Planar Calibration Research Articles

Image‐enhanced surgical navigation for endoscopic sinus surgery: evaluating calibration, registration and tracking

Endoscopic sinus surgery (ESS) is generally applied to treat sinusitis when medication is not effective in eliminating the symptoms. Images captured by the endoscope are viewed on a monitor placed near the surgeon. Due to the separation of the handling of the endoscope from the viewing of the image, ESS requires surgeons to have well-trained hand-eye coordination. Unlike the use of the stereo surgical microscope in ENT, the endoscope does not provide the stereo cue for depth perception, hence a surgeon can only perceive depth through motion and shading, which may affect the accuracy of tool placement. Whilst the skill and experience of the surgeon are important factors to the success of ESS, the assistance of image-enhanced surgical navigation (IESN) can further reassure the surgeon's judgement and enhance surgical performance. We developed and validated an IESN system (ARView) for a rigid zero-degree endoscope, typically used for ESS. We present the interface, and calibration and registration (pre-operative and intra-operative) methods of the system. We then quantitatively assess the performance of each of the steps needed to generate the overlay of a real endoscope image with its 'virtual' counterpart, obtained from computed tomography (CT) image data of a real skull. These steps include calibration, registration, motion tracking and final overlay. Calibration results using a planar calibration object displayed optimized object space errors of 0.025 +/- 0.013 mm, whilst a non-planar calibration object displayed errors of 0.12 +/- 0.08 mm. Target registration errors (TREs) near the region of interest (ROI), using our pre-operative registration method with the calibration object located near the mouth of the patient (skull), were 2.3 +/- 0.4 mm. The proposed photo-consistency method for intra-operative registration has not yet yielded satisfactory results for ESS-based IESN. (RMS) values for tracking accuracy were found to be around 1.2 mm in a typical workspace of 400 x 400 mm. Object space overlay errors in a small measurement volume of 10 x 10 x 10 mm were found to be around 0.4 +/- 0.02 mm. We conclude that, in agreement with individual experiments, the current overall overlay accuracy is of the order of 2-3 mm in the x-y plane, which is in line with current conventional SN systems. The method which is most in need of improvement is registration, hence we wish to investigate the application of the proposed photo-consistency method further.

Parameter-Free Radial Distortion Correction with Center of Distortion Estimation

We propose a method of simultaneously calibrating the radial distortion function of a camera and the other internal calibration parameters. The method relies on the use of a planar (or, alternatively, nonplanar) calibration grid which is captured in several images. In this way, the determination of the radial distortion is an easy add-on to the popular calibration method proposed by Zhang [24]. The method is entirely noniterative and, hence, is extremely rapid and immune to the problem of local minima. Our method determines the radial distortion in a parameter-free way, not relying on any particular radial distortion model. This makes it applicable to a large range of cameras from narrow-angle to fish-eye lenses. The method also computes the center of radial distortion, which, we argue, is important in obtaining optimal results. Experiments show that this point may be significantly displaced from the center of the image or the principal point of the camera.

A large-scale laser plane calibration system

A large-scale laser plane calibration system is developed. This plane is constructed by a 35 m long horizontal granite guide rail and a 1.5 m long vertical metal guide rail. Two dual-frequency interferometers are used to measure the coordinates of a target moving on the plane. One of them can measure the horizontal displacement while eliminating the Abbe errors caused by the straightness of the granite guide rail. Another measures the sum of horizontal displacement and vertical displacement. This laser plane can be used as a lab standard to calibrate portable coordinate measuring machines by measuring the target on the plane. Calibration tests for a laser tracker are given.

Improved Evaluation of Planar Calibration Standards Using the TDR Preselection Method

Calibration and correction methods for the Vector Network Analyzer (VNA) are based on the fundamental assumption of the constant error model, which is independent of connected calibration standards and/or devices under test (DUT). Unfortunately, this assumption is not satisfied well for planar calibration standards fabricated by etching technology on soft substrates. An evaluation of the error model is affected especially by variations in the manufacturing process and also by the reproducibility of an assembly. In this paper, we propose error minimization by selecting the best combination of available calibration standards based on time domain reflection (TDR) measurement, which can also be obtained by the fourier transformation from the measured S-parameters. The proposed method was verified experimentally using short, open, load and thru (SOLT) standards fabricated on an FR4 laminate substrate which achieves the essential reduction of the measurement error in the frequency range up to 15 GHz.

