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Accurate and robust marker localization algorithm for camera calibration
Abstract
We design a new scheme for the accurate localization of markers in images of calibration plates. This forms the basis of so-called fixed or strong camera calibration methods. We focus on the most widely used plates with circular markers arranged in a regular grid. Our algorithm is fully automatic and very robust. We assess its results by using synthetic images containing noise and other practical image detoriations. Compared with the ground truth of the marker positions, we obtain a localization precision of 0.01 pixel in high-quality images, and 0.03 pixel in very bad quality images (high noise, low contrast, lens distortion, CCD misplacements). With these results, the algorithm outperforms all existing algorithms from the literature.
... Motion capture can also be used in fields such as art and design. Knowledge about human movement can here be used to guide the design of ergonomically correct objects for humans to interact with, to animate virtual mannequins or as an expression in performance art (Redert, et. al., 2002). Motion capture has also been suggested for use in virtual tours through museums and galleries (Hernandez-Rebollar, et. al., 2004;Redert, et. al., 2002;Aggrwal and Cai, 1999;Molina, et. al., 2005b;Gavrila, 1997;Moeslund and Granum, 2001) ...
... wledge about human movement can here be used to guide the design of ergonomically correct objects for humans to interact with, to animate virtual mannequins or as an expression in performance art (Redert, et. al., 2002). Motion capture has also been suggested for use in virtual tours through museums and galleries (Hernandez-Rebollar, et. al., 2004;Redert, et. al., 2002;Aggrwal and Cai, 1999;Molina, et. al., 2005b;Gavrila, 1997;Moeslund and Granum, 2001) ...
... inary step to machine vision and is conducted to ensure that vision systems process data based on a correct interpretation of the scene (Gremban, et. al., 1988;Heikkila and Silven, 1997;Lee and Jeong, 2000;Tsai, 1987;Wei and Ma, 1994). To calibrate the capturing system, is therefore essential if one aims to capture and reconstruct accurate 3D data (Redert, et. al., 2002;Repko, 2005). The calibration process is commonly guided by information extracted from easily identifiable feature points within the scene referred to as calibration points. These calibration points can be generated by either natural scene characteristics or manually introduced markers, and the accuracy of the calibration process is infl ...
... He later applied this marker localization technique to camera calibration [6] [7] and, using a dihedron as target, obtained high-quality results with a residual error of 0.02 pixels. Developing this technique, Redert et al. added second-order corrections by weighting the pixel intensities with their true area and taking into account image curvature [8]. Residual errors as low as 0.01 pixels were obtained. ...
... The accuracy remains stable over most of the noise range and increases steadily with the interface perimeter of the calibration marker. For large calibration markers, calibration accuracy remains below 0.003 pixels even with a very low SNR of 8.2 dB, clearly outperforming other calibration techniques [3] [8] . This robustness is attributed to the averaging of the noise across the whole effective perimeter of the calibration marker. ...
Accurate measurement of the position of features in an image is subject to a fundamental compromise: The features must be both small, to limit the effect of nonlinear distortions, and large, to limit the effect of noise and discretization. This constrains both the accuracy and the robustness of image measurements, which play an important role in geometric camera calibration as well as in all subsequent measurements based on that calibration. In this paper, we present a new geometric camera calibration technique that exploits the complete camera model during the localization of control markers, thereby abolishing the marker size compromise. Large markers allow a dense pattern to be used instead of a simple disc, resulting in a significant increase in accuracy and robustness. When highly planar markers are used, geometric camera calibration based on synthetic images leads to true errors of 0.002 pixels, even in the presence of artifacts such as noise, illumination gradients, compression, blurring, and limited dynamic range. The camera parameters are also accurately recovered, even for complex camera models.
The 3D coordinates of measured point is embodied in 2D image coordinate of the optical characteristic point via the visual measurement system. Based on the gray square weighted centroid localization algorithm, the paper presents bicubic interpolation gray square weighted centroid localization algorithm, increases the number of effective pixels around the optical characteristic point imaging center, and reduces noise error via the gray square weighted, improves the imaging center location accuracy of optical characteristic point, realizes the accurate location of the optical characteristic points. Results indicate application of the proposed algorithm to location, the standard tolerance along the direction of x is 0.0022 Pixel, the standard tolerance along the direction of y is 0.0023 Pixel, compared with the others, the standard tolerance is minimum and discrete to a lesser degree distancing ideal image point, that is, the proposed algorithm has higher location accuracy. The maximum tolerance along the direction of x is 0.008 Pixel, the one along the direction of y is 0.007 Pixel, compared with the other two algorithms, the maximum tolerance is minimum .Results indicate that the stability of the proposed algorithm is better.
Model Deformation Measurement is becoming a major topic in wind tunnel testing, especially for commercial applications. Onera has developed a solution which is used in several wind tunnels. The system uses two cameras in stereoscopic arrangement and the model shape is measured with markers. The main steps are: camera calibration, initial shape recognition, alignment of the calibration body reference system on the model reference system, wind tunnel testing and post processing. The wing twist uncertainty is lower than 0.05° which is the main requirement. The system can work at is best in real time conditions and can be easily adapted to each test section.
