Calibration Of Multi-camera System Research Articles

Calibration accuracy evaluation method for multi-camera measurement systems

To address the limitations of Digital Image Correlation (DIC) technology in terms of single-view and resolution capabilities, multi-camera systems have emerged, expanding the measurement area by increasing the number of cameras. However, traditional multi-camera systems continue to face challenges in the calibration of global external parameters and error control, particularly when uniform calibration between camera subsystems is not achieved, making the calibration results difficult to evaluate and analyze. In response, this paper systematically investigates the sources of error in multi-camera system calibration and proposes a novel precision evaluation method. This method qualitatively analyzes the registration results of subsystems by examining the determinant of the rotation matrix used to transform local coordinate systems to the global coordinate system and quantitatively assesses the registration accuracy based on the alignment error of targets after registration. Furthermore, a series of experiments were conducted to validate the proposed evaluation method, with results demonstrating that the method not only offers high effectiveness in precision evaluation but also provides reliable technical support in complex engineering measurements.

NMC3D: Non-Overlapping Multi-Camera Calibration Based on Sparse 3D Map.

With the advancement of computer vision and sensor technologies, many multi-camera systems are being developed for the control, planning, and other functionalities of unmanned systems or robots. The calibration of multi-camera systems determines the accuracy of their operation. However, calibration of multi-camera systems without overlapping parts is inaccurate. Furthermore, the potential of feature matching points and their spatial extent in calculating the extrinsic parameters of multi-camera systems has not yet been fully realized. To this end, we propose a multi-camera calibration algorithm to solve the problem of the high-precision calibration of multi-camera systems without overlapping parts. The calibration of multi-camera systems is simplified to the problem of solving the transformation relationship of extrinsic parameters using a map constructed by multiple cameras. Firstly, the calibration environment map is constructed by running the SLAM algorithm separately for each camera in the multi-camera system in closed-loop motion. Secondly, uniformly distributed matching points are selected among the similar feature points between the maps. Then, these matching points are used to solve the transformation relationship between the multi-camera external parameters. Finally, the reprojection error is minimized to optimize the extrinsic parameter transformation relationship. We conduct comprehensive experiments in multiple scenarios and provide results of the extrinsic parameters for multiple cameras. The results demonstrate that the proposed method accurately calibrates the extrinsic parameters for multiple cameras, even under conditions where the main camera and auxiliary cameras rotate 180°.

Calibration of Ring Multicamera System With Transparent Target for Panoramic Measurement

The calibration of a multicamera system is a prerequisite for high-accuracy measurement. In this study, a method for calibrating a ring multicamera system with a transparent target combined with digital image correlation (DIC) technology is proposed to achieve panoramic dynamic and static measurement of the object. The transparent target is placed in the middle of the ring camera array, and the target can be driven by the turntable to calibrate multiple cameras simultaneously. A complete refraction correction model is built on the transparent side of the target, and the corrected calibration data are integrated into the multicamera DIC system. The global optimization further improves the overall calibration accuracy of the system. Special markers are attached to the target surface to automatically identify the refractive and nonrefractive surfaces of the target. This type of camera can establish a coordinate relationship with the cameras on the other side of the target although no overlapping field of view exists between adjacent cameras on the same side of the target. The calibration data are analyzed, and dynamic and static experiments are implemented to verify the measurement accuracy of the system. All experimental results show that the calibration and measurement accuracies of the proposed method are high, and the system can be fully used for high-precision panoramic dynamic and static measurements.