Which pattern? Biasing aspects of planar calibration patterns and detection methods

This paper provides a comparative study on the use of planar patterns in the generation of control points for camera calibration. This is an important but often neglected aspect in camera calibration. Two popular checkerboard and circular dot patterns are each examined with two detection strategies for invariance to the potential bias from projective transformations and nonlinear distortions. It is theoretically and experimentally shown that circular patterns can potentially be affected by both biasing sources. Guidelines are given to control such bias. In contrast, appropriate checkerboard detection is shown to be bias free. The findings have important implications for camera calibration, indicating that well accepted methods may give poorer results than necessary if applied naively.

Recognition and location of the internal corners of planar checkerboard calibration pattern image

The recognition and location of the internal corners of a planar checkerboard calibration pattern image is very important to camera calibration. An effective approach is proposed to automatically recognize and locate the internal corners of the planar checkerboard calibration pattern image based on the characteristics of local intensity and the grid line architecture of the planar checkerboard pattern image. The proposed procedure consists of the detection of image corners, the recognition of the corners at the intersections of black and white squares and the recognition of the corners at the intersections of two groups of grid lines. Experiments show that compared with the commonly used interactive method, the proposed approach obviously reduces the time cost for camera calibration, speeds up calibration process and is especially adapted for automatic calibration based on multiple images.

Radiometric calibration of vision cameras and intensity uncertainty estimation

The irradiance measurement performed by vision cameras is not noise-free due to both processing errors during CCD fabrication and the behaviour of the electronic device itself. A proper characterization of sensor performance, however, allows either removing the resulting noise from the image or accounting for it within image processing algorithms. This paper proposes a robust algorithm named R 2CIU for characterizing the noise sources affecting CCD performance with the aim of estimating the uncertainty of the intensity values yielded by vision cameras. R 2CIU makes use of sets of images of plane calibration cards such that, for every set, the average intensity changes. As it is shown in the paper, the (spatial) average and variance of (temporal) average images of every set lie in a parabola, while the (spatial) averages of the (temporal) average and variance images of every set lie in a straight line. R 2CIU exploits these two facts to compute the noise source distribution parameters by least-squares fitting. Intensity uncertainties are estimated next by a sum in quadrature of the variances of the different noise sources involved in the process of image formation. Experimental results and application examples can be found at the end of the paper.

Assessment of camera models for use in planar velocimetry calibration

The performance of three implementations of pinhole-based camera models for use in common light-sheet imaging arrangements is investigated on the background of application to particle image velocimetry (PIV) and Doppler global velocimetry (DGV). Calibration data obtained from translated planar calibration targets was found to yield camera attitude within 0.1° on four different test cases with object distance varying as little as 2% depending on the choice of camera model. Camera calibration using data from a single image of coplanar points is considered a viable alternative to manual triangulation of camera positions but is restricted to off-normal viewing directions.

Extensions of Plane-Based Calibration to the Case of Translational Motion in a Robot Vision Setting

In this paper, a technique for calibrating a camera using a planar calibration object with known metric structure, when the camera (or the calibration plane) undergoes pure translational motion, is presented. The study is an extension of the standard formulation of plane-based camera calibration where the translational case is considered as degenerate. We derive a flexible and straightforward way of using different amounts of knowledge of the translational motion for the calibration task. The theory is mainly applicable in a robot vision setting, and the calculation of the hand-eye orientation and the special case of stereo head calibration are also being addressed. Results of experiments on both computer-generated and real image data are presented. The paper covers the most useful instances of applying the technique to a real system and discusses the degenerate cases that needs to be considered. The paper also presents a method for calculating the infinite homography between the two image planes in a stereo head, using the homographies estimated between the calibration plane and the image planes. Its possible usage and usefulness for simultaneous calibration of the two cameras in the stereo head are discussed and illustrated using experiments

A fully automated calibration method for an optical see-through head-mounted operating microscope with variable zoom and focus

