Cone-Beam Angle Dependency of 3D Models Computed from Cone-Beam CT Images

Abstract

Cone-beam dental CT can provide high-precision 3D images of the teeth and surrounding bones. From the 3D CT images, 3D models, also called digital impressions, can be computed for CAD/CAM-based fabrication of dental restorations or orthodontic devices. However, the cone-beam angle-dependent artifacts, mostly caused by the incompleteness of the projection data acquired in the circular cone-beam scan geometry, can induce significant errors in the 3D models. Using a micro-CT, we acquired CT projection data of plaster cast models at several different cone-beam angles, and we investigated the dependency of the model errors on the cone-beam angle in comparison with the reference models obtained from the optical scanning of the plaster models. For the 3D CT image reconstruction, we used the conventional Feldkamp algorithm and the combined half-scan image reconstruction algorithm to investigate the dependency of the model errors on the image reconstruction algorithm. We analyzed the mean of positive deviations and the mean of negative deviations of the surface points on the CT-image-derived 3D models from the reference model, and we compared them between the two image reconstruction algorithms. It has been found that the model error increases as the cone-beam angle increases in both algorithms. However, the model errors are smaller in the combined half-scan image reconstruction when the cone-beam angle is as large as 10 degrees.

Keywords: cone-beam artifact; cone-beam dental CT; digital impression; half-scan image reconstruction; stereolithography.

Figure 1

The micro-CT used for the experiment. The rotating stage can be moved vertically to adjust the cone-beam angle of the ray passing through the center of the object.

Figure 2

The photographs and dimensions of the plaster models used for the micro-CT scan.

Figure 3

The cone-beam angles adopted in the micro-CT scan. The cone-beam angle is the vertical angle of the ray passing through the center of the object.

Figure 4

The half-scan geometry seen on the central plane. The half-scan range is from the starting angle (β₀) to the end of the blue arc. The region of reconstruction for this half-scan range is the shaded fan of an angular span of 2λ.

Figure 5

The plaster models, (a) Model 1 and (b) Model 2, in the STL format obtained from the optical scanning.

Figure 6

(a,b) show two regions of interest in the images reconstructed by the FDK algorithm. (c,d) show the corresponding regions in the images reconstructed by the CW-FDK algorithm. We can see that the cone-beam artifacts (indicated by the red arrow) have been much reduced in the images of the CW-FDK algorithm.

Figure 7

The 3D models computed from the CT images of (a,c) Model 1 and (b,d) Model 2 taken at the cone-beam angle of 10 degrees. The top and bottom rows have been obtained from the images reconstructed by FDK and CW-FDK, respectively.

Figure 8

The deviation maps of Model 1 as compared to the optical STL (reference). (a–c) show deviation maps computed from the FDK images taken at the cone-beam angles of 10, 5, and 0 degrees, respectively, while (d–f) show deviation maps computed from the CW-FDK images taken at the cone-beam angles of 10, 5, and 0 degrees, respectively.

Figure 9

The deviation maps of Model 2 as compared to the optical STL (reference). (a–c) show deviation maps computed from the FDK images taken at the cone-beam angles of 10, 5, and 0 degrees, respectively, while (d–f) show deviation maps computed from the CW-FDK images taken at the cone-beam angles of 10, 5, and 0 degrees, respectively.

Figure 10

The relative population of the deviations from the reference of (a) Model 1 and (b) Model 2 at three different cone-beam angles of 0, 5, and 10 degrees. The solid and dashed lines correspond to the cases of the FDK and CW-FDK algorithms.