A three-step camera calibration method

Camera calibration is a crucial problem for many industrial applications that incorporate visual sensing. In this paper, we compute the intrinsic and extrinsic calibration parameters in three steps. In the first step, the calibration parameters are approximated using the linear least-squares method. In the second step, we develop two alternative formulations to obtain an optimal rotation matrix from the calibration parameters computed in the first step. Further optimization of translational and perspective transformations is then performed based on the optimized rotation matrix. In the third step, a nonlinear optimization is performed to handle lens distortion. The solution of the nonlinear system not only minimizes the perspective transformation relations between the image points and the corresponding world coordinates, but also satisfies the orthonormality constraints on the rotational transformation. To assess the performance of our proposed method, the Euclidean norm of the error matrix between the calculated and the original 4×4 homogeneous transformation matrices is used as a basis for comparison with existing methods. Simulation results from applying the method show significant improvements both before and after the nonlinear optimization step     

Lens distortion models evaluation

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

Self-consistent way to determine relative distortion of axial symmetric lens systems

We present a simple method to determine the relative distortion of axially symmetric lens systems. This method uses graphs to determine every parametric value instead of nonlinear minimization computation and is composed of an LCD screen to display a square grid pattern of pixel-wide spots and a set of analyzing processes for the spots in the image. The two Cartesian components of the spot locations are processed by a two-step linear least-square fitting to third-order polynomials. The graphs for the coefficients enable us to determine the amount of decentering of the camera lens axis with respect to the center of the image array and the tip/tilt of the screen, which in turn gives the relative distortion coefficient. We present experimental results to demonstrate the utility of the method by comparing our results with the corresponding values determined by open source software available online.     

船用光电系统中摄像机参数的标定方法

基于一阶径向畸变的针孔摄像机模型,提出了一种新的线性三步摄像机定标方法,即通过径向排列约束计算摄像机参数的旋转矩阵、X轴平移矢量和Y轴平移矢量;根据透视投影的交比不变性解算一阶径向畸变参数;利用求得的摄像机参数建立有效焦距和Z轴平移矢量的线性方程,采用最小二乘法得到线性解。实验表明,该方法简单快捷,具有较高的标定精度,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性等问题。     

Optimized Photothermal Lens Determination of Nonlinear Absorption

An optimized pump–probe mode-mismatched photothermal lens experiment aimed at determination of nonlinear absorption of an optical sample is reported. The pump beam generates a local thermal gradient or thermal lens that is tested by the probe light. The pump beam is tightly focused, and the probe beam is highly collimated. Changes in the probe light transmission through a small aperture located at some distance from the sample provide the signal. Scanning of the sample around the focal point yields a single-peaked Z-scan signature with a width several times larger than the pump Rayleigh range for linear absorption. If nonlinear absorption is dominant, the width of the peak is significantly smaller and of the order of the Rayleigh range of the pump field. If linear and nonlinear absorption are present simultaneously, a double-peaked Z-scan signature is obtained. In this situation, the linear and nonlinear absorption contributions can be easily separated and compared to each other for calibration purposes. Using the known values of linear absorption, nonlinear absorption coefficients can be estimated with good accuracy. The method is tested by studying nonlinear absorption in nitrobenzene and iron oxide water colloids. The values of the effective nonlinear absorption coefficients are determined. The physical origin of nonlinear absorption in both types of samples is also discussed.     

现场勘察中广角镜头相机快速标定算法及实现

基于摄影资料的图像测距技术已广泛应用于交通事故、考古等不可复原的现场勘察工作中,利用普通相机进行摄影测量也日趋成熟。但是普通相机没有广角镜头相机的取景优势,现场分析也比较局限,因此广角镜头相机逐渐取代普通相机。而广角镜头相机容易产生图像畸变效应。为此,本文基于相机成像原理,通过精确网格模板标定图像,利用相机参数间物理关系计算出相机内参和畸变参数,提出了一种广角镜头相机的快速标定算法,结合拍摄现场图像,精确定位参考模板标志牌在照片中的成像结果,计算出广角镜头相机的外参,建立广角镜头相机摄影测量系统。现场实验应用表明,本算法标定快速、简单、测量精度高,可以应用于交通事故现场勘测。     

3D测量系统中的高精度摄像机标定算法

本文在分析完整的摄像机镜头畸变模型的基础上,提出了一种新的标定算法.该算法包括三个步骤,首先在不考虑镜头畸变的情况下利用标定块上的中间若干个点,采用线性优化方法求出除畸变系数以外的其他外部参数和主要的内部参数;然后固定上述已求得的参数,利用线性优化方法求解畸变系数;最后对所有内部参数和外部参数进行全局非线性优化.最后对本文的标定算法进行了标定实验,实验结果表明,本文算法的标定精度可以达到0.0367 mm,可以满足高精度三维测量及其他应用的要求.     

