Camera calibration method based on a flexible spliced pattern of equilateral triangles

A flexible calibration method based on small planar target for defocused cameras

An improved outdoor camera calibration method based on Extended Kalman Filter (EKF) is proposed in this paper. GPS coordinate system is introduced to establish world coordinate system in the calibration procedure. According to the characteristics of GPS coordinate converted to plane coordinate and the camera calibration model, we establish the mapping relations of reference points between image plane coordinate and the world coordinate. Further, we consider the world coordinate error, set the world coordinates as the measure quantities, use the method of EKF to get the optimal estimation of intrinsic and extrinsic camera parameters, in EKF the camera's intrinsic and extrinsic parameters are set as state variables, the transformation equations of image coordinate to the world coordinate are set as the measurement equations, and we let the observed feature points' image coordinates and corresponding world coordinates as the input of the filter. Experimental results confirmed that the proposed method with high precision. Index Terms - camera calibration, GPS coordinate, EKF, world coordinate error

This passage puts forward a kind of simple and convenient three-dimensional laser measurement technology for a small volume and complex shape space data acquisition of the object. This technology mainly uses the camera self calibration method for construction of three-dimensional model algorithm and creates the measurement environment of the measuring technique in machinery and hardware camp. The result of the experiment shows that the desktop 3D laser scanning measuring instrument is convenient, and can acquire spatial location ideal data with low cost.

Camera calibration plays a crucial role in 3D measurement tasks of machine vision. In typical calibration processes, camera parameters are iteratively optimized in the forward imaging process (FIP). However, the results can only guarantee the minimum of 2D projection errors on the image plane, but not the minimum of 3D reconstruction errors. In this paper, we propose a universal method for camera calibration, which uses the back projection process (BPP). In our method, a forward projection model is used to obtain initial intrinsic and extrinsic parameters with a popular planar checkerboard pattern. Then, the extracted image points are projected back into 3D space and compared with the ideal point coordinates. Finally, the estimation of the camera parameters is refined by a non-linear function minimization process. The proposed method can obtain a more accurate calibration result, which is more physically useful. Simulation and practical data are given to demonstrate the accuracy of the proposed method.

Camera calibration using one-dimensional information and its applications in both controlled and uncontrolled environments

Due to different modality and sampling density between LiDAR and camera, the correspondences between these two sensors are difficult to find. In this paper, we propose a novel method for Camera-LiDAR extrinsic parameters calibration based on the near-far dual targets. In our approach, a chessboard target is placed closer to the combined Camera-LiDAR device and a trihedron object of the structured scene is placed farther. Using the chessboard, camera motion can be estimated through the RGB images captured by the camera. The point cloud captured by LiDAR from the trihedron is then used for LiDAR motion estimation. By coordinating their motion constraints, our approach can reliably estimate the extrinsic parameters between two sensors by a classic hand-eye calibration process without facing the challenges of finding feature correspondences. Finally, the proposed method is evaluated on both simulated data and real data.

<p>El cálculo de los parámetros intrínsecos y extrínsecos de cámaras digitales usadas en los cultivos de Tilapias, facilita el ajuste de dichas cámaras a las medidas biométricas reales que se esperan obtener del cultivo. Con estos cálculos se busca crear un modelo matemático que permita relacionar las medidas en pixeles del sensor óptico de las cámaras con las medidas biométricas de las tilapias. Para encontrar la talla de la tilapia roja por medio de reconocimiento de imágenes digitales se determinaron las características internas, geométricas y ópticas de la cámara (Parámetros intrínsecos) y la posición de referencia de la cámara, con respecto al acuario o estanque (parámetros extrínsecos). El propósito era hallar un modelo matemático que permitiera obtener la información biométrica de las tilapias a partir de las imágenes digitales obtenidas por la cámara. Para este caso, se aplicó el método de calibración de Zhang, utilizando imágenes de un plano con patrones de intensidad específicos, capturados por la cámara en diferentes posiciones y orientaciones. Con los parámetros encontrados se buscó el modelo matemático que relacionara las medidas reales biométricas de las tilapias con el análisis de las imágenes digitalizadas.</p>

An algorithm for camera calibration using a three-dimensional reference point

Multicamera calibration is an important technique for generating free-view videos. By arranging multiple cameras in a scene after camera calibration and image processing, a multidimensional viewing experience can be presented to the audience. To address the problem that low texture cannot be robustly self-calibrated in common sports scenes when placing artificial markers or towers in the calibration process is impractical, this article proposes a robust multicamera calibration method based on sequence feature matching and fusion. Additionally, to validate the effectiveness of the proposed calibration algorithm, a virtual axis fast bullet-time synthesis algorithm is proposed for generating a free-view video. First, camera self-calibration is performed in low-texture situations by fusing dynamic objects in time series to enrich geometric constraints in scenes without the use of calibration panels or additional artificial markers. Second, a virtual-axis bullet-time video synthesis method based on the calibration result is proposed. In the calibrated multicamera scenario, a fast bullet-time video is generated by constructing a virtual axis. Qualitative and quantitative experiments in comparison with a state-of-the-art calibration method demonstrate the validity and robustness of the proposed calibration algorithm for free-view video synthesis tasks.

