Parameter-free radial distortion correction with center of distortion estimation

We propose a method of simultaneously calibrating the radial distortion function of a camera and the other internal calibration parameters. The method relies on the use of a planar (or, alternatively, nonplanar) calibration grid which is captured in several images. In this way, the determination of the radial distortion is an easy add-on to the popular calibration method proposed by Zhang [24]. The method is entirely noniterative and, hence, is extremely rapid and immune to the problem of local minima. Our method determines the radial distortion in a parameter-free way, not relying on any particular radial distortion model. This makes it applicable to a large range of cameras from narrow-angle to fish-eye lenses. The method also computes the center of radial distortion, which, we argue, is important in obtaining optimal results. Experiments show that this point may be significantly displaced from the center of the image or the principal point of the camera.     

Camera distortion self-calibration using the plumb-line constraint and minimal Hough entropy

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 have fewer curved lines, and therefore less spread in Hough space. Since the method does not rely on any image structure beyond the existence of edgels sharing some common orientations and does not use edge fitting, it is applicable to a wide variety of image types. For instance, it can be applied equally well to images of texture with weak but dominant orientations, or images with strong vanishing points. Finally, the method is performed on both synthetic and real data revealing that it is particularly robust to noise.     

基于参考像面法的CCD摄像机标定新技术

摄像机标定是计算机视觉检测中必不可少的步骤.在现有的摄像机参数标定算法中,纯线性算法标定速度快,但标定精度不是很高;相反如采用非线性搜索算法,标定精度高,但存在标定速度慢以及会出现不收敛现象.通过对现有线性标定算法的研究,提出一种既考虑摄像机的径向和切向畸变,又能实现全线性化求解的全新标定算法--参考像面法.经验证该方法标定速度快、精度较高、算法健壮,适用于大型视觉系统多摄像机的快速标定.     

Self-calibration of wireless cameras with restricted degrees of freedom

This paper presents an approach for the automatic calibration of low-cost cameras which are assumed to be restricted in their freedom of movement to either pan or tilt movements. Camera parameters, including focal length, principal point, lens distortion parameter and the angle and axis of rotation, can be recovered from a minimum set of two images of the camera, provided that the axis of rotation between the two images goes through the camera’s optical center and is parallel to either the vertical (panning) or horizontal (tilting) axis of the image. Previous methods for auto-calibration of cameras based on pure rotations fail to work in these two degenerate cases. In addition, our approach includes a modified RANdom SAmple Consensus (RANSAC) algorithm, as well as improved integration of the radial distortion coefficient in the computation of inter-image homographies. We show that these modifications are able to increase the overall efficiency, reliability and accuracy of the homography computation and calibration procedure using both synthetic and real image sequences.     

由灭点进行径向畸变的自动校正

目的镜头畸变影响着3维重建、几何量测等工作的质量。根据图像中的灭点几何约束条件,提出一种根据灭点进行弱径向畸变自动校正方法。方法为避免包含畸变中心参数的非线性模型优化结果的不稳定性,在求解径向畸变系数之后进一步对畸变中心进行优化。首先根据灭点几何约束条件建立关于灭点与径向畸变系数的非线性模型,使用Levenberg-Marquardt(LM)算法估计灭点坐标与径向畸变参数,然后根据质量评价准则对畸变中心和径向畸变系数进一步迭代优化;最后,通过真实图像对该方法的可行性进行分析验证。结果采用不同的数据对径向畸变进行了有效地校正,并采用校正后的数据进行了相机标定,标定结果相对于传统基于非量测校正方法有明显的提高。结论充分利用图像中的灭点属性,提出一种新的镜头径向畸变校正方法。实验结果表明,该方法能够有效地对径向畸变进行校正,并克服了传统基于非量测畸变校正方法的不稳定性。     

