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 discussed in this paper and their performance can be improved by applying a piecewise fitting idea. Our experimental results show that the geometrical distortion models always perform better than their radial distortion counterparts. Furthermore, the proposed geometric modeling method is more appropriate for cameras whose distortion is not perfectly radially symmetric around the center of distortion.
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, satisfacto…
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…
We present a new mathematical formulation to estimate the intrinsic parameters of a camera in active or robotic platforms. We show that the focal lengths can be estimated using only one point correspondence that relates images taken before and after a degenerate rotation of the camera. The estimated focal lengths are then treated as known parameters to obtain a linear set of equations to calculate the principal point. Assuming that the principal point is close to the image center, the accuracy of the linear equations are increased by integrating the image center into the formulation. We extens…
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 Alberta（阿尔伯塔大学）；Department of Computing Science（计算机科学系）
We introduce new linear mathematical formulations to calculate the focal length of a camera in an active platform. Through mathematical derivations, we show that the focal lengths in each direction can be estimated using only one point correspondence that relates images taken before and after a degenerate rotation of the camera. The new formulations will be beneficial in robotic and dynamic surveillance environments when the camera needs to be calibrated while it freely moves and zooms. By establishing a correspondence between only two images taken after slightly panning and tilting the camera…
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…
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…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Oxford（牛津大学）
In this paper we present a simple and robust method for self-correction of camera distortion using single images of scenes which contain straight lines. Since the most common distortion can be modelled as radial distortion, we illustrate the method using the Harris radial distortion model, but the method is applicable to any distortion model. The method is based on transforming the edgels of the distorted image to a 1-D angular Hough space, and optimizing the distortion correction parameters which minimize the entropy of the corresponding normalized histogram. Properly corrected imagery will h…
Learning-Based Framework for Camera Calibration with Distortion Correction and High Precision Feature Detection
Institute of Medical Robotics, Shanghai Jiao Tong University（上海交通大学医疗机器人研究院）；School of Biomedical Engineering, Shanghai Jiao Tong University（上海交通大学生物医学工程学院）；Department of Automation, Shanghai Jiao Tong University（上海交通大学自动化系）
Nonlinear lens distortion rectification is a common first step in image processing applications where the assumption of a linear camera model is essential. For rectifying the lens distortion, forward distortion model needs to be known. However, many self-calibration methods estimate the inverse distortion model. In the literature, the inverse of the estimated model is approximated for image rectification, which introduces additional error to the system. We propose a novel distortion rectification method that uses the inverse distortion model directly. The method starts by mapping the distorted…
National University of Singapore（新加坡国立大学）；NEC Laboratories America, Inc.（NEC美国实验室公司）；University of California, San Diego（加利福尼亚大学圣迭戈分校）
Self-calibration of camera intrinsics and radial distortion has a long history of research in the computer vision community. However, it remains rare to see real applications of such techniques to modern Simultaneous Localization And Mapping (SLAM) systems, especially in driving scenarios. In this paper, we revisit the geometric approach to this problem, and provide a theoretical proof that explicitly shows the ambiguity between radial distortion and scene depth when two-view geometry is used to self-calibrate the radial distortion. In view of such geometric degeneracy, we propose a learning a…
We propose a generic event camera calibration framework using image reconstruction. Instead of relying on blinking LED patterns or external screens, we show that neural-network-based image reconstruction is well suited for the task of intrinsic and extrinsic calibration of event cameras. The advantage of our proposed approach is that we can use standard calibration patterns that do not rely on active illumination. Furthermore, our approach enables the possibility to perform extrinsic calibration between frame-based and event-based sensors without additional complexity. Both simulation and real…
In this paper we consider critical motion sequences (CMSs) of rolling-shutter (RS) SfM. Employing an RS camera model with linearized pure rotation, we show that the RS distortion can be approximately expressed by two internal parameters of an "imaginary" camera plus one-parameter nonlinear transformation similar to lens distortion. We then reformulate the problem as self-calibration of the imaginary camera, in which its skew and aspect ratio are unknown and varying in the image sequence. In the formulation, we derive a general representation of CMSs. We also show that our method can explain th…
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.