傅里叶变换轮廓术中三维坐标同时校准方法

在相位测量型光学三维面形测量中,最终都要将相位信息转换成被测物体的高度分布信息,这个过程往往是通过对已知世界空间坐标的特征点事先标定,获得测量系统的内外特征参数后,完成被测物体的三维坐标转换.因此,标定是三维面形测量的关键环节.本文基于双向二次相位-高度映射方法和摄像机针孔模型线性无畸变标定技术,充分利用傅里叶变换的频谱方向特性,提出了对含有特征点的二维标定物表面变形条纹的频谱进行方向滤波操作,同时获取测量系统XYZ三个方向上的标定数据,对测量系统进行立体校准的系统标定方法.结合旋转风扇叶片形变的测量系统,给出了该方法的标定结果:在XY面内(230mm×230mm)的标准偏差小于0.27mm;在Z方向上小于0.022mm,位移测量灵敏度优于0.05mm.该方法为测量系统的实用化奠定了基础.     

光栅投影式三维摄影测量仪的几何标定方法

光栅投影式三维摄影测量仪利用了时域结构光投影技术和立体视觉测量原理获得三维点坐标。针对传统标定方法易受镜头畸变影响和标定约束方程少导致精度下降的问题,采用了非线性的摄像机和投影机模型,并提出了二维的投影机模型;使用多平面法标定了系统测量所需的摄像机和投影机几何参数;为进一步提高参数精度,采用Levenberg-Marquardt算法优化了摄像机和投影机模型。实验结果表明,该方法操作简单,无需精确的位置和姿态调整,标定的绝对精度为0.2pixel,相对精度为1/5000。     

星敏感器参数标定及误差补偿

针对CCD星敏感器光学系统存在焦距不准确、CCD平面倾斜和旋转及光学镜头畸变等误差因素,在理想针孔模型的基础上,用几何方法建立了星敏感器模型。利用地面实验数据,以最小二乘法解算该数学模型,求出焦距、CCD平面倾斜和旋转因子及畸变因子等待标定参数。将标定出的参数代回数学模型,便可由星象点测量坐标直接计算并修正入射光方向矢量,从而对光学系统的误差进行了补偿。计算结果表明:星对角距统计偏差由标定前41″降到了17″,提高了计算精度。     

Astigmatic phase correction for the magneto-optic spatial light modulator

We report a simple low-cost technique for evaluating the phase distortion in a magneto-optic spatial light modulator. We find that the dominant distortion is caused by astigmatism and is easily compensated by encoding of the complex-conjugate pattern onto the device. Two experimental results are shown. First, the focused spot size from a Fresnel lens is sharpened when the aberrations are corrected. Second, we show that the pattern that generates a first-order Bessel-function nondiffracting beam does not work unless the aberrations are corrected.     

Unified calibration technique and its applications in optical triangular profilometry

A unified calibration technique based on ray tracing for optical triangular profilometry is presented. The proposed technique based on the inherent geometric relation between depth and a distorted signal is capable of speedy and accurate measurement without the determination of geometric parameters. The technique can also reduce calibration error caused by the lens distortion of the projector and the camera owing to the reasonable assumption that mapping in a small local area is a linear transformation and the coefficients of the linear transformation may be varied in different local areas. Three classical systems of triangular profilometry, spot inspection, a single-line system, and a projection-grating system, are discussed and demonstrated by experiment.     

Absolute linearity measurement of photodetectors using sinusoidal modulated radiation

A method is presented for characterizing the linearity of photodetectors based on time-domain analysis of response to sinusoidal excitation. Nonlinearity is quantified solely from the output distortion. Relative response is converted to absolute response by including two calibration points. For low signal level, one calibration point is required, while using dark current as the second point. The response is mapped over a wider range using a series of overlapping sinusoids for calibration transfer. The method is demonstrated with a relatively linear photodiode and a nonlinear phototransistor. A Michelson interferometer is used to generate sinusoidal modulation of a laser source. Results demonstrate the potential of the proposed technique.     

火箭橇试验橇体时空位置全程测试——单台光电经纬仪法

本文针对火箭橇试验橇体时空位置的全程测试问题,提出了单台光电经纬仪时空位置测试法,该方法采用单台光电经纬仪对火箭橇试验橇体全程运动图像进行跟踪拍摄,通过跟踪图像判读获得的测角信息、光电经纬仪站址信息、火箭橇轨道直线方程3者之间的关系,事后处理出火箭橇全程时空位置．同时提出了采用同帧画幅处理与多点标定事后误差曲线拟合的方法对时空位置事后数据进行逐点修正,可大幅提高测试数据精度．     

三维重构视觉系统的标定

文章基于改进两步法的标定思想,在三维重构中提出了一种新的视觉系统参数标定与镜头畸变修正方法.该方法根据图像中心附近点畸变量较小的性质,利用中心附近点和全场视点对CCD相机和DLP投影仪的内外部参数标定和镜头畸变修正进行分离.在标定过程中,所设计的带标准圆阵列的靶标和伪随机连续方形编码可以实现特征点的自动识别和匹配.实验表明,该方法能快速、方便地对视觉系统参数进行标定和镜头畸变修正.     

