Enhancing Single-Plane Fluoroscopy: A Self-Calibrating Bundle Adjustment for Distortion Modeling

Abstract

Single-plane fluoroscopy systems with image intensifiers remain commonly employed in a clinical setting. The imagery they capture is vulnerable to several types of geometric distortions introduced by the system's components and their assembly as well as interactions with the local and global magnetic fields. In this study, the application of a self-calibrating bundle adjustment is investigated as a method to correct geometric distortions in single-plane fluoroscopic imaging systems. The resulting calibrated imagery is then applied in the quantitative analysis of diaphragmatic motion and potential diagnostic applications to hemidiaphragm paralysis. The calibrated imagery is further explored and discussed in its potential impact on areas of surgical navigation. This work was accomplished through the application of a controlled experiment with three separate Philips Easy Diagnost R/F Systems. A highly redundant (~2500 to 3500 degrees-of-freedom) and geometrically strong network of 18 to 22 images of a low-cost target field was collected. The target field comprised 121 pre-surveyed tantalum beads embedded on a 25.4 mm × 25.4 mm acrylic base plate. The modeling process resulted in the estimation of five to eight distortion coefficients, depending on the system. The addition of these terms resulted in 83-85% improvement in terms of image point precision (model fit) and 85-95% improvement in 3D object reconstruction accuracy after calibration. This study demonstrates significant potential in enhancing the accuracy and reliability of fluoroscopic imaging, thereby improving the overall quality and effectiveness of medical diagnostics and treatments.

Keywords: 3D point reconstruction; geometric distortion correction; quantitative measurement; self-calibration; single-plane fluoroscopy.

Figure 1

Single-fluoroscopic imaging system self-calibration network. Each image location (red triangle) around the calibration frame (blue circles) is shown.

Figure 2

The target labeling process began with an example of captured imagery (top left) followed by morphological enhancement (top right). Extracted binary labels (bottom left) were then semi-automatically matched to image point labels through user selection. The centroids of the target field (bottom right) could then be extracted from the imagery. Note the significant curvilinear distortions visible in the image of the square target grid.

Figure 3

The overall methodology of the application of the self-calibrating bundle adjustment can be seen to begin with image capture and image point processing. The procedure is followed by the application of the calibration and subsequent analysis to determine the effectiveness of the applied correction.

Figure 4

The virtual image of a checkerboard differenced with the distortion profile map for each fluoroscopic system. The distortion for all imagery can be seen to increase radially from the center, with the greatest magnitude of distortion towards the image edges. The largest distortion parameter magnitude for system F1 is affinity distortion, that of system C1 is decentering distortion closely followed by local distortion, and that of system C2 is affinity distortion.

Figure 5

Imagery captured across fluoroscopy systems pre-correction and post-correction using distortion model parameters. Imagery is annotated with the curve of the tantalum beads represented by the green curve and an idealized straight line of the beads with a red line.

Figure 6

Imagery captured from a fluoroscopic sniff test at peak expiration from a case study of chronic left hemidiaphragm elevation [19]. A frame from the video fluoroscopy was captured pre-application of calibration (left). The geometric distortion coefficient and resulting calibration was applied to the imagery and differenced (right). Note the significant difference in the top of the diaphragm in the left of the image (right) between calibrated and non-calibrated imagery.

Figure 7

Fluoroscopic spot image of the right hemidiaphragm from a fluoroscopic sniff test at peak expiration from a case study of chronic left hemidiaphragm elevation [19]. Calibrated imagery (right) and non-calibrated imagery (left) are compared. The primary shadow along the centerline represents the diaphragm’s surface. The difference in geometric position between calibrated and non-calibrated imagery can be noted.

Figure 8

Video fluoroscopy from a case study of chronic left hemidiaphragm elevation [19] during normal inspiration. The resulting video imagery is stacked along the z-axis for a total of 229 frames of images. The image volume can then be visualized, with contrast adjustments applied for improved visualization. The movement of the lungs caused by the diaphragm can subsequently be visualized.

Figure 9

Video fluoroscopy from a case study of chronic left hemidiaphragm elevation [19] during normal inspiration of the right hemidiaphragm. The image volume is sliced along the y–z plane at a point near the diaphragm to visualize its movement. The geometric distortion coefficients were applied as a calibration to each frame within the video fluoroscopy. The resulting imagery is superimposed (left) and differenced (right). The distortion is most evident at peaks and troughs corresponding to the relaxation and contraction of the diaphragm, respectively.