An important task in most 3D measurement systems based on machine vision is camera calibration, whose objective is to estimate the internal and external parameters of each camera. A new accurate calibration method with multilevel process of camera parameter is presented. Flexibly making use of geometry imaging theory, our algorithm obtain all the parameters through logical organization of solving order, accordingly avoid obtaining possible local optimized problem when solving the non-linear equation. The camera model is aimed at efficient computation of camera extrinsic and intrinsic parameters considering lens distortion, which are solved dividedly. Built on strict geometry constraint, our calibration method gets over the relativity influence of every unknown parameters of traditional calibration way, and makes the error distributed among the constraint relation of parameters, in order to guarantee the accuracy. Experimental results are provided to show that the accuracy is high.
Camera calibration is one of critical steps in computer vision, also an exhaustive process because substantial human computer interactions are frequently required to deal with the matching problem. In this paper, an automatic matching method of markers for camera calibration is presented based on the local architecture characteristics of a new planar circle pattern, which can be applied to a wide range of spoiled images including those of distortion, noise, and blur. Firstly, a robust ellipse detector is developed to extract ellipses from the image. After the centroids of the ellipses are triangulated into triangle network by Delaunay method to find k annular neighborhood of each ellipse, a cost function is defined to locate orientation ellipses for the homography matrix between the image and the calibration pattern. Then the correspondences between the marker ellipses and the marker circles are established by a homography method followed by a point sets registration strategy. Finally, the method is tested with real and transformed images to show its accuracy and robustness, which is entirely unsupervised and easily embedded into the exiting algorithms.
In this paper, the authors present a new practicable method and the related measurement station for digital-to-analog converters (DAC) characterization. The method relies on the accurate reconstruction of a sine-wave test signal generated by the DAC under test based on the simultaneous acquisitions of the signal attained by filtering the DAC output and the difference between the DAC output and the filter output. Thus, due to straightforward data processing, the signal generated by the DAC is gained with a resolution much better than the resolution (usually poor) of the analog-to-digital converter (ADC) exploited for the acquisition. The main feature of the method is the ease of implementation that requires only traditional electronics and actual measurement instrumentation. In this paper, the authors also suggest simple rules aimed at evaluating the resolution achievable by each guessed measurement station. To confirm the expected encouraging outcomes, experimental results obtained through a measurement station implemented by using a two-channel 8-bit digital scope and based on the presented method are discussed. In particular, signals generated by 12- and 14-bit DACs have been acquired and processed with the measurement station and reconstructed, with a resolution greater than 17 equivalent bits, due to the proposed method.
In this paper, a prototype system that is able to reproduce all the functionalities of an automatic glass inspection system is presented. The proposed quality inspection system assures several advantages with respect to the human-made inspection, such as objectivity and accuracy, and it is attractive for small enterprises with respect to commercial vision systems because it guarantees good results and considerable reliability with low incidence on manufacturing costs. In particular, it was proposed in this paper a method, based on morphological operations, for registering the acquisition system, which is composed of several cameras that acquire different partial images of the entire glass sheet moving on a conveyor. A method for digitally correcting the nonuniformities of the lighting system is also discussed; it is based on a least squares spline approximation of the intensity profile. The presented methods are rather general and can be applied to the calibration of image acquisition systems in other application fields.
In this paper, the problem of detecting and measuring the defects of satin glass is investigated, and an in-line PC-based visual inspection system is proposed; this system is able to analyze the glass surface under inspection, to discover and classify its defects, and to assess the product quality. A working prototype of this system has been designed, built and tested to validate the proposed approach and to reproduce the real issues of an in-line quality control system. The developed prototype includes three subsystems: an array of several CMOS cameras, a controllable roller conveyor, and a PC-based image processing system that is also responsible for the control of the other subsystems. The detection of the defects is performed by means of Canny edge detection, with thresholds chosen according to some statistics of the images being processed. Currently, the prototype is under further development in cooperation with a specialized electronic industry.
In this paper we present a technique for the accurate calibration of a multiple-camera image acquisition systems used for applications to 3D reconstruction of scenes. The main characteristic of this technique is the fact that it allows us to obtain highly accurate calibrations even when using a very simple and inexpensive calibration target such as a planar pattern. This has been made possible by exploiting the geometry constraints of a multiple-camera acquisition system and by applying a self-calibrating approach that estimates the camera parameters and, at the same time, refines the estimation of the exact position of the calibration pattern's fiducial points. Experiments with rather different setups have been carried out in order to test the proposed calibration techniques in a variety of conditions. The calibration performance, in terms of accuracy of the measured camera parameters, have been predicted through error propagation analysis and verified experimentally through measurement error estimation.
This monograph by one of the world's leading vision researchers provides a thorough, mathematically rigorous exposition of a broad and vital area in computer vision: the problems and techniques related to three-dimensional (stereo) vision and motion. The emphasis is on using geometry to solve problems in stereo and motion, with examples from navigation and object recognition.