Auto calibration of multi‐camera system for human pose estimation

The multi-camera calibration is an essential step for many spatially aware applications, such as robotic navigation, augmented reality, and 3D human pose estimation. Traditional calibration methods use off-the-shelf checkerboards or triangles as the known world coordinate system and their corresponding corners are set as control points, which heavily depends on specific calibration patterns and is not suitable for calibration pattern-denied environments. In this paper, an automatic calibration method is proposed to calibrate the multi-camera system without the aid of a known calibration pattern. The key idea of the proposed method is that the authors consider the human body, which is always available, as the counterpart of the calibration pattern. The authors’ approach starts with binocular camera calibration, in which the extrinsic and intrinsic parameters are calculated in order and followed by a joint optimisation. With the results of each pair of binocular camera calibration, the multi-camera system calibration is carried out in three steps: (i) parameters initialisation, (ii) extrinsic parameters optimisation, and (iii) jointly optimising intrinsic and extrinsic parameters. Since the authors’ approach does not require additional calibration patterns except for one visible person, it is flexible and easy to be implemented. Real experiments are conducted in different scenes, camera angles, and camera settings. Human pose estimation with the multi-camera system is additionally performed for exhaustive experiments. The experimental results demonstrate that the authors’ method shows superior performance than the traditional method with the aid of a specific calibration pattern.

Information-Theoretic Online Multi-Camera Extrinsic Calibration

Calibration of multi-camera systems is essential for lifelong use of vision-based headsets and autonomous robots. In this work, we present an information-based framework for online extrinsic calibration of multi-camera systems. While previous work largely focuses on monocular, stereo, or strictly non-overlapping field-of-view (FoV) setups, we allow arbitrary configurations while also exploiting overlapping pairwise FoV when possible. In order to efficiently solve for the extrinsic calibration parameters, which increase linearly with the number of cameras, we propose a novel entropy-based keyframe measure and bound the backend optimization complexity by selecting informative motion segments that minimize the maximum entropy across all extrinsic parameter partitions. We validate the pipeline on three distinct platforms to demonstrate the generality of the method for resolving the extrinsics and performing downstream tasks. Our code is available at <uri>https://github.com/edexheim/info_ext_calib</uri>.

Using images of partially visible chart for multi-camera system calibration

Incorporating in the geometric calibration images in which the calibration chart is only partially visible can help to make calibration process much more efficient and more accurate. This is particularly true in the case of systems involving a larger number of cameras. A calibration tool developed by us that makes it possible to utilize also images in which only a part of the chart can be detected is described and the benefits of using such a tool compared to the traditional checkerboard chart calibration are demonstrated. Examples illustrating the implications of the requirement that all chart points must be detected in the image on the spatial distribution of the corner points used for calibration are shown and the impact of the resulting distribution on the accuracy of the calibration is analyzed, using both synthetic and real data sets.

Efficient vision ray calibration of multi-camera systems.

Vision ray calibration provides imaging properties of cameras for application in optical metrology by identifying an independent vision ray for each sensor pixel. Due to this generic description of imaging properties, setups of multiple cameras can be considered as one imaging device. This enables holistic calibration of such setups with the same algorithm that is used for the calibration of a single camera. Obtaining reference points for the calculation of independent vision rays requires knowledge of the parameters of the calibration setup. This is achieved by numerical optimization which comes with high computational effort due to the large amount of calibration data. Using the collinearity of reference points corresponding to individual sensor pixels as the measure of accuracy of system parameters, we derived a cost function that does not require explicit calculation of vision rays. We analytically derived formulae for gradient and Hessian matrix of this cost function to improve computational efficiency of vision ray calibration. Fringe projection measurements using a holistically vision ray calibrated system of two cameras demonstrate the effectiveness of our approach. To the best of our knowledge, neither any explicit description of vision ray calibration calculations nor the application of vision ray calibration in holistic camera system calibration can be found in literature.

극한지 탐사 로버에 탑재된 다중 카메라 시스템의 캘리브레이션 실험

극한환경지역에서 무인 로버는 다양한 센서와 장비를 탑재하고 지형정보와 환경정보를 수집한다. 본 연구에서 제작한 무인 로버의 다중 카메라 시스템은 로버 원격 조작을 위한 6대의 주행 카메라와 지형 정보 구축을 위한 2대의 마스트 카메라로 구성된다. 로버의 다중 카메라 시스템으로부터 정확한 지형 정보와 효율적인 주행 정보를 취득하기 위해 캘리브레이션을 수행하였다. 먼저 로버에 탑재된 6대의 원근투영 카메라와 2대의 어안 등입체각 카메라를 대상으로 카메라 캘리브레이션을 수행하여 내부표정요소를 측정하였다. 시스템 캘리브레이션은 원-스텝과 투-스텝 기법을 이용하였고 카메라들의 상대적 외부표정요소를 측정하였다. 마지막으로 캘리브레이션의 결과와 오차원인을 분석하여, 향후 개선된 캘리브레이션을 수행하기 위한 방안을 고찰하였다.

