Eccentricity error compensation for geometric camera calibration based on circular features

Geometric camera calibration is the process of determining a mapping between points in world coordinates and the corresponding image locations of the points. In previous methods, calibration typically involved the iterative solution to a system of nonlinear equations. A method is presented for performing camera calibration that provides a complete, accurate solution, using only linear systems of equations. By using two calibration planes, a line-of-sight vector is defined for each pixel in the image. The effective focal point of a camera can be obtained by solving the system that defines the intersection point of the line-of-sight vectors. Once the focal point has been determined, a complete camera model can be obtained with a straightforward least-squares procedure. This method of geometric camera calibration has the advantages of being accurate, efficient, and practical for a wide variety of applications. >

Geometrical sensor calibration is essential for space applications based on high accuracy optical measurements, in this case for the thermal infrared push-broom imaging spectrometer MERTIS. The goal is the determination of the interior sensor orientation. A conventional method is to measure the line of sight for a subset of pixels by single pixel illumination with collimated light. To adjust angles, which define the line of sight of a pixel, a manipulator construction is used. A new method for geometrical sensor calibration is using Diffractive Optical Elements (DOE) in connection with laser beam equipment. Diffractive optical elements (DOE) are optical microstructures, which are used to split an incoming laser beam with a dedicated wavelength into a number of beams with well-known propagation directions. As the virtual sources of the diffracted beams are points at infinity, the resulting image is invariant against translation. This particular characteristic allows a complete geometrical sensor calibration with only one taken image avoiding complex adjustment procedures, resulting in a significant reduction of calibration effort. We present a new method for geometrical calibration of a thermal infrared optical system, including an thermal infrared test optics and the MERTIS spectrometer bolometer detector. The fundamentals of this new approach for geometrical infrared optical systems calibration by applying diffractive optical elements and the test equipment are shown.

Geometric calibration of all-sky cameras using sun and moon positions: A comprehensive analysis

Flexible calibration method for line-scan cameras using a stereo target with hollow stripes

With increasing demands in real-time or near real-time remotely sensed imagery applications in such as military deployments, quick response to terrorist attacks and disaster rescue, the on-board geometric calibration problem has attracted the attention of many scientists in recent years. This paper presents an on-board geometric calibration method for linear CCD sensor arrays using FPGA chips. The proposed method mainly consists of four modules—Input Data, Coefficient Calculation, Adjustment Computation and Comparison—in which the parallel computations for building the observation equations and least squares adjustment, are implemented using FPGA chips, for which a decomposed matrix inversion method is presented. A Xilinx Virtex-7 FPGA VC707 chip is selected and the MOMS-2P data used for inflight geometric calibration from DLR (Köln, Germany), are employed for validation and analysis. The experimental results demonstrated that: (1) When the widths of floating-point data from 44-bit to 64-bit are adopted, the FPGA resources, including the utilizations of FF, LUT, memory LUT, I/O and DSP48, are consumed at a fast increasing rate; thus, a 50-bit data width is recommended for FPGA-based geometric calibration. (2) Increasing number of ground control points (GCPs) does not significantly consume the FPGA resources, six GCPs is therefore recommended for geometric calibration. (3) The FPGA-based geometric calibration can reach approximately 24 times faster speed than the PC-based one does. (4) The accuracy from the proposed FPGA-based method is almost similar to the one from the inflight calibration if the calibration model and GCPs number are the same.

Wide angle star sensors are becoming more prevalent in aeronautics. A wide angle lens provides a greater field of view for star detection, but consequently incurs significant lens distortion. The effects of distortion complicate star identification, causing algorithms to fail or report false identifications. We address the issue of calibrating a wide angle star sensor without any specialized equipment, by analyzing two time-separated images captured from a static camera. An initial estimate of the focal length is obtained by observing the displacement of stars between the images. The focal length is subsequently used to build an initial estimate of camera intrinsics, and to identify stars in the image. A RANSAC-augmented Kabsch algorithm is implemented to determine camera orientation, while simultaneously removing false identifications. The identified stars are used to provide a precise estimate of camera focal length, before applying non-linear optimization in a radial search algorithm. The methodology was tested on two cameras, demonstrating the effectiveness of this algorithm in achieving a precise geometric calibration using real hardware, without any specialized calibration equipment.