In this paper the problem of obtaining 3D models from image sequences is addressed. The presented method deals with uncalibrated monocular image sequences. No prior knowledge about the scene or about the camera is necessary to build the 3D models. This approach is very flexible, even allowing the camera zoom to be used, and has no restriction on the size of the scenes.
The use of a flat calibration object with a known 2-D control point distribution for simultaneous estimation of internal and external camera parameters in whole-body movement studies allows coverage of the full observation area as required to avoid extrapolation errors in subsequent 3-D trajectory reconstruction, without the cumbersomeness of more conventional 3-D calibration objects designed to cover the whole observation area. In this adaptation of Simultaneous Multiframe Analytical Calibration (S.M.A.C.), the use of certain oblique (convergent) observations or frames on a planar control distribution allows full recovery of all internal camera parameters, by simultaneous estimation of the various frame positions and attitudes with respect to the camera. Calibration of a second camera whether real or virtual as in mirror photography may be conducted by observing at least one frame through both cameras. The procedure is initialized by means of the fractional linear transformation describing central projection between two planes; the only a priori information required in this approach is an approximate value for the camera principal point; no initial values are generally required for camera principal distance or for the various frame positions and attitudes. In the present paper, the theory and implementation of planar S.M.A.C. are discussed, followed by results from simulation studies. Experimental work is currently in progress.
A new technique for three-dimensional (3D) camera calibration for machine vision metrology using off-the-shelf TV cameras and lenses is described. The two-stage technique is aimed at efficient computation of camera external position and orientation relative to object reference coordinate system as well as the effective focal length, radial lens distortion, and image scanning parameters. The two-stage technique has advantage in terms of accuracy, speed, and versatility over existing state of the art. A critical review of the state of the art is given in the beginning. A theoretical framework is established, supported by comprehensive proof in five appendixes, and may pave the way for future research on 3D robotics vision. Test results using real data are described. Both accuracy and speed are reported. The experimental results are analyzed and compared with theoretical prediction. Recent effort indicates that with slight modification, the two-stage calibration can be done in real time.
In geometrical camera calibration the objective is to determine a set of camera parameters that describe the mapping between 3-D reference coordinates and 2-D image coordinates. Various methods for camera calibration can be found from the literature. However surprisingly little attention has been paid to the whole calibration procedure, i.e., control point extraction from images, model fitting, image correction, and errors originating in these stages. The main interest has been in model fitting, although the other stages are also important. In this paper we present a four-step calibration procedure that is an extension to the two-step method. There is an additional step to compensate for distortion caused by circular features, and a step for correcting the distorted image coordinates. The image correction is performed with an empirical inverse model that accurately compensates for radial and tangential distortions. Finally, a linear method for solving the parameters of the inverse model is presented
In this article, we present some simple and effective techniques
for accurately calibrating a multi-camera acquisition system. The
proposed methods were proven to be capable of accurate results even when
using very simple calibration target sets and low-cost imaging devices,
such as standard TV-resolution cameras connected to commercial
frame-grabbers. In fact, the performance of our calibration approach
yielded results that were about the same as that of other traditional
calibration methods based on large 3D target sets. The proposed
calibration strategy is based on a multi-view multi-camera approach.
This was based on the analysis of a number of views of a simple
calibration target-set placed in different (unknown) positions.
Furthermore, the method is based on a self-calibration approach, which
can refine the a priori knowledge of the world coordinates of the
targets (even when such information is very poor) while estimating the
parameters of the camera model. Finally we proposed a method, to make
the calibration technique adaptive through the analysis of natural scene
features, allowing the camera parameters to hold accurate throughout the
acquisition session in the presence of parameter drift
This thesis develops new algorithms to obtain the calibration parameters of a camera using only information contained in an image sequence, with the objective of using the camera calibration to compute a Euclidean reconstruction. This problem is known as selfcalibration. The motivation for this work is to allow the Euclidean reconstruction of a scene using only a pre-recorded image sequence where no information is available on the camera or the objects in the scene. The approach used is to utilise known motion constraints, which are common for cameras mounted on mobile vehicles or robotic arms, to simplify the algebraic complexity of the self-calibration problem. The algorithms are designed to be easily extendible to use multiple images rather than the minimum number of three required for self-calibration. The uncertainty of the parameters are also computed to give a measure of confidence in the camera calibration. The first method uses a pure camera translation to allow the problem to...
The design of a camera calibration system
- I Van Den Eelaart
I. van den Eelaart, "The design of a camera calibration
system", Research report, ICT Group, Delft University
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Flexible acquisition of 3D structure from motion
- M Pollefeys
- R Koch
- M Vergauwen
- L Van Gool
M. Pollefeys, R. Koch, M. Vergauwen and L. Van Gool,
"Flexible acquisition of 3D structure from motion", in
Proceedings of the IEEE Image and Multidimensional
Digital Signal Processing (IMDSP) Workshop '98, pp.
195-198, 1998