Modelling Errors in X-Ray Fluoroscopic Imaging Systems Using Photogrammetric Bundle Adjustment With a Data-Driven Self-Calibration Approach

Abstract

X-ray imaging is a fundamental tool of routine clinical diagnosis. Fluoroscopic imaging can further acquire X-ray images at video frame rates, thus enabling non-invasive in-vivo motion studies of joints, gastrointestinal tract, etc. For both the qualitative and quantitative analysis of static and dynamic X-ray images, the data should be free of systematic biases. Besides precise fabrication of hardware, software-based calibration solutions are commonly used for modelling the distortions. In this primary research study, a robust photogrammetric bundle adjustment was used to model the projective geometry of two fluoroscopic X-ray imaging systems. However, instead of relying on an expert photogrammetrist's knowledge and judgement to decide on a parametric model for describing the systematic errors, a self-tuning data-driven approach is used to model the complex non-linear distortion profile of the sensors. Quality control from the experiment showed that 0.06 mm to 0.09 mm 3D reconstruction accuracy was achievable postcalibration using merely 15 X-ray images. As part of the bundle adjustment, the location of the virtual fluoroscopic system relative to the target field can also be spatially resected with an RMSE between 3.10 mm and 3.31 mm.

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

“…Nearby residuals in the image field are assumed to be spatially correlated because they are under the influence of a similar systematic error. In [13] the systematic error part is estimated by averaging 'k' neighbouring residuals. When many data points are available and are evenly distributed, this is a reasonable estimation.…”

“…The first step, removal of image distortion, is often divided into two categories: global methods [14], [18]- [20], [26], [27], where a polynomial is fitted to all the points in the image, or local methods [13], [17], [22], [28], where a more regional averaging or polynomial fitting is performed (e.g. local weighted mean, local unwarping polynomial).…”

“…This article builds on a previous publication, [13], where a new automatic X-ray calibration method was proposed. Improvements to the geometric accuracy of fluoroscopic imaging systems was made by separating the residuals in a photogrammetric bundle adjustment into systematic and random components, and then modelling the systematic errors using a non-parametric machine learning method, the k-nearestneighbour (kNN) regression.…”