From power stations to power tools, from the smallest watch to the largest car, all contain round components. In precision machining of cylindrical parts, the measurement and evaluation of roundness (also called circularity in ASME Geometric Dimensioning & Tolerancing Y14.5) and cylindricity are indispensable components to quantify form tolerance. Of all the methods of measuring these form errors, the most precise is the one with accurate spindle/turntable type measuring instrument. On the instrument, the component is rotated on a highly accurate spindle which provides an imaginary circular datum. The workpiece axis is aligned with the axis of the spindle by means of a centering and tilt adjustment leveling table. In this article, the authors have investigated the dependence of circularity form error on instrument’s centering error (also known as eccentricity) and tilt error. It would be intriguing to map this nonlinear relationship within its effective boundaries and to investigate the limits beyond which the measurement costs and time remain no more efficient. In this study, a test part with different circular and cylindrical features were studied with varying levels of predetermined instrument eccentricity and tilt errors. Additionally, this article explores the significance of incorporating these parameters into undergraduate and graduate engineering curricula, and be taught as an improved toolkit to the aspiring engineers, process engineers and quality control professionals.

According to a small, lightweight, low-cost high performance inertial Measurement Units(IMU), an effective calibration method is implemented to evaluate the performance of Micro-Electro-Mechanical Systems(MEMS) sensors suffering from various errors to get acceptable navigation results. A prototype development board based on FPGA, dual core processor's configuration for INS/GPS integrated navigation system is designed for experimental testing. The significant error sources of IMU such as bias, scale factor, and misalignment are estimated in virtue of static tests, rate tests, thermal tests. Moreover, an effective intelligent calibration method combining with Kalman Filter is proposed to estimate parameters and compensate errors. The proposed approach has been developed and its efficiency is demonstrated by various experimental scenarios with real MEMS data.

We present a method for geometric point light source calibration. Unlike prior works that use Lambertian spheres, mirror spheres, or mirror planes, we use a calibration target consisting of a plane and small shadow casters at unknown positions above the plane. We show that shadow observations from a moving calibration target under a fixed light follow the principles of pinhole camera geometry and epipolar geometry, allowing joint recovery of the light position and 3D shadow caster positions, equivalent to how conventional structure from motion jointly recovers camera parameters and 3D feature positions from observed 2D features. Moreover, we devised a unified light model that works with nearby point lights as well as distant light in one common framework. Our evaluation shows that our method yields light estimates that are stable and more accurate than existing techniques while having a much simpler setup and requiring less manual labor.

Water equivalent diameter (Dw) reflects patient's attenuation and is a sound descriptor of patient size, and is used to determine size-specific dose estimator from a CT examination. Calculating Dw from CT localizer radiographs makes it possible to utilize Dw before actual scans and minimizes truncation errors due to limited reconstructed fields of view. One obstacle preventing the user community from implementing this useful tool is the necessity to calibrate localizer pixel values so as to represent water equivalent attenuation. We report a practical method to ease this calibration process. Dw is calculated from water equivalent area (Aw) which is deduced from the average localizer pixel value (LPV) of the line(s) in the localizer radiograph that correspond(s) to the axial image. The calibration process is conducted to establish the relationship between Aw and LPV. Localizer and axial images were acquired from phantoms of different total attenuation. We developed a program that automates the geometrical association between axial images and localizer lines and manages the measurements of Dw and average pixel values. We tested the calibration method on three CT scanners: a GE CT750HD, a Siemens Definition AS, and a Toshiba Acquilion Prime80, for both posterior-anterior (PA) and lateral (LAT) localizer directions (for all CTs) and with different localizer filters (for the Toshiba CT). The computer program was able to correctly perform the geometrical association between corresponding axial images and localizer lines. Linear relationships between Aw and LPV were observed (with R2 all greater than 0.998) on all tested conditions, regardless of the direction and image filters used on the localizer radiographs. When comparing LAT and PA directions with the same image filter and for the same scanner, the slope values were close (maximum difference of 0.02mm), and the intercept values showed larger deviations (maximum difference of 2.8mm). Water equivalent diameter estimation on phantoms and patients demonstrated high accuracy of the calibration: percentage difference between Dw from axial images and localizers was below 2%. With five clinical chest examinations and five abdominal-pelvic examinations of varying patient sizes, the maximum percentage difference was approximately 5%. Our study showed that Aw and LPV are highly correlated, providing enough evidence to allow for the Dw determination once the experimental calibration process is established.