Shadowgraph imaging is a promising technique for volumetric velocity measurements, which features a high framing rate, long depth focus, and a cheap light source. The main objective of the current study is to develop a camera calibration algorithm for collimated shadowgraph systems, which is an essential procedure for 3D particle tracking velocimetry (PTV) strategies. First, the optical model of a two-view collimated shadowgraph system is established, which can be described by the orthographic projection model. The image distortion effect is also taken into consideration. Then, the calibration algorithm is developed using a flexible planar-target-based method. Aiming towards 3D PTV applications, the extrinsic parameters, including rotation and translation relationships between the two camera imaging coordinates, have been derived. The ambiguity around the sign confirmation of the extrinsic parameters has been solved by introducing extra information from the relative positions of the two views. Moreover, extrinsic parameters self-calibration (EPSC) has been implemented to deal with unavoidable camera drifts during the experiments. The results indicate that the EPSC is effective in removing the global system error in the current two-view system. The proposed calibration algorithm has been verified using synthetic images, which has shown a mean reprojection error of less than 0.1 pixels. In a water jet experiment, the mean reprojection error is around 0.3 pixels (about 0.019 mm in reality) after the board calibration. The relative error evaluated from the reconstruction points is less than 1%. The results indicate that the proposed calibration procedure is effective and feasible for collimated shadowgraph imaging systems. The 3D-particle positions of a sample frame have been reconstructed successfully. It is believed that the high quality shadowgraph images can offer high precision measurements for further implementations of 3D PTV algorithms.

This paper presents a new algorithm of traditional camera calibration which is based on Extended Kalman Filter. The Extended Kalman Filter is a set of mathematical equations that provides an efficient way to estimate the state of a process. The technique of camera calibration can be divided into three kinds in practice, among which the traditional camera calibration has the highest precision. The substance of camera calibration is to figure out the intrinsic and extrinsic parameters of a camera for its further application in computer vision. In this paper, the image coordinates of the characteristics and the corresponding world coordinates are taken as the filter's inputs, the estimate value of these parameters are taken as the filter's outputs. Simulation and experiments results show the well optimization of this method.

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.

In order to be able to match correctly the track elements produced by a muon in the Tracker and the Muon System of the CMS experiment [1] the mutual alignment precision between the Tracker and the Barrel Muon System must be no worse than 100-400 micrometers depending on the radial distance of the muon chambers from the Tracker. To fulfill this requirement an alignment system had to be designed. This system contains subsystems for determining the positions of the barrel and endcap chambers while a third one connects these two to the Tracker. Since the Barrel muon chambers are embedded into the magnet yoke of the experiment a nonconventional alignment method had to be developed. In this paper we restrict ourselves to the Barrel Alignment System and the calibration methods of its components.

The conventional calibration methods based on a perspective camera model are not suitable for the underground camera with two-layer glasses, which is specially designed for explosion proof and dust removal in a coal mine. Underground camera modeling and calibration algorithms are urgently needed to improve the precision and reliability of underground visual measurement systems. This article presents a novel geometrically driven underground camera calibration algorithm for a boom-type roadheader. The underground camera model is established under coplanarity constraints, considering explicitly the impact of refraction triggered by the two-layer glasses and deriving the geometrical relationship of equivalent collinearity equations. On this basis, we perform parameters calibration based on a geometrically driven calibration model, which are 2D-2D correspondences between the image points and object coordinates of the planar target. A hybrid Levenberg-Marqurdt (LM) and particle swarm optimization (PSO) algorithm is further proposed in terms of the dynamic combination of the LM and PSO, which optimizes the underground camera calibration results by minimizing the error of the nonlinear underground camera model. The experimental results demonstrate that the pose errors caused by the two-layer glass refraction are well corrected by the proposed method. The accuracy of the cutting-head pose estimation has increased by 55.73%, meeting the requirements of underground excavations.

In mathematical terms, a camera maps all points on a 3D target object surface to a collection of 2D points on the image plane; a <i>camera model</i> thus relates the image coordinates to the physical locations of the object points in the FOV. Camera calibration refers to the process of deriving the internal (<i>intrinsic</i>) and external (<i>extrinsic</i>) parameters of the camera model and image-capture hardware. Intrinsic parameters embody the characteristics of the optical system and its geometric relationship with the image sensor, while extrinsic parameters relate the location and orientation of the camera with respect to the 3D object (Euclidean) space. The 3D object space is used for measuring the collection of object point coordinates [R{(<i>x_o</i>, <i>y_o</i>, <i>z_o</i>)}] in physical units that make up the target scene in the FOV. Extrinsic parameters are derived as a set of rigid body transformation matrices: three rotations about the <i>x</i>, <i>y</i>, and <i>z</i> axes, and three translations along these axes (block 1 in Fig. 8.1). The two sets of output from the extrinsic calibration process are fed into the intrinsic calibration process to make up the complete camera calibration model. In cinematography, rotations about the <i>x</i>, <i>y</i>, and <i>z</i> axes are called <i>pan</i>, <i>tilt</i>, and <i>roll</i>, respectively, and the movement along the <i>z</i> axis is called <i>zooming</i>.