Ever since the development of the first applications in image-guided therapy (IGT), the use of head-mounted displays (HMDs) was considered an important extension of existing IGT technologies. Several approaches to utilizing HMDs and modified medical devices for augmented reality (AR) visualization were implemented. These approaches include video-see through systems, semitransparent mirrors, modified endoscopes, and modified operating microscopes. Common to all these devices is the fact that a precise calibration between the display and three-dimensional coordinates in the patient's frame of reference is compulsory. In optical see-through devices based on complex optical systems such as operating microscopes or operating binoculars-as in the case of the system presented in this paper-this procedure can become increasingly difficult since precise camera calibration for every focus and zoom position is required. We present a method for fully automatic calibration of the operating binocular Varioscope M5 AR for the full range of zoom and focus settings available. Our method uses a special calibration pattern, a linear guide driven by a stepping motor, and special calibration software. The overlay error in the calibration plane was found to be 0.14-0.91 mm, which is less than 1% of the field of view. Using the motorized calibration rig as presented in the paper, we were also able to assess the dynamic latency when viewing augmentation graphics on a mobile target; spatial displacement due to latency was found to be in the range of 1.1-2.8 mm maximum, the disparity between the true object and its computed overlay represented latency of 0.1 s. We conclude that the automatic calibration method presented in this paper is sufficient in terms of accuracy and time requirements for standard uses of optical see-through systems in a clinical environment.

Multiview camera-calibration framework for nonparametric distortions removal

This paper proposes a technique that uses a planar calibration object and projective constraints to calibrate parametric and nonparametric distortions. An iterative surface fitting is first used to constrain a B-spline distortion model by fusing the corrective distortion maps obtained from multiple views. The model is then refined within the whole camera-calibration process.

S-PIV comparative assessment: image dewarping+misalignment correction and pinhole+geometric back projection

This study describes the comparative analysis of two stereoscopic particle image velocimetry (S-PIV) techniques. Emphasis is given to the accuracy of the calibration procedure. Both techniques are related to the angular displacement concept. The first method is based on the pinhole model and is taken as a reference. The second method is based on two steps: the cross-correlation of a calibration pattern to obtain the image’s dewarping function; and the cross-correlation of experimental images to evaluate and correct for the misalignment between the calibration and measurement planes. The methods’ accuracy is compared on the basis of experimental data from a translation–rotation stage, which allows to simulate uniform displacements and misalignments in terms of offset and rotation. The simulation shows that the measurement accuracy is highly sensitive to relative misalignment between the target and measurement planes. A misalignment correction procedure taking into account the residual disparity between the dewarped images is proposed, compensating for most of the error with an overall less sensitive method to the misalignment.

Precision open-ended coaxial probes for in vivo and ex vivo dielectric spectroscopy of biological tissues at microwave frequencies

Hermetic stainless-steel open-ended coaxial probes have been designed for precision dielectric spectroscopy of biological tissue, such as breast tissue, over the 0.5-20-GHz frequency range. Robust data-processing techniques have also been developed for extracting the unknown permittivity of the tissue under test from the reflection coefficient measured with the precision probe and a vector network analyzer. The first technique, referred to as a reflection-coefficient deembedding method, converts the reflection coefficient measured at the probe's calibration plane to the desired aperture-plane reflection coefficient. The second technique uses a rational function model to solve the inverse problem, i.e., to convert the aperture-plane reflection coefficient to the tissue permittivity. The results of the characterization and validation studies demonstrate that these precision probes, used with the prescribed measurement protocols and data-processing techniques, provide highly accurate and reliable in vivo and ex vivo biological tissue measurements, including breast tissue spectroscopy.

Calibration of a fringe projection profilometry system using virtual phase calibrating model planes

A novel virtual phase calibrating model plane method for coordinate calibration in fringe projection profilometry is presented in this paper. Plane (X-axis and Y-axis) calibration and height (Z-axis) calibration are studied respectively. The virtual phase calibrating model plane method is designed to calibrate the coordinates. Experimental results show that the proposed calibration procedure using the virtual phase calibrating model plane method is more efficient in that it needs only to grab and process one series of images of the model plane, whereas the traditional calibration method requires at least two series of images.