GDCNet: Calibrationless geometric distortion correction of echo planar imaging data using deep learning
Columbia University in the City of New York（纽约市哥伦比亚大学）；Icahn School of Medicine at Mount Sinai（西奈山伊坎医学院）；Columbia University Medical Center（哥伦比亚大学医学中心）；John Hopkins University（约翰斯·霍普金斯大学）
Centre for Mathematical Sciences Lund University（隆德大学数学科学中心）；Linköping University（林雪平大学）
In this paper we present a novel algorithm for onboard radial distortion correction for unmanned aerial vehicles (UAVs) equipped with an inertial measurement unit (IMU), that runs in real-time. This approach makes calibration procedures redundant, thus allowing for exchange of optics extemporaneously. By utilizing the IMU data, the cameras can be aligned with the gravity direction. This allows us to work with fewer degrees of freedom, and opens up for further intrinsic calibration. We propose a fast and robust minimal solver for simultaneously estimating the focal length, radial distortion pro…
The University of Tokyo（东京大学）；Tokyo Institute of Technology（东京工业大学）
We propose a spatial calibration method for wide Field-of-View (FoV) Near-Eye Displays (NEDs) with complex image distortions. Image distortions in NEDs can destroy the reality of the virtual object and cause sickness. To achieve distortion-free images in NEDs, it is necessary to establish a pixel-by-pixel correspondence between the viewpoint and the displayed image. Designing compact and wide-FoV NEDs requires complex optical designs. In such designs, the displayed images are subject to gaze-contingent, non-linear geometric distortions, which explicit geometric models can be difficult to repre…
Faculty of Mathematics and Informatics, Babeș-Bolyai University of Cluj-Napoca（巴比什-波雅依大学数学与信息学院）；Robert Bosch SRL（罗伯特·博世有限责任公司）
Most distortion correction methods focus on simple forms of distortion, such as radial or linear distortions. These works undistort images either based on measurements in the presence of a calibration grid, or use multiple views to find point correspondences and predict distortion parameters. When possible distortions are more complex, e.g. in the case of a camera being placed behind a refractive surface such as glass, the standard method is to use a calibration grid. Considering a high variety of distortions, it is nonviable to conduct these measurements. In this work, we present a single vie…
In this work, we propose a camera self-calibration algorithm for generic cameras with arbitrary non-linear distortions. We jointly learn the geometry of the scene and the accurate camera parameters without any calibration objects. Our camera model consists of a pinhole model, a fourth order radial distortion, and a generic noise model that can learn arbitrary non-linear camera distortions. While traditional self-calibration algorithms mostly rely on geometric constraints, we additionally incorporate photometric consistency. This requires learning the geometry of the scene, and we use Neural Ra…
Electronics and Telecommunications Research Institute (ETRI)（电子通信研究院（ETRI））
In this paper, we present a novel zero-shot camera calibration method that estimates camera parameters with no calibration image. It is common sense that we need at least one or more pattern images for camera calibration. However, the proposed method estimates camera parameters from the horizontal and vertical field of view information of the camera without any image acquisition. The proposed method is particularly useful for wide-angle or fisheye cameras that have large image distortion. Image distortion is modeled in the way fisheye lenses are designed and estimated based on the square pixel…
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.
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…
Compact and low-cost devices are needed for autonomous driving to image and measure distances to objects 360-degree around. We have been developing an omnidirectional stereo camera exploiting two hyperbolic mirrors and a single set of a lens and sensor, which makes this camera compact and cost efficient. We establish a new calibration method for this camera considering higher-order radial distortion, detailed tangential distortion, an image sensor tilt, and a lens-mirror offset. Our method reduces the calibration error by 6.0 and 4.3 times for the upper- and lower-view images, respectively. Th…
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 …
Image splicing is a common form of image forgery. Such alterations may leave no visual clues of tampering. In recent works camera characteristics consistency across the image has been used to establish the authenticity and integrity of digital images. Such constant camera characteristic properties are inherent from camera manufacturing processes and are unique. The majority of digital cameras are equipped with spherical lens and this introduces radial distortions on images. This aberration is often disturbed and fails to be consistent across the image, when an image is spliced. This paper desc…
National Chiao Tung University（国立交通大学）；University of California San Diego（加州大学圣迭戈分校）；Industrial Technology Research Institute（工业技术研究院）；University of Washington（华盛顿大学）
Camera calibration is a crucial prerequisite in many applications of computer vision. In this paper, a new, geometry-based camera calibration technique is proposed, which resolves two main issues associated with the widely used Zhang's method: (i) the lack of guidelines to avoid outliers in the computation and (ii) the assumption of fixed camera focal length. The proposed approach is based on the closed-form solution of principal lines (PLs), with their intersection being the principal point while each PL can concisely represent relative orientation/position (up to one degree of freedom for bo…
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…
In many computer vision domains, the input images must conform with the pinhole camera model, where straight lines in the real world are projected as straight lines in the image. Performing computer vision tasks on live sports broadcast footage imposes challenging requirements where the algorithms cannot rely on a specific calibration pattern must be able to cope with unknown and uncalibrated cameras, radial distortion originating from complex television lenses, few visual clues to compensate distortion by, and the necessity for real-time performance. We present a novel method for single-image…
