Stratified camera calibration algorithm based on the calibrating conic.

This paper presents a new framework for analyzing the geometry of multiple 3D scene points from multiple uncalibrated images, based on decomposing the projection of these points on the images into two stages: (i) the projection of the scene points onto a (real or virtual) physical reference planar surface in the scene; this creates a virtual “image” on the reference plane, and (ii) the re-projection of the virtual image onto the actual image plane of the camera. The positions of the virtual image points are directly related to the 3D locations of the scene points and the camera centers relative to the reference plane alone. All dependency on the internal camera calibration parameters and the orientation of the camera are folded into homographies relating each image plane to the reference plane.Bi-linear and tri-linear constraints involving multiple points and views are given a concrete physical interpretation in terms of geometric relations on the physical reference plane. In particular, the possible dualities in the relations between scene points and camera centers are shown to have simple and symmetric mathematical forms. In contrast to the plane+parallax (p+p) representation, which also uses a reference plane, the approach described here removes the dependency on a reference image plane and extends the analysis to multiple views. This leads to simpler geometric relations and complete symmetry in multi-point multiview duality.The simple and intuitive expressions derived in the reference-plane based formulation lead to useful applications in 3D scene analysis. In particular, simpler tri-focal constraints are derived that lead to simple methods for New View Synthesis. Moreover, the separation and compact packing of the unknown camera calibration and orientation into the 2D projection transformation (a homography) allows also partial reconstruction using partial calibration information.

Camera calibration has been studied extensively in computer vision and photogrammetry. But almost all the camera calibration techniques iterate with the general minimizing function by minimizing the discrepancy between the real position in pixels of a 2D image point and the calculated projection of the 3D object point on the image plane. Though the imaging distance errors are equal, the spatial anti-projection distance errors are not identical at different distance before the camera. As far as vision measurement system, its final object is to obtain the accurate space coordinate of the measured point. Theoretically, the space point should on the optical ray generated by its projection image point and the center of camera. To satisfy the special request of vision measurement system for camera calibration parameters, we present a valid camera calibration method based on new minimizing function using high precision virtual stereo calibration pattern, which is formed by moving an infrared light-emitting diode (IR LED) feature point with CMM on pre-defined paths. Radial distortion and decentering distortion are molded. The proposed technique consists of linear optimization parameter estimation and nonlinear refinement, which is carried out by minimizing the distance of all the 3D space points from the corresponding optical ray generated by their projections image points and the center of camera. Simulated data and real data are both shown that the calibration precision of the proposed method is better than that of the general minimizing the distance between the imaged points and the modeled projections. This method considerable reduces the distance of all the 3D space points from the corresponding optical ray generated from their projections image points and the center of camera, enhances the precision of camera calibration parameters, and improves the precision of the vision measurement system.

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 with their intersection being the principal point while each principal line can concisely represent relative orientation/position (up to one degree of freedom for both) between a special pair of coordinate systems of image plane and calibration pattern. With such analytically tractable image features, computations associated with the calibration are greatly simplified, while the guidelines in (i) can be established intuitively. Experimental results for synthetic and real data show that the proposed approach does compare favorably with Zhang's method, in terms of correctness, robustness, and flexibility, and addresses issues (i) and (ii) satisfactorily.

Objectives: Recent high zoom lens as CCD (Charge Coupled Device) camera is released with the resolution to be able to easily acquire the digital image that has been variously utilized, from day-to-day utilization to take advantage of specialized domain such as computer vision (computer vision). It has a number of advantages for obtaining a normal zoom lens CCD camera video which is now commercially available, however the camera calibration in the actual image process geometrically have been the considerable difficulties due to the unstable capture and the movement of the pick-up process in a variety of zoom lens camera. Methods: The camera parameters for the zoom lens calibration will be test variables calculated over a camera lens, a variety of focal lengths whenever the zoom occur, especially if you already have zoom movement at the point the lens test is complete, recalculation of the camera calibration parameters cause the difficulties. In this research the zoom lens to correct the distortion of image obtaining the camera calibration, and a method that extracts the camera parameters through the DLT (Direct Linear Transformation) test method is proposed. Findings: DLT accuracy of the camera is black was carried out in the following two aspects. The first was to analyze the three dimensional position differences between the estimated position and the actual three-dimensional observation that is calculated by the model formula to moderate, and the second is that pixel position that is pixels accuracy projected onto the image plane in the three-dimensional space of the object the accuracy was evaluated in an absolute manner. In this study, under the assumption that the aperture condition is fixed zoom, the zoom was determined the relationship between the camera and variable focus for the condition setting. A zoom lens camera model by setting the zoom and focus conditions at regular intervals as short-focus lens model was established by the DLT method and each camera parameter is tested individually. Applications: In future research the image correction software will be develop for the 3-dimensional location information based on three-dimensional information generating process based on camera calibration method by the DLT method.Keywords: Camera Lens, Camera Parameter, Computer Vision, Direct Linear Transformation

