the plenoptic camera significantly. In this paper, we propose a novel unconstrained two-parallel-plane (TPP) model with 7 parameters to describe a 4D light field. By reconstructing scene points from ray-ray association, a 3D projective transformation is deduced to establish the relationship between the scene structure and the TPP parameters. Based on the transformation, we simplify the f…
Multi-camera calibration with pattern rigs, including for non-overlapping cameras: CALICO
USDA-ARS-AFRS（美国农业部农业研究服务局农业和食品研究处）；University of Florida（佛罗里达大学）；University of California-Davis（加州大学戴维斯分校）；Embrapa Digital Agriculture（巴西农业研究公司数字农业研究所）
In this paper, we focus on fully automatic traffic surveillance camera calibration, which we use for speed measurement of passing vehicles. We improve over a recent state-of-the-art camera calibration method for traffic surveillance based on two detected vanishing points. More importantly, we propose a novel automatic scene scale inference method. The method is based on matching bounding boxes of rendered 3D models of vehicles with detected bounding boxes in the image. The proposed method can be used from arbitrary viewpoints, since it has no constraints on camera placement. We evaluate our me…
Deep Learning for Camera Calibration and Beyond: A Survey
Institute of Information Science, Beijing Jiaotong University（北京交通大学信息科学研究所）；Tampere University（坦佩雷大学）；School of Computer Science, Faculty of Engineering, The University of Sydney（悉尼大学工程学院计算机科学学院）
Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）
Metric auto calibration of a camera network from multiple views has been reported by several authors. Resulting 3D reconstruction recovers shape faithfully, but not scale. However, preservation of scale becomes critical in applications, such as multi-party telepresence, where multiple 3D scenes need to be fused into a single coordinate system. In this context, we propose a camera network configuration that includes a stereo pair with known baseline separation, and analytically demonstrate Euclidean auto calibration of such network under mild conditions. Further, we experimentally validate our …
University of Michigan（密歇根大学）；Adobe Research（奥多比研究院）
Geometric camera calibration is often required for applications that understand the perspective of the image. We propose perspective fields as a representation that models the local perspective properties of an image. Perspective Fields contain per-pixel information about the camera view, parameterized as an up vector and a latitude value. This representation has a number of advantages as it makes minimal assumptions about the camera model and is invariant or equivariant to common image editing operations like cropping, warping, and rotation. It is also more interpretable and aligned with huma…
Maria Curie Sklodowska University（玛丽亚·居里-斯克沃多夫斯卡大学）；Warsaw University of Technology（华沙理工大学）
This paper presents a method for extrinsic camera calibration (estimation of camera rotation and translation matrices) from a sequence of images. It is assumed camera intrinsic matrix and distortion coefficients are known and fixed during the entire sequence. %This allows to decrease a number of pairs of corresponding keypoints between images needed to estimate epipolar geometry compared to uncalibrated case. Performance of the presented method is evaluated on a number of multi-view stereo test datasets. Presented algorithm can be used as a first stage in a dense stereo reconstruction system.
Monocular camera sensors are vital to intelligent vehicle operation and automated driving assistance and are also heavily employed in traffic control infrastructure. Calibrating the monocular camera, though, is time-consuming and often requires significant manual intervention. In this work, we present an extrinsic camera calibration approach that automatizes the parameter estimation by utilizing semantic segmentation information from images and point clouds. Our approach relies on a coarse initial measurement of the camera pose and builds on lidar sensors mounted on a vehicle with high-precisi…
A challenge in image based metrology and forensics is intrinsic camera calibration when the used camera is unavailable. The unavailability raises two questions. The first question is how to find the projection model that describes the camera, and the second is to detect incorrect models. In this work, we use off-the-shelf extended PnP-methods to find the model from 2D-3D correspondences, and propose a method for model validation. The most common strategy for evaluating a projection model is comparing different models' residual variances - however, this naive strategy cannot distinguish whether…
The College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China（航空科学与工程学院，国防科技大学，长沙410073，中国）；The GNSS Research Center, Wuhan University, Wuhan 430000, China（导航定位研究室，武汉大学，武汉430000，中国）
Existing 3D human pose estimation algorithms trained on distortion-free datasets suffer performance drop when applied to new scenarios with a specific camera distortion. In this paper, we propose a simple yet effective model for 3D human pose estimation in video that can quickly adapt to any distortion environment by utilizing MAML, a representative optimization-based meta-learning algorithm. We consider a sequence of 2D keypoints in a particular distortion as a single task of MAML. However, due to the absence of a large-scale dataset in a distorted environment, we propose an efficient method …
Lahore University of Management Sciences（拉合尔管理科学大学）
Camera calibration is a necessity in various tasks including 3D reconstruction, hand-eye coordination for a robotic interaction, autonomous driving, etc. In this work we propose a novel method to predict extrinsic (baseline, pitch, and translation), intrinsic (focal length and principal point offset) parameters using an image pair. Unlike existing methods, instead of designing an end-to-end solution, we proposed a new representation that incorporates camera model equations as a neural network in multi-task learning framework. We estimate the desired parameters via novel camera projection loss …
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；FZI Research Center for Information Technology（FZI信息技术研究中心）
In this paper, we present TEScalib, a novel extrinsic self-calibration approach of LiDAR and stereo camera using the geometric and photometric information of surrounding environments without any calibration targets for automated driving vehicles. Since LiDAR and stereo camera are widely used for sensor data fusion on automated driving vehicles, their extrinsic calibration is highly important. However, most of the LiDAR and stereo camera calibration approaches are mainly target-based and therefore time consuming. Even the newly developed targetless approaches in last years are either inaccurate…
German Research Center for Artificial Intelligence（德国人工智能研究中心）；University of Kaiserslautern（凯泽斯劳滕大学）
The ability to create an accurate three-dimensional reconstruction of a captured scene draws attention to the principles of light fields. This paper presents an approach for light field camera calibration and rectification, based on pairwise pattern-based parameters extraction. It is followed by a correspondence-based algorithm for camera parameters refinement from arbitrary scenes using the triangulation filter and nonlinear optimization. The effectiveness of our approach is validated on both real and synthetic data.
We address the problem of estimating the 3D pose of a network of cameras for large-environment wide-baseline scenarios, e.g., cameras for construction sites, sports stadiums, and public spaces. This task is challenging since detecting and matching the same 3D keypoint observed from two very different camera views is difficult, making standard structure-from-motion (SfM) pipelines inapplicable. In such circumstances, treating people in the scene as "keypoints" and associating them across different camera views can be an alternative method for obtaining correspondences. Based on this intuition, …
University of Minnesota（明尼苏达大学）；ENS Cachan（卡尚高等师范学校）；École des Ponts ParisTech（巴黎高科桥路学院）
This paper addresses the high precision measurement of the distortion of a digital camera from photographs. Traditionally, this distortion is measured from photographs of a flat pattern which contains aligned elements. Nevertheless, it is nearly impossible to fabricate a very flat pattern and to validate its flatness. This fact limits the attainable measurable precisions. In contrast, it is much easier to obtain physically very precise straight lines by tightly stretching good quality strings on a frame. Taking literally "plumb-line methods", we built a "calibration harp" instead of the classi…
