Effects of point configuration on the accuracy in 3D reconstruction from biplane images

Abstract

Two or more angiograms are being used frequently in medical imaging to reconstruct locations in three-dimensional (3D) space, e.g., for reconstruction of 3D vascular trees, implanted electrodes, or patient positioning. A number of techniques have been proposed for this task. In this simulation study, we investigate the effect of the shape of the configuration of the points in 3D (the "cloud" of points) on reconstruction errors for one of these techniques developed in our laboratory. Five types of configurations (a ball, an elongated ellipsoid (cigar), flattened ball (pancake), flattened cigar, and a flattened ball with a single distant point) are used in the evaluations. For each shape, 100 random configurations were generated, with point coordinates chosen from Gaussian distributions having a covariance matrix corresponding to the desired shape. The 3D data were projected into the image planes using a known imaging geometry. Gaussian distributed errors were introduced in the x and y coordinates of these projected points. Gaussian distributed errors were also introduced into the gantry information used to calculate the initial imaging geometry. The imaging geometries and 3D positions were iteratively refined using the enhanced-Metz-Fencil technique. The image data were also used to evaluate the feasible R-t solution volume. The 3D errors between the calculated and true positions were determined. The effects of the shape of the configuration, the number of points, the initial geometry error, and the input image error were evaluated. The results for the number of points, initial geometry error, and image error are in agreement with previously reported results, i.e., increasing the number of points and reducing initial geometry and/or image error, improves the accuracy of the reconstructed data. The shape of the 3D configuration of points also affects the error of reconstructed 3D configuration; specifically, errors decrease as the "volume" of the 3D configuration increases, as would be intuitively expected, and shapes with larger spread, such as spherical shapes, yield more accurate reconstructions. These results are in agreement with an analysis of the solution volume of feasible geometries and could be used to guide selection of points for reconstruction of 3D configurations from two views.

Figure 1

Schematic example of image and object coordinate system for biplane projection views with arbitrary relative orientation.

Figure 2

Two views of the left coronary system. Bifurcations are indicated by the white disks. Ten frames were used, and the positions of the bifurcation points were used to estimate the covariance matrix of the “flattened cigar” distribution.

Figure 3

Typical 3D configurations shown as 3D scatterplots of 50 points: flattened cigar (upper left), pancake (upper right), cigar (lower left), ball (lower right).

Figure 4

Empirical dependence of L1 on the number of points in the configuration for the pancake shape

Figure 5

Dependence of L1 and the volume of the feasible solution space on configuration shape (N=10). Configuration numbers correspond to (1) flattened cigar, (2) cigar, (3) pancake, (4) ball, (5) pancake with remote point 5 cm distant, (6) pancake with remote point 10 cm distant, (7) pancake with remote point 15 cm distant, (8) pancake with remote point 30 cm distant. Trends for the configurations in the EMF method are similar to those for the solution volume, except for the pancake shape (3), i.e., errors decrease as the volume of the 3D configuration increase.