Reconstructing a 3D structure from a set of its 2D X-ray projections requires that the source position and image plane orientation in 3D space be obtained with high accuracy for each of the imaging chain positions. This knowledge is generally obtained through a geometrical calibration of the data acquisition system. In this paper, we present a fully automatic method for such a geometrical calibration, well suited to a 3D X-ray imaging system which acquires sets of 2D projections during a rotation of the imaging chain. This method is based on (1) the use of a dedicated calibration phantom with reference points, (2) an automatic algorithm to detect and identify the reference points on the phantom's 2D X-Ray projections, and (3) the estimation of the imaging chain geometrical parameters by minimizing the reprojection mean quadratic error measured on these reference points. Results obtained both from simulation data and from data acquired on an experimental bench are presented.

Thermal imaging is increasingly applied in remote sensing to identify material degradation, monitor structural integrity, and support energy diagnostics. However, its adoption is limited by the low spatial resolution of thermal sensors compared to RGB cameras. This study proposes a modular pipeline to generate thermally enriched 3D point clouds by fusing RGB and thermal imagery acquired simultaneously with a dual-sensor unmanned aerial vehicle system. The methodology includes geometric calibration of both cameras, image undistortion, cross-spectral feature matching, and projection of radiometric data onto the photogrammetric model through a computed homography. Thermal values are extracted using a custom parser and assigned to 3D points based on visibility masks and interpolation strategies. Calibration achieved 81.8% chessboard detection, yielding subpixel reprojection errors. Among twelve evaluated algorithms, LightGlue retained 99% of its matches and delivered a reprojection accuracy of 18.2% at 1 px, 65.1% at 3 px and 79% at 5 px. A case study on photovoltaic panels demonstrates the method’s capability to map thermal patterns with low temperature deviation from ground-truth data. Developed entirely in Python, the workflow integrates into Agisoft Metashape or other software. The proposed approach enables cost-effective, high-resolution thermal mapping with applications in civil engineering, cultural heritage conservation, and environmental monitoring applications.

In previous work, we have developed a cost-effective small-animal SPECT imaging system by adding a multi-pinhole cylinder collimator into an animal PET scanner. To achieve high-quality reconstructed SPECT image, accurate geometrical calibration of the collimator is critical. The pinhole position in PET-scanner's coordinate system (PSC) could be factorized into two parts: pinhole position in collimator's coordinate system (fixed, only need one measurement) and collimator position in PSC (would vary after times of use after times of use). In this paper, we propose a novel geometrical calibration method for the second part based on the coincidental beta-gamma events of LYSO background radiation of the PET scanner. To obtain sufficient conditions for describing the collimator in PSC, a mark ball was added to one end of the collimator and imaged with collimator by LYSO background radiation simultaneously. With the reconstructed image of the collimator and the add-on mark ball, the axis of the collimator and the center of the mark ball were derived using least-squares fitting and centroid calculation, individually. Monte-Carlo simulation studies with five groups of different positions of collimator were implemented and geometrical parameters were calibrated. The proposed method was implied on a real system. Both simulation and experiment studies show that the proposed method could achieve high accuracy for parameter calibration. In conclusion, it is a practical and efficient way to perform SPECT collimator calibration by using PET scanner's LYSO background radiation in the studied PET/SPECT system.

An improved geometrical calibration method for stereo deflectometry by using speckle pattern

Micro-pinhole SPECT system with conventional multiple-head gamma cameras has the advantage of high magnification factor for imaging of small animals such as rodents. However, several geometric factors should be calibrated to obtain the SPECT image with good image quality. We developed a simplified geometric calibration method for rotating triple- head pinhole SPECT system and assessed the effects of the calibration using several phantom and rodent imaging studies. Trionix Triad XLT9 triple-head SPECT scanner with 1.0 mm pinhole apertures were used for the experiments. Approximately centered one point source was scanned to track the angle- dependent positioning errors. The centroid of point source was determined by the center of mass calculation. Axially departed two point sources were scanned to calibrate radius of rotation from pinhole to center of rotation. To verify the improvements by the geometric calibrations, we compared the spatial resolution of the reconstructed image of Tc-99m point source with and without the calibration. SPECT image of micro performance phantom with hot rod inserts was acquired and several animal imaging studies were performed. Exact sphere shape of the point source was obtained by applying the calibration and axial resolution was improved. Lesion detectability and image quality was also much improved by the calibration in the phantom and animal studies. Serious degradation of micro-pinhole SPECT images due to the geometric errors could be corrected using a simplified calibration method using only one or two point sources.