X-ray Imaging Calibration via Projection Matrix Decomposition
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for calibrating X-ray imaging systems are inefficient, time-consuming, and often based on inaccurate assumptions, particularly when dealing with non-ideal source trajectories and detector assembly sag, which affects the accuracy of three-dimensional image reconstruction.
Innovation Solution
The calibration method decomposes the non-ideal projection matrix into a flexible and rigid projection sub-matrix, allowing for periodic recalibration of the flexible sub-matrix daily or weekly and the rigid sub-matrix every 6-12 months, without the need for a phantom, enabling on-the-fly calibration and reducing costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional calibration methods are used to ensure accurate geometric relationships, then image reconstruction accuracy is improved, but calibration time and system downtime increase significantly
Solution Approach 1:
The projection matrix is divided into two separate sub-matrices: a rigid projection sub-matrix that remains constant over time and a flexible projection sub-matrix that varies with detector assembly sag. This segmentation allows different calibration frequencies for different components, reducing overall calibration time while maintaining accuracy.
Solution Approach 2:
The calibration process is made periodic rather than continuous. The rigid sub-matrix is calibrated infrequently (every 6-12 months), while the flexible sub-matrix is recalibrated more frequently (daily or weekly) to account for detector sag variations, optimizing the balance between accuracy and downtime.
2Measurement precision
If frequent full calibration is performed to maintain accuracy, then geometric relationship precision is improved, but productivity and system uptime deteriorate
Solution Approach 1:
The calibration process is segmented into rigid and flexible components with different recalibration schedules. The rigid sub-matrix requires minimal recalibration, while only the flexible sub-matrix needs frequent updates, significantly reducing the time the system is taken offline for calibration.
Solution Approach 2:
The calibration approach changes from treating the entire projection matrix as a single entity requiring uniform recalibration to differentiating between rigid parameters (calibrated infrequently) and flexible parameters (calibrated frequently), optimizing system uptime while maintaining accuracy.
3Measurement precision
If traditional calibration methods accounting for detector sag are used, then measurement accuracy is improved, but device complexity and calibration cost increase
Solution Approach 1:
The detector assembly sag is extracted as a separate, identifiable factor affecting the flexible projection sub-matrix. By isolating this variable, the calibration process can针对性地 address only the affected components rather than recalibrating the entire system, reducing complexity.
Solution Approach 2:
The flexible projection sub-matrix acts as an intermediary that captures the effects of detector sag without requiring direct measurement and correction of the physical sag itself. This mathematical intermediary simplifies the calibration process by working with computable parameters rather than physical measurements.
Data Source
AI summary
A system includes determination of a first sub-matrix of a projection matrix which describes a geometrical relationship between points of a three-dimensional coordinate system of the imaging system and points of a two-dimensional coordinate system of an image detector, determination of a second sub-matrix of the projection matrix, where the first and second sub-matrixes comprise a decomposition of the projection matrix, conversion of a first point of the two-dimensional coordinate system to a first point of the three-dimensional coordinate system based on the first and second sub-matrixes, determination of an updated first sub-matrix of an updated projection matrix, where the updated projection matrix describes a second geometrical relationship between points of the three-dimensional coordinate system and points of the two-dimensional coordinate system, and conversion of a second point of the two-dimensional coordinate system to a second point of the three-dimensional coordinate system based on the updated first and second sub-matrixes.