Visvesvaraya National Institute of Technology（维什韦什瓦拉亚国家理工学院）；Polytechnique Montréal（蒙特利尔综合理工学院）
We propose a method for automatic calibration of a traffic surveillance camera with wide-angle lenses. Video footage of a few minutes is sufficient for the entire calibration process to take place. This method takes in the height of the camera from the ground plane as the only user input to overcome the scale ambiguity. The calibration is performed in two stages, 1. Intrinsic Calibration 2. Extrinsic Calibration. Intrinsic calibration is achieved by assuming an equidistant fisheye distortion and an ideal camera model. Extrinsic calibration is accomplished by estimating the two vanishing points…
Wide-angle cameras are uniquely positioned for mobile robots, by virtue of the rich information they provide in a small, light, and cost-effective form factor. An accurate calibration of the intrinsics and extrinsics is a critical pre-requisite for using the edge of a wide-angle lens for depth perception and odometry. Calibrating wide-angle lenses with current state-of-the-art techniques yields poor results due to extreme distortion at the edge, as most algorithms assume a lens with low to medium distortion closer to a pinhole projection. In this work we present our methodology for accurate wi…
Beyond Reprojection Error: Camera Calibration with 3D Targets
Fraunhofer Institute for Computer Graphics Research（弗劳恩霍夫计算机图形研究所）；Technical University of Applied Sciences Würzburg-Schweinfurt（维尔茨堡-施韦因富特应用技术大学）；Technical University Darmstadt（达姆施塔特工业大学）
Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera model alone can not be used and a distortion correction step is required. By directly modeling the geometry of the refractive media, we build the image generation process by tracing individual light rays from the camera to a target. Comparing the generated images to their distorted - observed - counterparts, we estimate the geometry parameters of the refracti…
This paper presents a novel calibration algorithm for Multi-Focus Plenoptic Cameras (MFPCs) using raw images only. The design of such cameras is usually complex and relies on precise placement of optic elements. Several calibration procedures have been proposed to retrieve the camera parameters but relying on simplified models, reconstructed images to extract features, or multiple calibrations when several types of micro-lens are used. Considering blur information, we propose a new Blur Aware Plenoptic (BAP) feature. It is first exploited in a pre-calibration step that retrieves initial camera…
Camera calibration methods usually consist of capturing images of known calibration patterns and using the detected correspondences to optimize the parameters of the assumed camera model. A meaningful evaluation of these methods relies on the availability of realistic synthetic data. In previous works concerned with conventional cameras the synthetic data was mainly created by rendering perfect images with a pinhole camera and subsequently adding distortions and aberrations to the renderings and correspondences according to the assumed camera model. This method can bias the evaluation since no…
Camera calibration for estimating the intrinsic parameters and lens distortion is a prerequisite for various monocular vision applications including feature tracking and video stabilization. This application paper proposes a model for estimating the parameters on the fly by fusing gyroscope and camera data, both readily available in modern day smartphones. The model is based on joint estimation of visual feature positions, camera parameters, and the camera pose, the movement of which is assumed to follow the movement predicted by the gyroscope. Our model assumes the camera movement to be free,…
Zhejiang University（浙江大学）；NED University of Engineering and Technology（NED工程技术大学）；Sungkyunkwan University（成均馆大学）；Chosun University（朝鲜大学）
A technique for object localization based on pose estimation and camera calibration is presented. The 3-dimensional (3D) coordinates are estimated by collecting multiple 2-dimensional (2D) images of the object and are utilized for the calibration of the camera. The calibration steps involving a number of parameter calculation including intrinsic and extrinsic parameters for the removal of lens distortion, computation of object's size and camera's position calculation are discussed. A transformation strategy to estimate the 3D pose using the 2D images is presented. The proposed method is implem…
This paper presents a novel calibration algorithm for plenoptic cameras, especially the multi-focus configuration, where several types of micro-lenses are used, using raw images only. Current calibration methods rely on simplified projection models, use features from reconstructed images, or require separated calibrations for each type of micro-lens. In the multi-focus configuration, the same part of a scene will demonstrate different amounts of blur according to the micro-lens focal length. Usually, only micro-images with the smallest amount of blur are used. In order to exploit all available…
ETH Zürich（苏黎世联邦理工学院）；Czech Technical University in Prague（布拉格捷克理工大学）；Microsoft Mixed Reality & AI Zürich 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）
Multi-camera systems are an important sensor platform for intelligent systems such as self-driving cars. Pattern-based calibration techniques can be used to calibrate the intrinsics of the cameras individually. However, extrinsic calibration of systems with little to no visual overlap between the cameras is a challenge. Given the camera intrinsics, infrastucture-based calibration techniques are able to estimate the extrinsics using 3D maps pre-built via SLAM or Structure-from-Motion. In this paper, we propose to fully calibrate a multi-camera system from scratch using an infrastructure-based a…