Research on Calibration Method of Multi-camera System without Overlapping Fields of View Based on SLAM

The basis of multi-camera system measurement is the calibration of the multi-camera system. Although multi-camera system calibration has achieved certain results, there are still problems such as tedious calibration process and high calibration cost. In this paper, we propose a practical calibration method for multi-camera systems without overlapping fields of view. Firstly, a global 3D model of the scene is reconstructed using Simultaneous Localization and Mapping (SLAM). Then, each camera is calibrated using the 2D-3D correspondence between the images acquired by the multi-camera system and the 3D model. Finally, the external parameters of the multi-camera system are calibrated. In the process of using SLAM to build the model, the graph optimization is used to improve the accuracy of the modeling, and the accuracy of the calibration depends on the accuracy of the modeling. After several experiments, the experimental results show that the method is feasible.

Flexible global calibration of multiple cameras with nonoverlapping fields of view using circular targets.

Global calibration of multicamera systems is a difficult problem. The key is to find an appropriate calibration target. This paper proposes a flexible method to construct a global calibration target with circular targets. Any object that is to be measured by the system can be used as a calibration target with the help of a hand-held scanner. The calibration method does not need a special calibration target or multiple shots, which makes it flexible in applications. Circular targets pasted on the calibration target are used as features that are captured by cameras. The particle swarm optimization method is employed to correct the eccentricity error in the projection of circular targets. The eccentricity correction method does not need any prior knowledge except the cameras' intrinsic parameters. A synthetic data experiment was performed to validate the eccentricity correction method, and a physical experiment in a train wheelset inner-side distance measurement system was performed to validate the global calibration method. The measurement accuracy of the system was better than 0.1 mm, and the eccentricity correction method improved the three-dimensional reconstruction accuracy by about 0.1 mm.

Calibration of multi-camera photogrammetric systems

Abstract. Due to the low-cost and off-the-shelf availability of consumer grade cameras, multi-camera photogrammetric systems have become a popular means for 3D reconstruction. These systems can be used in a variety of applications such as infrastructure monitoring, cultural heritage documentation, biomedicine, mobile mapping, as-built architectural surveys, etc. In order to ensure that the required precision is met, a system calibration must be performed prior to the data collection campaign. This system calibration should be performed as efficiently as possible, because it may need to be completed many times. Multi-camera system calibration involves the estimation of the interior orientation parameters of each involved camera and the estimation of the relative orientation parameters among the cameras. This paper first reviews a method for multi-camera system calibration with built-in relative orientation constraints. A system stability analysis algorithm is then presented which can be used to assess different system calibration outcomes. The paper explores the required calibration configuration for a specific system in two situations: major calibration (when both the interior orientation parameters and relative orientation parameters are estimated), and minor calibration (when the interior orientation parameters are known a-priori and only the relative orientation parameters are estimated). In both situations, system calibration results are compared using the system stability analysis methodology.

Multi-camera System Calibration with Built-in Relative Orientation Constraints (Part 1) Theoretical Principle

In recent years, multi-camera systems have been recognized as an affordable alternative for the collection of 3D spatial data from physical surfaces. The collected data can be applied for different mapping(e.g., mobile mapping and mapping inaccessible locations)or metrology applications (e.g., industrial, biomedical, and architectural). In order to fully exploit the potential accuracy of these systems and ensure successful manipulation of the involved cameras, a careful system calibration should be performed prior to the data collection procedure. The calibration of a multi-camera system is accomplished when the individual cameras are calibrated and the geometric relationships among the different system components are defined. In this paper, a new single-step approach is introduced for the calibration of a multi-camera system (i.e., individual camera calibration and estimation of the lever-arm and boresight angles among the system components). In this approach, one of the cameras is set as the reference camera and the system mounting parameters are defined relative to that reference camera. The proposed approach is easy to implement and computationally efficient. The major advantage of this method, when compared to available multi-camera system calibration approaches, is the flexibility of being applied for either directly or indirectly geo-referenced multi-camera systems. The feasibility of the proposed approach is verified through experimental results using real data collected by a newly-developed indirectly geo-referenced multi-camera system.