Estimating three-dimensional vehicle motion in an outdoor scene using stereo image sequences

We propose a motion estimation system that uses stereo image pairs as the input data. To perform experimental work, we also obtain a sequence of outdoor stereo images taken by two metric cameras. The system consists of four main stages, which are (1) determination of point correspondences on the stereo images, (2) correction of distortions in image coordinates, (3) derivation of 3D point coordinates from 2D correspondences, and (4) estimation of motion parameters based on 3D point correspondences. For the first stage of the system, we use a four-way matching algorithm to obtain matched point on two stereo image pairs at two consecutive time instants (t_i and t_{i + 1}). Since the input data are stereo images taken by cameras, it has two types of distortions, which are (i) film distortion and (ii) lens distortion. These two distortions must be corrected before any process can be applied on the matched points. To accomplish this goal, we use (i) bilinear transform for film distortion correction and (ii) lens formulas for lens distortion correction. After correcting the distortions, the results are 2D coordinates of each matched point that can be used to derive 3D coordinates. However, due to data noise, the calculated 3D coordinates to not usually represent a consistent rigid structure that is suitable for motion estimation; therefore, we suggest a procedure to select good 3D point sets as the input for motion estimation. The procedure exploits two constraints, rigidity between different time instants and uniform point distribution across the object on the image. For the last stage, we use an algorithm to estimate the motion parameters. We also wish to know what is the effect of quantization error on the estimated results; therefore an error analysis based on quantization error is performed on the estimated motion parameters. In order to test our system, eight sets of stereo image pairs are extracted from an outdoor stereo image sequence and used as the input data. The experimental results indicate that the proposed system does provide reasonable estimated motion parameters.     

Flexible structured-light-based three-dimensional profile reconstruction method considering lens projection-imaging distortion

Structured-light profilometry is a powerful tool to reconstruct the three-dimensional (3D) profile of an object. Accurate profile acquisition is often hindered by not only the nonlinear response (i.e., gamma effect) of electronic devices but also the projection-imaging distortion of lens used in the system. In this paper, a flexible 3D profile reconstruction method based on a nonlinear iterative optimization is proposed to correct the errors caused by the lens distortion. It can be easily extended to measurements for which a more complex projection-imaging distortion model is required. Experimental work shows that the root-mean-square (RMS) error is reduced by eight times and highly accurate results with errors of less than 1‰ can be achieved by the proposed method.     

A calibration and measurement method of a tri-six-port networkanalyzer suitable for on-wafer characterization of three-port devices

A calibration and measurement method using a wideband tri-six-port network and analyzer (TSPNA) is proposed. The scattering parameters of a three-port device under test are found to be the unknowns of a set of nine simultaneous complex linear equations. These equations are established via a group of three calibrated linearly independent excitations. No isolators are required for calibration and measurement procedures. Three unknown reciprocal two-port standards are needed for the calibration of the TSPNA. The proposed method is rigorous, explicit, and suitable for wideband on-wafer three-port device S-parameter measurements. It can easily be adapted for heterodyne automated network analyzers equipped with three reflection test-set units     

Scattered data approximation by regular grid weighted smoothing

Scattered data approximation refers to the computation of a multi-dimensional function from measurements obtained from scattered spatial locations. For this problem, the class of methods that adopt a roughness minimization are the best performing ones. These methods are called variational methods and they are capable of handling contrasting levels of sample density. These methods express the required solution as a continuous model containing a weighted sum of thin-plate spline or radial basis functions with centres aligned to the measurement locations, and the weights are specified by a linear system of equations. The main hurdle in this type of method is that the linear system is ill-conditioned. Further, getting the weights that are parameters of the continuous model representing the solution is only a part of the effort. Getting a regular grid image requires re-sampling of the continuous model, which is typically expensive. We develop a computationally efficient and numerically stable method based on roughness minimization. The method leads to an algorithm that uses standard regular grid array operations only, which makes it attractive for parallelization. We demonstrate experimentally that we get these computational advantages only with a little compromise in performance when compared with thin-plate spline methods.     

Blind removal of lens distortion

Virtually all imaging devices introduce some amount of geometric lens distortion. A technique is presented for blindly removing these distortions in the absence of any calibration information or explicit knowledge of the imaging device. The basic approach exploits the fact that lens distortion introduces specific higher-order correlations in the frequency domain. These correlations can be detected by using tools from polyspectral analysis. The amount of distortion is then estimated by minimizing these correlations.