Being put forward by the researchers in computer vision, self calibration commonly deals with camera with linear model. Since the distortion is practically existed especially for ordinary camera, the result of calibration can't meet the demand of vision measurement with high accuracy regardless of the distortion. Being obedience to systematism mainly, the distortion is the target function of distortion coefficient, principal point, principal distance ratio and skew factor etc. So there exists a group of parameters including of distortion coefficient, principal point, principal distance ratio and skew factor and fundamental matrix which make homologous point meets epipolar restriction theoretically. Accordingly, the paper advances the way titled self calibration of camera with non-linear imaging model which is on basis of the Kruppa equation. In calculating the fundamental matrix, we can obtain interior elements except principal distance by taking into account distortion correction about image coordinate. Then the principal distance can be obtained by using Kruppa equation. This way only need some homologous points between two images, not need any known information about objects. Lots of experiments have proven its correctness and reliability.

The camera calibration for the intrinsic parameters such as the principal point and the principal distance is one of the most important techniques for the 3-D measurement applications based on the cameras' 2D images: the principal point is the intersection of optical axis of camera and image plane, and the principal distance is the distance between the center of lens and principal point. Though the techniques of camera parameter calibration have been intensively investigated by many researchers, the calibration errors were just examined through limited experiments and simulations and no more. Taking up the two-fiducial-plane camera calibration technique, this paper examined the calibration errors theoretically for various conditions such as the fiducial-plane translation, and the principal distances where the extraction errors of image coordinates of the fiducial points were considered as the source of the errors. The estimation error of F and P are theoretically formulized with the analytical equations, and the effectiveness of the formulas is confirmed by comparing the values by the theory with those by the simulations.

Ouk Choi Professor Ouk Choi from Incheon National University, Korea, talks to Electronics Letters about the paper ‘Robust alternating optimization for extrinsic calibration of RGB-D cameras’, page 992. My research field is computer vision, and I am currently interested in the acquisition, processing, and understanding of 3D data. During my Ph.D. studies, my research topic was to solve highly ambiguous correspondence problems such as matching windows in image pairs of buildings. After receiving my Ph.D. degree, I joined the Samsung Advanced Institute of Technology, where I conducted research projects on time-of-flight cameras. I was intrigued by the fact that time-of-flight cameras can acquire 3D data without solving difficult correspondence problems. Since then, my research has been directed toward 3D computer vision. Nowadays, I am building systems that can acquire multi-view depth images of subjects, so that the acquired datasets can be used for machine learning and other research purposes. Early time-of-flight cameras had many problems such as depth noise, low resolution, and phase wrapping. Many of these problems seem to have been solved in commercially available RGB-D cameras such as the Kinect v2. In addition, they are factory calibrated, so that we can access the intrinsic parameters without calibration. However, if we want to use multiple RGB-D cameras with their 3D measurements represented in the same reference coordinate system, finding the extrinsic parameters such as the rotation and translation between the cameras needs to be done manually. In my Letter, we describe a robust and efficient bundle adjustment algorithm that is indispensable in realising a fully automatic, easy-to-use, and online extrinsic calibration method. In a previous work referenced in my Letter, Su et al. proposed an efficient bundle adjustment algorithm, which alternates between solving for better extrinsic parameters and solving for better calibration target locations. In the presence of outliers, the algorithm tends to fail but this problem was not addressed in their work. On the other hand, in our previous work, Kwon et al. proposed a robust bundle adjustment algorithm, which works in the presence of outliers. However, the algorithm is highly inefficient. In my Letter, my colleagues and I have reported a bundle adjustment algorithm that is as efficient as Su et al.’s algorithm and as robust as Kwon et al.’s algorithm. The most attractive point of our work is that we can perform online bundle adjustment with the proposed algorithm. Although the execution time is not real-time with a single processor, the computational complexity of the algorithm is linear with the number of RGB-D cameras and the number of calibration images. In addition, the algorithm is highly parallelisable, which means that it can be implemented to work in real-time with sufficient computing resources. This will enable online extrinsic calibration of multiple RGB-D cameras. Once we compute an initial solution, we can add images of the spherical calibration target and apply our bundle adjustment algorithm frame-by-frame until a certain level of accuracy is attained. We plan to capture 3D data of human subjects as such data can be used to build a learning-based generative model of 3D human shape and pose as well as establish a parametric generative model. In addition, such a multi-view capture system can be used for analysing the interaction between a person and an object or for analysing social behaviour among people. The collected data and developed algorithms will be used to realise a virtual agent who seems to act human. In the future, it will be possible to generate a movie with only a scenario, using the virtual actors and their human-like behaviours. Traditionally, 3D computer vision was a combination of theories on multiple-view geometry and optimisation-based parameter estimation algorithms. Many research projects have contributed to building 3D models of our surrounding world, and it is now easy to access the online 3D maps provided by Google or Apple. Optimisation-based estimation algorithms require good initial solutions based on theories and feature correspondence across multiple views. Recently, machine learning algorithms such as random forests and deep neural networks are directly applied to raw data, successfully replacing the expert-knowledge-based methods for finding initial solutions. In addition, the research interest is being shifted from static scenes to dynamic objects. Deep learning-based methods are now applied to reconstructing and analysing human performance capture, from which we can obtain a generative model, which can change its shape, pose, and facial expression. As generated models get more accurate and realistic, we will be able to see virtual humanoids in the 3D maps of our surrounding world. I guess that it will take no more than ten years to see such human-like dynamic agents.