Multi-camera System Calibration with Built-in Relative Orientation Constraints (Part 2) Automation, Implementation, and Experimental Results

Multi-camera systems have been widely used as cost-effective tools for the collection of geospatial data for various applications. In order to fully achieve the potential accuracy of these systems for object space reconstruction, careful system calibration should be carried out prior to data collection. Since the structural integrity of the involved cameras' components and system mounting parameters cannot be guaranteed over time, multi-camera system should be frequently calibrated to confirm the stability of the estimated parameters. Therefore, automated techniques are needed to facilitate and speed up the system calibration procedure. The automation of the multi-camera system calibration approach, which was proposed in the first part of this paper, is contingent on the automated detection, localization, and identification of the object space signalized targets in the images. In this paper, the automation of the proposed camera calibration procedure through automatic target extraction and labelling approaches will be presented. The introduced automated system calibration procedure is then implemented for a newly-developed multi-camera system while considering the optimum configuration for the data collection. Experimental results from the implemented system calibration procedure are finally presented to verify the feasibility the proposed automated procedure. Qualitative and quantitative evaluation of the estimated system calibration parameters from two-calibration sessions is also presented to confirm the stability of the cameras' interior orientation and system mounting parameters.

Improved foundamental matrix computation and optimization method in parallel calibration of multi-camera system

Multi-camera system has a number of cameras and complex space distribution,hence the calibration in multicamera system is inefficient.The calculation of fundamental matrix and nonlinear optimization are the key steps in camera calibration algorithm.In the light of independent marked points in multi-camera system calibration,fundamental matrix based on RANdom SAmple Consensus(RANSAC) and increment equation in nonlinear optimization were improved,and a parallel calibration algorithm for multi-camera system was proposed.Based on the analysis of the parallel process of calibration,this algorithm improved the efficiency of the calibration time.Compared with the traditional camera calibration algorithm,it makes the time complexity of calibration reduce from O(n3) to O(n).The experiments show that the parallel algorithm reduces the time obviously without any loss in precision,thus realizing fast multi-camera system calibration.

Comparative Analysis of Different Approaches for Multi-camera System Calibration

Mobile mapping systems integrate a set of imaging sensors and a position and orientation system. To fully achieve the accuracy of the utilized sensors, a careful system calibration should be carried out. The system calibration involves individual sensor calibration and the mounting parameters calibration relating the system components. For multi-camera systems, the mounting parameters involve two sets of relative orientation parameters (ROP): the ROP among the cameras and the ROP between the cameras and the navigation sensors. This paper proposes a mathematical model for a single-step photogrammetric system calibration suitable for both single and multi-camera systems. As a special case of this model, indirect geo-referencing can be performed with relative orientation constraints (ROC). A general model which allows the estimation of ROP as wells as the incorporation of prior information on the ROP among the cameras during the integrated sensor orientation (ISO) is also proposed. This general model can be used for the indirect georeferencing with ROC as well as ISO without ROP among the cameras. To evaluate the performance of the single-step system calibration using the different models, real dataset captured by a hand-held multi-camera system is used. The system calibration is performed by using five different models and the performance is compared among these models.

Calibration of multi-camera systems with refractive interfaces

A method for performing bundle adjustment–based calibration of a multi-camera setup with refractive interfaces in the optical path is presented. The method contributes to volumetric multi-camera fluid experiments, where it is desirable to avoid tedious alignment of calibration grids in multiple locations and where a premium is placed on accurately locating world points. Cameras are calibrated from image point correspondences of unknown world points, and the location of the refractive interface need not be accurately known a priori. Physical models for two practically relevant imaging configurations are presented; the first is a planar wall separating cameras and a liquid, and the second is a liquid-containing cylindrical tank with finite wall thickness. Each model allows the cameras to be in general location and orientation relative to the interface. A thorough numerical study demonstrates the ability of the calibration method to accurately estimate camera parameters, interface orientation, and world point locations. The numerical study explores the convergence, accuracy, and sensitivity of the calibration method as a function of initialization, camera configuration, volume size, and interface type. The technique is applied to real calibration data where the algorithm is supplied with errant initial parameter estimates and shown to provide accurate results. The ease of implementation and accuracy of the refractive calibration method make the approach attractive for three-dimensional multi-camera fluid measurement methods.

