Novel camera calibration method based on invariance of collinear points and pole-polar constraint

To address the eccentric error of circular marks in camera calibration,a circle location method based on the invariance of collinear points and pole–polar constraint is proposed in this paper.Firstly,the centers of the ellipses are extracted,and the real concentric circle center projection equation is established by exploiting the cross ratio invariance of the collinear points.Subsequently,since the infinite lines passing through the centers of the marks are parallel,the other center projection coordinates are expressed as the solution problem of linear equations.The problem of projection deviation caused by using the center of the ellipse as the real circle center projection is addressed,and the results are utilized as the true image points to achieve the high precision camera calibration.As demonstrated by the simulations and practical experiments,the proposed method performs a better location and calibration performance by achieving the actual center projection of circular marks.The relevant results confirm the precision and robustness of the proposed approach.

Non-Metric CCD Camera Calibration Algorithm in a Digital Photogrammetry System

Camera calibration is a critical process in photogrammetry and a necessary step to acquire 3D information from a 2D image. In this paper, a flexible approach for CCD camera calibration using 2D direct linear transformation （DLT） and bundle adjustment is proposed. The proposed approach assumes that the camera interior orientation elements are known, and addresses a new closed form solution in planar object space based on homogenous coordinate representation and matrix factorization. Homogeneous coordinate representation offers a direct matrix correspondence between the parameters of the 2D DLT and the collinearity equation. The matrix factorization starts by recovering the elements of the rotation matrix and then solving for the camera position with the collinearity equation. Camera calibration with high precision is addressed by bundle adjustment using the initial values of the camera orientation elements. The results show that the calibration precision of principal point and focal length is about 0.2 and 0.3 pixels respectivelv, which can meet the requirements of close-range photogrammetry with high accuracy.

NEW VERSATILE CAMERA CALIBRATION TECHNIQUE BASED ON LINEAR RECTIFICATION

A new versatile camera calibration technique for machine vision usingoff-the-shelf cameras is described. Aimed at the large distortion of the off-the-shelf cameras, anew camera distortion rectification technology based on line-rectification is proposed. Afull-camera-distortion model is introduced and a linear algorithm is provided to obtain thesolution. After the camera rectification intrinsic and extrinsic parameters are obtained based onthe relationship between the homograph and absolute conic. This technology needs neither ahigh-accuracy three-dimensional calibration block, nor a complicated translation or rotationplatform. Both simulations and experiments show that this method is effective and robust.

A new technique for high precision sub-regional camera calibration based on checkerboard pattern

Camera calibration is critical in computer vision measurement system, affecting the accuracy of the whole system. Many camera calibration methods have been proposed, but they cannot consider precision and operation complexity at the same time. In this paper, a new technique is proposed to calibrate camera. Firstly, the global calibration method is described in de-tail. It requires the camera to observe a checkerboard pattern shown at a few different orientations. The checkerboard corners are obtained by Harris algorithm. With direct linear transformation and non-linear optimal algorithm, the global calibration pa-rameters are obtained. Then, a sub-regional method is proposed. Those corners are divided into two groups, middle corners and edge corners, which are used to calibrate the corresponding area to get two sets of calibration parameters. Finally, some experimental images are used to test the proposed method. Experimental results demonstrate that the average projection error of sub-region method is decreased at least 16% compared with the global calibration method. The proposed technique is simple and accurate. It is suitable for the industrial computer vision measurement.

A Review of RGB-D Camera Calibration Methods

RGB-D camera is a new type of sensor,which can obtain the depth and texture information in an unknown 3D scene simultaneously,and they have been applied in various fields widely.In fact,when implementing such kinds of applications using RGB-D camera,it is necessary to calibrate it first.To the best of our knowledge,at present,there is no existing a systemic summary related to RGB-D camera calibration methods.Therefore,a systemic review of RGB-D camera calibration is concluded as follows.Firstly,the mechanism of obtained measurement and the related principle of RGB-D camera calibration methods are presented.Subsequently,as some specific applications need to fuse depth and color information,the calibration methods of relative pose between depth camera and RGB camera are introduced in Section 2.Then the depth correction models within RGB-D cameras are summarized and compared respectively in Section 3.Thirdly,considering that the angle of the view field of RGB-D camera is smaller and limited to some specific applications,we discuss the calibration models of relative pose among multiple RGB-D cameras in Section 4.At last,the direction and trend of RGB-D camera calibration are prospected and concluded.