This research aimed to optimize the camera calibration process by identifying the optimal distance and angle for capturing checkered board images, with a specific focus on understanding the factors that influence the reprojection error (ϵRP). The objective was to improve calibration efficiency by exploring the impacts of distance and orientation factors and the feasibility of independently manipulating these factors. The study employed Zhang's camera calibration method, along with the 2k full-factorial analysis method and the Latin Hypercube Sampling (LHS) method, to identify the optimal calibration parameters. Three calibration methods were devised: calibration with distance factors (D, H, V), orientation factors (R, P, Y), and the combined two influential factors from both sets of factors. The calibration study was carried out with three different stereo cameras. The results indicate that D is the most influential factor, while H and V are nearly equally influential for method A; P and R are the two most influential orientation factors for method B. Compared to Zhang's method alone, on average, methods A, B, and C reduce ϵRP by 25%, 24%, and 34%, respectively. However, method C requires about 10% more calibration images than methods A and B combined. For applications where lower value of ϵRP is required, method C is recommended. This study provides valuable insights into the factors affecting ϵRP in calibration processes. The proposed methods can be used to improve the calibration accuracy for stereo cameras for the applications in object detection and ranging. The findings expand our understanding of camera calibration, particularly the influence of distance and orientation factors, making significant contributions to camera calibration procedures.

This paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution. Camera calibration is the process of determining the intrinsic or internal parameters (i.e., aspect ratio, focal length, and principal point) of a camera, and it is important for both motion estimation and metric reconstruction of 3D models. In this paper, a novel and simple calibration technique is introduced, which is based on exploiting the symmetry of images of surfaces of revolution. Traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern (such as a calibration grid). The use of surfaces of revolution, which are commonly found in daily life (e.g., bowls and vases), makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects. In this paper, it is shown that two images of a surface of revolution will provide enough information for determining the aspect ratio, focal length, and principal point of a camera with fixed intrinsic parameters. The algorithms presented in this paper have been implemented and tested with both synthetic and real data. Experimental results show that the camera calibration method presented is both practical and accurate.

Camera calibration from circles has great advantages, but for paracatadioptric camera, the estimation of intrinsic parameters using circle images is still an open and challenging problem. Previous work proved that the paracatadioptric projection of a circle is a quartic curve. But due to the partial occlusion, only part of the quartic curve is visible on the image plane. Consequently, circle image cannot be directly estimated using image points extracted from the visible part and camera parameters cannot be calibrated. To solve this problem, In this paper, we study the properties of paracatadioptric circle image and application in calibrating the focal length for the case that aspect ratio is 1 and skew is 0. Firstly, we derive the necessary and sufficient conditions that must be satisfied by paracatadioptric circle image. Next, based on these conditions, a new object function is presented to correctly estimate the circle image. Then, we show that the focal length can be computed from the estimated paracatadioptric circle image and the principal point that is estimated from the projected contour of parabolic mirror. Experimental results on both simulated and real image data have demonstrated the effectiveness of our method.

