Bundle Adjustment-Based Stability Analysis Method With a Case Study of a Dual Fluoroscopy Imaging System

Abstract

A fundamental task in photogrammetry is the temporal stability analysis of a camera/imaging-system’s calibration parameters. This is essential to validate the repeatability of the parameters’ estimation, to detect any behavioural changes in the camera/imaging system and to ensure precise photogrammetric products. Many stability analysis methods exist in the photogrammetric literature; each one has different methodological bases, and advantages and disadvantages. This paper presents a simple and rigorous stability analysis method that can be straightforwardly implemented for a single camera or an imaging system with multiple cameras. The basic collinearity model is used to capture differences between two calibration datasets, and to establish the stability analysis methodology. Geometric simulation is used as a tool to derive image and object space scenarios. Experiments were performed on real calibration datasets from a dual fluoroscopy (DF; X-ray-based) imaging system. The calibration data consisted of hundreds of images and thousands of image observations from six temporal points over a two-day period for a precise evaluation of the DF system stability. The stability of the DF system – for a single camera analysis – was found to be within a range of 0.01 to 0.66 mm in terms of 3D coordinates root-mean-square-error (RMSE), and 0.07 to 0.19 mm for dual cameras analysis. It is to the authors’ best knowledge that this work is the first to address the topic of DF stability analysis.

Assessing the Influence of Temperature Changes on the Geometric Stability of Smartphone- and Raspberry Pi Cameras

“…If changes of the camera geometry occur due to temperature changes, it is important to estimate the impact at measurements in 3D object space [36][37][38]. The Monte-Carlo simulation was used to evaluate how different changes of the camera geometry affect errors in object space.…”

“…Therefore, sets of k (k ∈ N) parameters, reflecting the IOP, are randomly generated n-times (n ∈ N) considering residuals and mathematically correlations, to project n regular grids of image points onto a virtual object plane in 3D object space. As indicated by [36,38], IOP-related variations in object space are highly correlated with the reference object that is used for intersection and "should be as close as possible to the expected object products of the photogrammetric application of interest" [36]. If this is not considered, more degrees of freedom related to the object scene are introduced that might mitigate or intensify IOP-related variations due to depth variations of the reference object.…”

Robust Self-Supervised Learning of Deterministic Errors in Single-Plane (Monoplanar) and Dual-Plane (Biplanar) X-Ray Fluoroscopy

“…In practice, steps 2) and 3) are often combined, resulting in a two-step procedure: 1) correction of image distortion; and 2) 3D space calibration [22]- [24]. In recent years, all three steps are combined into a unified optimization process to account for the parameter correlations that exist between the steps [14], [15], [25]. While there are certain benefits of doing a single optimization (e.g.…”

“…There are incentives for achieving an accurate calibration with reduced data (i.e. by using less time to acquire and process the data); for example, more imaging time can be allocated to patients, or the fluoroscope can be calibrated more frequently to ensure its optimal performance ( [15] suggested that fluoroscopic systems may exhibit submillimeter 3D changes in measurement error over the course of a day).…”