Camera Calibration for 3D Color Scanning System Using Virtual 3D Model

Instead of traditionally using a 3D physical model with many control points on it, a calibration plate with printed chess grid and movable along its normal direction is implemented to provide large area 3D control points with variable Z values. Experiments show that the approach presented is effective for reconstructing 3D color objects in computer vision system.

Flexible Planar-Scene Camera Calibration Technique

A flexible camera calibration technique using 2D-DLT and bundle adjustment with planar scenes is proposed. The equation of principal line under image coordinate system represented with 2D-DLT parameters is educed using the correspondence between collinearity equations and 2D-DLT. A novel algorithm to obtain the initial value of principal point is put forward. Proof of Critical Motion Sequences for calibration is given in detail. The practical decomposition algorithm of exterior parameters using initial values of principal point, focal length and 2D-DLT parameters is discussed elaborately. Planar\|scene camera calibration algorithm with bundle adjustment is addressed. Very good results have been obtained with both computer simulations and real data calibration. The calibration result can be used in some high precision applications, such as reverse engineering and industrial inspection.

Camera Calibration from Profile of Revolution

This paper focuses on the problem of calibrating a pinhole camera from images of profile of a revolution. In this paper, the symmet ry of images of profiles of revolution has been extensively exploited and a prac tical and accurate technique of camera calibration from profiles alone has been developed. Compared with traditional techniques for camera calibration, for inst ance, it may involve taking images of some precisely machined calibration patter n (such as a calibration grid), or edge detection for determining vanish points which are often far from images center or even do not physically exist, or calcu lation of fundamental matrix and Kruppa equations which can be numerically unsta ble, the method presented here uses just profiles of revolution, which are commo nly found in daily life (e.g. bowls and vases), to make the process easier as a result of the reduced cost and increased accessibility of the calibration object s. This paper firstly analyzes the relationship between the symmetry property of profile of revolution and the intrinsic parameters of a camera, and then shows how to use images of profile of revolution to provide enough information for det ermining intrinsic parameters. During the process, high-accurate profile extrac tion algorithm has also been used. Finally, results from real data are presented , demonstrating the efficiency and accuracy of the proposed methods.

Non-parametric camera calibration method using single-axis rotational target

The ability to build an imaging process is crucial to vision measurement.The non-parametric imaging model describes an imaging process as a pixel cluster,in which each pixel is related to a spatial ray originated from an object point.However,a non-parametric model requires a sophisticated calculation process or high-cost devices to obtain a massive quantity of parameters.These disadvantages limit the application of camera models.Therefore,we propose a novel camera model calibration method based on a single-axis rotational target.The rotational vision target offers 3D control points with no need for detailed information of poses of the rotational target.Radial basis function(RBF)network is introduced to map 3D coordinates to 2D image coordinates.We subsequently derive the optimization formulization of imaging model parameters and compute the parameter from the given control points.The model is extended to adapt the stereo camera that is widely used in vision measurement.Experiments have been done to evaluate the performance of the proposed camera calibration method.The results show that the proposed method has superiority in accuracy and effectiveness in comparison with the traditional methods.

Camera calibration method for an infrared horizon sensor with a large field of view

Inadequate geometric accuracy of cameras is the main constraint to improving the precision of infrared horizon sensors with a large field of view(FOV).An enormous FOV with a blind area in the center greatly limits the accuracy and feasibility of traditional geometric calibration methods.A novel camera calibration method for infrared horizon sensors is presented and validated in this paper.Three infrared targets are used as control points.The camera is mounted on a rotary table.As the table rotates,these control points will be evenly distributed in the entire FOV.Compared with traditional methods that combine a collimator and a rotary table which cannot effectively cover a large FOV and require harsh experimental equipment,this method is easier to implement at a low cost.A corresponding three-step parameter estimation algorithm is proposed to avoid precisely measuring the positions of the camera and the control points.Experiments are implemented with 10 infrared horizon sensors to verify the effectiveness of the calibration method.The results show that the proposed method is highly stable,and that the calibration accuracy is at least 30%higher than those of existing methods.