Fish-eye lenses are common in several computer vision applications, such as four-camera surround view driver assistance, where a very wide angle (e.g., 180 degrees) of view is available. Nevertheless, their applicability is usually limited by the lack of an accurate and easy-to-use calibration procedure. In this paper, we present a camera calibration method for fish-eye lenses and a panoramic image stitching framework for calibrated surround images. To achieve the calibration of fish-eye captured images, it only requires to observe a reference planar pattern (e.g., chessboard), followed by offline estimating extrinsic and intrinsic parameters and save the related parameters. Each fish-eye distorted image can then be efficiently online corrected. Then, each calibrated image is transformed to its top-down view (or bird's-eye view) via the perspective transformation based on the estimated homography matrix. As a result, these surround bird'seye view images can be stitched to generate the final panoramic image. It is expected that the proposed framework would be applicable to AVM (around view monitoring) system or ADAS (advanced driver assistance system) of vehicles in the future.

Camera calibration from very few images based on soft constraint optimization

This paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution. Camera calibration is the process of determining the intrinsic or internal parameters (i.e. aspect ratio, focal length and principal point) of a camera, and is important for both motion estimation and metric reconstruction of 3D models. In this paper, a novel and simple calibration technique has been introduced which is based on the symmetry of images of surfaces of revolution. Traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern (such as a calibration grid). The use of surfaces of revolution, which are commonly found in daily life (e.g. bowls and vases), makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects. In this paper, it is shown that 2 images of surface of revolution will provide enough information for determining the aspect ratio, focal length and principal point of a camera. An analytical error model is developed, providing variances and confidence intervals of the parameters estimated. The techniques presented in this paper have been implemented and tested with both synthetic and real data. Experiment results show that the camera calibration method presented here is both practical and accurate.

Based on analyzing and partially testing the current methods for camera calibration in computer vision, inspired by Zhang’s technique, we introduced a new method for binocular stereovision camera calibration. In this method, a planar object with a series of circles was used as calibration template, and the centers of circles were regarded as control points. The proposed method requires the two cameras with relatively fixed position to simultaneously observe the calibration template at a few (at least two) different orientations by moving the cameras or planar object freely, then extracts the centers’ coordinates of circles or ellipses by image processing technique. On this basis, calculate every camera’ intrinsic and extrinsic parameters, then calculate the position parameters of the two cameras. The main point of this method is that it can match the points in the model plane and their image points easily; compared with Zhang’s calibration methods, it can reduce the errors of extracting control points. Experimental results and contrast tests show proposed method is accurate and very applicative to camera calibration of binocular stereovision system.

A high-precision camera calibration method for binocular stereo vision system based on a multi-view template and alternative bundle adjustment is presented in this paper. The proposed method could be achieved by taking several photos on a specially designed calibration template that has diverse encoded points in different orientations. In this paper, the method utilized the existing algorithm used for monocular camera calibration to obtain the initialization, which involves a camera model, including radial lens distortion and tangential distortion. We created a reference coordinate system based on the left camera coordinate to optimize the intrinsic parameters of left camera through alternative bundle adjustment to obtain optimal values. Then, optimal intrinsic parameters of the right camera can be obtained through alternative bundle adjustment when we create a reference coordinate system based on the right camera coordinate. We also used all intrinsic parameters that were acquired to optimize extrinsic parameters. Thus, the optimal lens distortion parameters and intrinsic and extrinsic parameters were obtained. Synthetic and real data were used to test the method. The simulation results demonstrate that the maximum mean absolute relative calibration errors are about 3.5e-6 and 1.2e-6 for the focal length and the principal point, respectively, under zero-mean Gaussian noise with 0.05 pixels standard deviation. The real result shows that the reprojection error of our model is about 0.045 pixels with the relative standard deviation of 1.0e-6 over the intrinsic parameters. The proposed method is convenient, cost-efficient, highly precise, and simple to carry out.