一种基于基本矩阵的相机畸变差自动校正方法

在计算机视觉的应用领域中,为了提高图像量测和3维重建的精度,必须对相机的畸变误差进行修正。为此提出了一种基于基本矩阵的相机径向畸变的自动校正方法,该方法不需要预先获得场景的结构信息和相机的内部参数,仅利用两张影像同名点集之间的内在几何关系,即可求取相机的径向畸变系数,进而可对这两幅图像的畸变误差进行自动校正。试验结果表明,该方法是一种有效的畸变图像校正算法,能够获得到满意的校正结果。     

Implicit and explicit camera calibration: theory and experiments

By implicit camera calibration, we mean the process of calibrating a camera without explicitly computing its physical parameters. Implicit calibration can be used for both three-dimensional (3-D) measurement and generation of image coordinates. In this paper, we present a new implicit model based on the generalized projective mappings between the image plane and two calibration planes. The back-projection and projection processes are modelled separately to ease the computation of distorted image coordinates from known world points. A set of constraints of perspectivity is derived to relate the transformation parameters of the two calibration planes. Under the assumption of the radial distortion model, we present a computationally efficient method for explicitly correcting the distortion of image coordinates in frame buffer without involving the computation of camera position and orientation. By combining with any linear calibration techniques, this method makes explicit the camera physical parameters. Extensive experimental comparison of our methods with the classic photogrammetric method and Tsai's (1986) method in the aspects of 3-D measurement (both absolute and relative errors), the prediction of image coordinates, and the effect of the number of calibration points, is made using real images from 15 different depth values     

Multiple Light Source Estimation in a Single Image

Many high‐level image processing tasks require an estimate of the positions, directions and relative intensities of the light sources that illuminated the depicted scene. In image‐based rendering, augmented reality and computer vision, such tasks include matching image contents based on illumination, inserting rendered synthetic objects into a natural image, intrinsic images, shape from shading and image relighting. Yet, accurate and robust illumination estimation, particularly from a single image, is a highly ill‐posed problem. In this paper, we present a new method to estimate the illumination in a single image as a combination of achromatic lights with their 3D directions and relative intensities. In contrast to previous methods, we base our azimuth angle estimation on curve fitting and recursive refinement of the number of light sources. Similarly, we present a novel surface normal approximation using an osculating arc for the estimation of zenith angles. By means of a new data set of ground‐truth data and images, we demonstrate that our approach produces more robust and accurate results, and show its versatility through novel applications such as image compositing and analysis.     

Hand–eye calibration with epipolar constraints: Application to endoscopy

In this paper, we propose a new calibration method for a hand–eye system equipped with a camera undergoing radial distortion as a rigid endoscope. While classic methods propose either a separated estimation of the camera intrinsics and the hand–eye transform or a mixed non-linear estimation of both hand–eye and camera intrinsics assuming a pin-hole model, the proposed approach enables a simultaneous refinement of the hand–eye and the camera parameters including the distortion factor with only three frames of the calibrated pattern. We propose and compare two criteria to minimize: (i) the first one is based on the epipolar constraint between pairs of frames and (ii) the second one expresses the camera extrinsic with respect to hand–eye and world-grid transforms in the single frame reprojection error. We run bundle-adjustment on each criterion with respect to the distortion parameters, the camera intrinsics and the hand–eye transform. Our method allows us to recover more accurate 3D shapes when compared to state-of-the-art non-linear methods.     

摄像机线性三步定标方法研究

计算机视觉中，在对景物进行定量分析或对物体进行精确定位时，都需要进行摄像机标定，即准确确定摄像机的内部参数和外部参数。由于真实的摄像机光学模型存在很多类型的畸变，因而导致透视投影关系是非线性的。为了解决标定过程的非线性最优化问题，针对常用的带有一阶径向畸变的摄像机模型，提出了一种新的线性三步摄像机定标方法，即首先通过径向排列约束计算摄像机参数的旋转矩阵、x轴平移向量和y轴平移向量；然后根据透视投影的交比不变性解算一阶径向畸变参数；最后利用求得的摄像机参数建立有效焦距和z轴平移向量的线性方程，采用最小二乘法来得到线性解。实验表明，该方法简单快捷，不仅具有较高的标定精度，而且解决了原有算法采用非线性搜索寻优可能存在的解不稳定的问题。     