Multi-Camera Network Calibration with a Non-Planar Target

The rapid calibration of multi-camera systems using a planar target is typically impractical due to the difficulty of viewing the target in each camera simultaneously. To address these short-comings, a complete calibration methodology using a novel non-planar target for rapid calibration of inward-looking visual sensor networks (VSNs) is presented. We discuss the practical limitations of the approach, arising from an analysis of implementation issues when using spheres as calibration targets such as target-to-target and target-to-camera orientation relationships. This procedure is applied to fully calibrate (intrinsic and extrinsic camera parameters) a twelve camera inward-looking VSN, using only a single image per camera. Results from the calibration are compared for nominal and measured dimensions of the target.

Global Calibration of Multi-camera System Based on 1D Target

Based on the property that all feature points of 1D target are collinear, a global calibration method of multi-camera system is proposed.The global coordinate frame is constructed based on one of cameras, called the base camera.1D dimensional target is positioned arbitrarily in front of both the base camera and the camera to be calibrated.The vanishing point of 1D target in the image is determined.According to the property that all feature points of 1D target are collinear, the coordinates of all feature points on 1D target in each camera coordinate frame are computed.The transformation matrix from the camera to be calibrated to the base camera is solved, and optimized by using the non-linear optimization method.The global calibration of multi-camera system is realized by pair-wise calibration between the base camera and each of the cameras to be calibrated.The proposed method can be carried out without any high-accuracy 3D measuring equipment.Experiment results show that the method is simple and practical.

Image sequence based automatic multi-camera system calibration techniques

An image sequence-based, fully automatic and rather flexible procedure for the calibration of stationary multi-camera systems for 3-D observation of dynamic events is presented and analysed. While conventional close-range camera calibration techniques are either based on a stable point-field with known reference coordinates or on a temporarily stationary point-field with only approximately known 3-D coordinates, which is imaged from different locations and under different orientations with one single camera, the presented technique is based on stationary cameras and moving targets, making use of the image sequence acquisition nature of most solid state cameras. In the simplest version, only one easily detectable marker has to be tracked through image sequences of multiple pre-calibrated cameras, thus avoiding the necessity of homologous feature identification for the establishment of multi-view correspondences; 3-D coordinates of the marker position are not required. This single-marker method does not allow for the determination of the interior orientation. In an extended version allowing for full camera orientation and calibration, a reference bar of known length is moved through object space, with the problem of feature identification and establishment of multi-view correspondences being reduced to the tracking of two targets. The method can only be used with multi-camera systems and is most useful for 3-D motion analysis applications, but may be adapted to a wide range of other applications. The advantages of the method over conventional self-calibration techniques are the trivial establishment of multi-view correspondences, the fact that no temporarily stable target field has to be constructed, and the fact that each camera has to be set up only once. After an explanation of the technique, its performance is examined in detail based on extensive computer simulations, and the practical effectiveness is shown in a pilot study on industrial robot calibration. Based on these studies, recommendations are given concerning the number of reference bar locations, preferable reference bar orientation schemes and the achievable accuracy potential.

Accurate and simple geometric calibration of multi-camera systems

In this paper we present a low-cost, accurate and flexible approach to the calibration of multi-camera acquisition systems for 3D scene modeling. The adopted calibration target-set is just a marked planar surface, which is imaged in several positions in order to emulate a larger 3D target-frame. In order to obtain a better camera parameter estimation, the proposed approach is able to refine the a priori knowledge on the target-set through a process of self-calibration. This allows us to start with rough measurements of the coordinates of the calibration targets. We formalize our parameter estimation problem as a particular case of the more general class of inverse problem. In particular, we derive an analytic prediction of the calibration performance, based on error propagation analysis, whose correctness is demonstrated through simulation experiments. Finally, the results of a series of calibration experiments on real data is presented, which confirm the effectiveness of approach in a variety of experimental conditions.