A Linear Approach for Depth and Colour Camera Calibration Using Hybrid Parameters

Many recent applications of computer graphics and human computer interaction have adopted both colour cameras and depth cameras as input devices. Therefore, an effective calibration of both types of hardware taking different colour and depth inputs is required. Our approach removes the numerical difficulties of using non-linear optimization in previous methods which explicitly resolve camera intrinsics as well as the transformation between depth and colour cameras. A matrix of hybrid parameters is introduced to linearize our optimization. The hybrid parameters offer a transformation from a depth parametric space （depth camera image） to a colour parametric space （colour camera image） by combining the intrinsic parameters of depth camera and a rotation transformation from depth camera to colour camera. Both the rotation transformation and intrinsic parameters can be explicitly calculated from our hybrid parameters with the help of a standard QR factorisation. We test our algorithm with both synthesized data and real-world data where ground-truth depth information is captured by Microsoft Kinect. The experiments show that our approach can provide comparable accuracy of calibration with the state-of-the-art algorithms while taking much less computation time （1/50 of Herrera＇s method and 1/10 of Raposo＇s method） due to the advantage of using hybrid parameters.

Velocity Calculation by Automatic Camera Calibration Based on Homogenous Fog Weather Condition

A novel algorithm for vehicle average velocity detection through automatic and dynamic camera calibration based on dark channel in homogenous fog weather condition is presented in this paper. Camera fixed in the middle of the road should be calibrated in homogenous fog weather condition, and can be used in any weather condition. Unlike other researches in velocity calculation area, our traffic model only includes road plane and vehicles in motion. Painted lines in scene image are neglected because sometimes there are no traffic lanes, especially in un-structured traffic scene. Once calibrated, scene distance will be got and can be used to calculate vehicles average velocity. Three major steps are included in our algorithm. Firstly, current video frame is recognized to discriminate current weather condition based on area search method （ASM）. If it is homogenous fog, average pixel value from top to bottom in the selected area will change in the form of edge spread function （ESF）. Secondly, traffic road surface plane will be found by generating activity map created by calculating the expected value of the absolute intensity difference between two adjacent frames. Finally, scene transmission image is got by dark channel prior theory, camera s intrinsic and extrinsic parameters are calculated based on the parameter calibration formula deduced from monocular model and scene transmission image. In this step, several key points with particular transmission value for generating necessary calculation equations on road surface are selected to calibrate the camera. Vehicles pixel coordinates are transformed to camera coordinates. Distance between vehicles and the camera will be calculated, and then average velocity for each vehicle is got. At the end of this paper, calibration results and vehicles velocity data for nine vehicles in different weather conditions are given. Comparison with other algorithms verifies the effectiveness of our algorithm.

Segment Based Camera Calibration

The basic idea of calibrating a camera system in previous approaches is to determine camera parameters by using a set of known 3D points as calibration reference.In this paper,we present a method of camera calibration in which camera parameters are determined by a set of 3D lines.A set of constraints is derived on camera parameters in terms of perspective line mapping.From these con- straints,the same perspective transformation matrix as that for point mapping can be computed linearly.The minimum number of calibration lines is 6.This result generalizes that of Lin,Huang and Faugeras for camera location determination in which at least 8 line correspondences are re- quired for linear computation of camera location.Since line segments in an image can be located easi- ly and more accurately than points,the use of lines as calibration reference tends to ease the compu- tation in image preprocessing and to improve calibration accuracy.Experimental results on the calibration along with stereo reconstruction are reported.

Optical focal plane based on MEMS light lead-in for geometric camera calibration

The focal plane of a collimator used for the geometric calibration of an optical camera is a key element in the calibration process.The traditional focal plane of the collimator has only a single aperture light lead-in,resulting in a relatively unreliable calibration accuracy.Here we demonstrate a multi-aperture micro-electro-mechanical system(MEMS)light lead-in device that is located at the optical focal plane of the collimator used to calibrate the geometric distortion in cameras.Without additional volume or power consumption,the random errors of this calibration system are decreased by the multi-image matrix.With this new construction and a method for implementing the system,the reliability of high-accuracy calibration of optical cameras is guaranteed.

Camera Calibration with 1D Rotating Objects

In this paper,we use 1D rotating objects to calibrate camera.The calibration object has three collinear points.It is not necessary for the object to rotate around one of its endpoints as before;instead,it rotates around the middle point in a plane.In this instance,we can use two calibration constraints to compute the intrinsic parameters of a camera.In addition,when the 1D object moves in a plane randomly,the proposed technique remains valid to compute the intrinsic parameters of a camera.Experiments with simulated data as well as with real images show that our technique is accurate and robust.