一种考虑二阶径向畸变的主动视觉自标定算法

基于主动视觉的摄像机自标定是摄像机标定的一个重要分支 ,由于普通的 CCD摄像机拍摄的像片存在着各种类型的几何畸变 ,其中以径向畸变最为严重 ,因此研究考虑径向畸变的自标定技术有着重要的意义 .为了使标定结果更精确 ,提出了一种考虑二阶径向畸变的内参数自标定方法 ,并通过推导考虑二阶径向畸变的极线几何约束 ,得出了如果能控制摄像机做 4次不在同一平面上的平移运动 ,则可以标定摄像机的内参数和二阶径向畸变系数的结论 .仿真实验结果表明 ,该算法精度很高 ,且具有一定的鲁棒性 ,可用于摄像机的标定 .     

基于灭点的径向畸变自动校正方法

镜头畸变影响着三维重建、几何量测等工作的质量。本文根据图像中的灭点几何约束条件,提出一种基于灭点的弱径向畸变自动校正方法。为避免包含畸变中心参数的非线性模型优化结果的不稳定性,本文在求解径向畸变系数之后进一步对畸变中心进行优化。首先根据灭点几何约束条件建立关于灭点与径向畸变系数的非线性模型,使用LM算法估计灭点坐标与径向畸变参数,然后根据质量评价准则对畸变中心和径向畸变系数进一步迭代优化;最后,通过真实图像对该方法的可行性进行分析验证。本文充分利用图像中的灭点属性,提出一种新的镜头径向畸变校正方法。实验结果表明,该方法能够有效的对径向畸变进行校正,并克服了传统校正方法的不稳定性。     

Generalized Camera Calibration Including Fish-Eye Lenses

A method is described for accurately calibrating cameras including radial lens distortion, by using known points such as those measured from a calibration fixture. Both the intrinsic and extrinsic parameters are calibrated in a single least-squares adjustment, but provision is made for including old values of the intrinsic parameters in the adjustment. The distortion terms are relative to the optical axis, which is included in the model so that it does not have to be orthogonal to the image sensor plane. These distortion terms represent corrections to the basic lens model, which is a generalization that includes the perspective projection and the ideal fish-eye lens as special cases. The position of the entrance pupil point as a function of off-axis angle also is included in the model. (The complete camera model including all of these effects often is called CAHVORE.) A way of adding decentering distortion also is described. A priori standard deviations can be used to apply weight to given initial approximations (which can be zero) for the distortion terms, for the difference between the optical axis and the perpendicular to the sensor plane, and for the terms representing movement of the entrance pupil, so that the solution for these is well determined when there is insufficient information in the calibration data. For the other parameters, initial approximations needed for the nonlinear least-squares adjustment are obtained in a simple manner from the calibration data and other known information. (Weight can be given to these also, if desired.) Outliers among the calibration points that disagree excessively with the other data are removed by means of automatic editing based on analysis of the residuals. The use of the camera model also is described, including partial derivatives for propagating both from object space to image space and vice versa. These methods were used to calibrate the cameras on the Mars Exploration Rovers.     

Camera calibration with distortion models and accuracy evaluation

A camera model that accounts for major sources of camera distortion, namely, radial, decentering, and thin prism distortions is presented. The proposed calibration procedure consists of two steps: (1) the calibration parameters are estimated using a closed-form solution based on a distribution-free camera model; and (2) the parameters estimated in the first step are improved iteratively through a nonlinear optimization, taking into account camera distortions. According to minimum variance estimation, the objective function to be minimized is the mean-square discrepancy between the observed image points and their inferred image projections computed with the estimated calibration parameters. The authors introduce a type of measure that can be used to directly evaluate the performance of calibration and compare calibrations among different systems. The validity and performance of the calibration procedure are tested with both synthetic data and real images taken by tele- and wide-angle lenses     

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.     