Geometric calibration of digital cameras through multi-view rectification

This paper introduces a new and very effective method for high-precision geometric calibration of digital cameras. The internal and external geometry are estimated: (1) by extracting features with subpixel accuracy from various views of a planar calibration plate; and (2) by mapping these feature sets into the corresponding points of the undistorted and rectified image that would be generated by an ideal pinhole digital camera with the same focal length as the camera to calibrate but devoid of lens distortion and perspective warp. The rectification of the views is formulated as a nonlinear least-squares optimization problem where a quadratic cost function expressing the residual registration error has to be minimized. The views are first prealigned with the reference image by means of a simplified mathematical model. This initialization, together with the closed-form computation of the gradient of the cost function, allows the Levenberg-Marquardt algorithm employed to find its minimum to rapidly converge to the optimal solution. The performance of the new calibration algorithm is tested with a set of real images available on the Internet and discussed in the paper. Also, its accuracy is assessed by means of synthetic versions of the actual images generated with the estimated parameters.

Camera calibration with moving one-dimensional objects

In this paper, we show that the rotating 1D calibrating object used in the literature is in essence equivalent to a familiar 2D planar calibration object. In addition, we also show that when the 1D object undergoes a planar motion rather than rotating around a fixed point, such equivalence still holds but the traditional way fails to handle it. Experiments are carried out to verify the theoretical correctness and numerical robustness of our results.

Constructing feature points for calibrating a structured light vision sensor by viewing a plane from unknown orientations

To calibrate a structured light vision sensor, it is necessary to obtain at least four non-collinear feature points that fall on the light stripe plane. We propose a novel method to construct non-collinear feature points used for calibrating a structured light vision sensor with a planar calibration object. After the planar calibration object is moved freely in the range of measuring of the structured light vision sensor at least twice, all the local world coordinates of the feature points falling on the light stripe plane can be readily obtained in site. The global world coordinates of the non-collinear feature points in the local world coordinate frame can be computed through the three-dimensional (3D) camera coordinate frame. A planar calibration object is designed according to the proposed approach to provide accurate feature points. The experiments conducted on a real structured light vision sensor that consists of a camera and a single-light-stripe-plane laser projector reveal that the proposed approach has high accuracy and is practical in the vision inspection applications. The proposed approach greatly reduces the cost of the calibration equipment and simplifies the calibrating procedure. It advances structured light vision inspection one step from laboratory environments to real world use.

Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry

A new method for both the phase-height mapping and the 3-D coordinate calibration in phase-measuring profilometry (PMP) is presented. A calibration gauge containing four virtual calibration planes is designed. The application of the calibration gauge avoids the translation of the standard plane during the calibration process. Furthermore, circular steps are designed to calibrate lateral coordinates automatically. With this calibration gauge, both the phase-height mapping and lateral coordinates calibration could be done simultaneously through only one measurement. Additionally, to recover a continuous phase distribution of all the steps with the same height, an iterative procedure is proposed. The effectiveness of the proposed method is demonstrated by experimental results.

A new easy camera calibration technique based on circular points

Inspired by Zhang's work on flexible calibration technique, a new easy technique for calibrating a camera based on circular points is proposed. The proposed technique only requires the camera to observe a newly designed planar calibration pattern (referred to as the model plane hereinafter) which includes a circle and a pencil of lines passing through the circle's center, at a few (at least three) different unknown orientations, then all the five intrinsic parameters can be determined linearly. The main advantage of our new technique is that it needs to know neither any metric measurement on the model plane, nor the correspondences between points on the model plane and image ones, hence the whole calibration process becomes extremely simple. The proposed technique is particularly useful for those people who are not familiar with computer vision. Experiments with simulated data as well as with real images show that our new technique is robust and accurate.

Enhanced on-wafer time-domain waveform measurement through removal of interconnect dispersion and measurement instrument jitter

We have measured the output waveshape and rise time of two high-speed digital circuits on a wafer using a 50-GHz prototype of a new instrument. The instrument uses vector error correction to de-embed the component under test like a network analyzer, but reads out in the time domain after the fashion of an equivalent-time oscilloscope. With the calibration plane of the instrument set at the tips of the wafer probes, errors arising from dispersion in the connection hardware are removed. We show that the random jitter in the measurement system is removed without the convolution penalty usually incurred by averaging so that anomalies such as pattern-dependent jitter are exposed. The system rise time is 7 ps, compared to a system rise time of 12-13 ps for a conventional equivalent-time oscilloscope of the same bandwidth in the presence of wafer probes, bias networks, and cables.