Analysis of the Pencil of Conics with Double Complex Contact and Its Application to Camera Calibration

In this paper, we introduce a novel class of coplanar conics, the pencil of which can doubly contact to calibrate camera and estimate pose. We first analyze the properties of con-axes and con-eccentricity ellipses, which consist of a naturM extending pattern of concentric circles. Then the general case that two ellipses have two repeated complex intersection points is presented. This degenerate configuration results in a one-parameter family of homographies which map the planar pattern to its image. Although it is unable to compute the complete homography, an indirect 3-degree polynomial or 5-degree polynomial constraint on intrinsic parameters from one image can also be used for camera calibration and pose estimation under the minimal conditions. Furthermore, this nonlinear problem can be treated as a polynomial optimization problem （POP） and the global optimization solution can be also obtained by using SparsePOP （a sparse semidefinite programming relaxation of POPs）, Finally, the experiments with simulated data and real images are shown to verify the correctness and robustness of the proposed technique.

A universal method for camera calibration in UITS scenes

A universal approach to camera calibration based on features of some representative lines on traffic ground is presented. It uses only a set of three parallel edges with known intervals and one of their intersected lines with known slope to gain the focal length and orientation parameters of a camera. A set of equations that computes related camera parameters has been derived from geometric properties of the calibration pattern. With accurate analytical implementation, precision of the approach is only decided by accuracy of the calibration target selecting. Final experimental results have showed its validity by a snapshot from real automatic visual traffic surveillance （AVTS） scencs.

Camera Calibration Method Based on Self-made 3D Target

A camera calibration algorithm based on self-made target is proposedin this paper, which can solve the difficulty of making high precision 3Dtarget. Theself-made target consists of two intersecting chess board. With the classic scalemethod, the 3D coordinates of selected points in the target were derived from thedistance matrix. The element in distance matrix is the distance between every twopoints, which can be obtained by measurement. The spatial location precision ofpoints in the target was ensured by measurement instead of manufacturing, whichreduced the production cost and the requirements for the production accuracygreatly. Camera calibration was completed using 3D target based method. It canbe further extended to the applications where the target cannot be produced. Theexperimental results show the validity of this method.

Constructing a Virtual Large Reference Plate with High-precision for Calibrating Cameras with Large FOV

It is well known that the accuracy of camera calibration is constrained by the size of the reference plate,it is difficult to fabricate large reference plates with high precision.Therefore,it is non-trivial to calibrate a camera with large field of view(FOV).In this paper,a method is proposed to construct a virtual large reference plate with high precision.Firstly,a high precision datum plane is constructed with a laser interferometer and one-dimensional air guideway,and then the reference plate is positioned at different locations and orientations in the FOV of the camera.The feature points of reference plate are projected to the datum plane to obtain a virtual large reference plate with high-precision.The camera is moved to several positions to get different virtual reference plates,and the camera is calibrated with the virtual reference plates.The experimental results show that the mean re-projection error of the camera calibrated with the proposed method is 0.062 pixels.The length of a scale bar with standard length of 959.778mm was measured with a vision system composed of two calibrated cameras,and the length measurement error is 0.389mm.

Development and calibration of the Moon-based EUV camera for Chang'e-3

The process of development and calibration for the first Moon-based ex- treme ultraviolet （EUV） camera to observe Earth＇s plasmasphere is introduced and the design, test and calibration results are presented. The EUV camera is composed of a multilayer film mirror, a thin film filter, a photon-counting imaging detector, a mech- anism that can adjust the direction in two dimensions, a protective cover, an electronic unit and a thermal control unit. The center wavelength of the EUV camera is 30.2 nm with a bandwidth of 4.6nm. The field of view is 14.7° with an angular resolution of 0.08°, and the sensitivity of the camera is 0.11 count s-1 Rayleigh-1. The geomet- ric calibration, the absolute photometric calibration and the relative photometric cal- ibration are carried out under different temperatures before launch to obtain a matrix that can correct geometric distortion and a matrix for relative photometric correction, which are used for in-orbit correction of the images to ensure their accuracy.