基于单幅图片的相机完全标定

现有相机标定方法的标定过程比较繁琐,不利于标定相机的广泛使用。为此,从摄像机镜头畸变矫正着手,结合标定板信息及消失点约束,提出一种基于单张图片的相机标定方法。利用非线性迭代得到相机镜头的畸变系数,通过线性求解得出相机的内参,直接计算得到相机的外参,从而实现仅需拍摄单张标定板图片的相机完全标定。实验结果表明,该方法在标定板与视平面夹角小于45°的情况下均能成功标定,并且重投影误差小于0.3像素。     

一种基于斜率的摄像机畸变校正方法

普通 CCD摄像机在成像时都存在畸变成像误差 ,在机器人视觉检测及自动装配中 ,有效地进行误差校正对准确确定物体的位置具有重要的意义 .本文采用带有一阶径向畸变的小孔摄像机模型 ,提出一种基于线段斜率的方法 ,对摄像机镜头的径向畸变进行校正 ,不必标定太多的摄像机的外参数 ,方法简洁 ,适合于视觉系统中对摄像机畸变的实时校正 ,或对摄像机捕获的图像进行几何校正 .实验表明 ,具有很强的鲁棒性和较高的校正精度     

基于投影变换的图像测量系统标定

图像测量系统标定是计算机视觉获取三维信息的前提和基础。为了进一步提高标定精度和速度,提出了一种新的基于投影变换标定法。首先,构造模版图像,将该图像经投影变换得到无畸变图像,然后,将其与由原始图像经消除畸变后所得的无畸变图像进行对比,通过差值来确定畸变模型系数。在求出畸变模型的基础上,再求解其他相机参数。该方法迴避了传统方法繁多的迭代步骤,避免了由于初始参数的估计不准所产生的误差,具有直观、精确和相对快速等优点。并通过实验仿真,验证了该算法的可行性与准确性。     

一种简单而精确的径向畸变标定方法

为了用普通低成本的广角镜头摄像机实现较大视场的精确定量的图像测量，必须对畸变图像进行校正。提出了一种简单而精确的径向畸变标定方法，该方法使用栅格阵列标定模板。首先根据畸变图像中特征点之间的相互位置关系构造出理想图像中的特征点位置；然后以不同的畸变中心假设，计算畸变和理想特征点的矢径坐标，并通过解线性方程组或多项式拟合求出它们之间的函数关系；最后取矢径均方误差最小的参数组作为标定结果。该法可同时获得畸变变换和矫正变换的参数。文中还推导了畸变变换多项式系数与校正图像分辨率之间的反幂比例关系，讨论了畸变函数的阶对校正结果的影响，实验结果表明，取4阶或5阶多项式拟合的结果较好。     

On improved calibration method for the catadioptric omnidirectional vision with a single viewpoint

The single viewpoint constraint is a principal optical characteristic for most catadioptric omnidirectional vision. Single viewpoint catadioptric omnidirectional vision is very useful because it allows the generation of geometrically correct perspective images from one omnidirectional image. Therefore precise calibration for single viewpoint constraint is needed during system assembling. However, in most image detection based calibration methods, the nonlinear optical distortion brought by lens is often neglected. Hence the calibration precision is poor. In this paper, a new calibration method of single viewpoint constraint for the catadioptric omni-directional vision is proposed. Firstly, an image correction algorithm is obtained by training a neural network. Then, according to characteristics of the space circular perspective projection, the corrected image of the mirror boundary is used to estimate its position and attitude relative to the camera to guide the calibration. Since the estimate is conducted based on actual imaging model rather than the simplified model, the estimate error is largely reduced, and the calibration accuracy is significantly improved. Experiments are conducted on simulated images and real images to show the accuracy and the effectiveness of the proposed method.