An active contour method for bone cement reconstruction from C-arm x-ray images

Abstract

A novel algorithm is presented to segment and reconstruct injected bone cement from a sparse set of X-ray images acquired at arbitrary poses. The sparse X-ray multi-view active contour (SxMAC-pronounced "smack") can 1) reconstruct objects for which the background partially occludes the object in X-ray images, 2) use X-ray images acquired on a noncircular trajectory, and 3) incorporate prior computed tomography (CT) information. The algorithm's inputs are preprocessed X-ray images, their associated pose information, and prior CT, if available. The algorithm initiates automated reconstruction using visual hull computation from a sparse number of X-ray images. It then improves the accuracy of the reconstruction by optimizing a geodesic active contour. Experiments with mathematical phantoms demonstrate improvements over a conventional silhouette based approach, and a cadaver experiment demonstrates SxMAC's ability to reconstruct high contrast bone cement that has been injected into a femur and achieve sub-millimeter accuracy with four images.

Fig. 1

System overview showing (a) robotic cement injector, (b) optical tracker, (c) intra-operative reconstruction overlaid on X-ray images, and (d) finite-element analysis of femur.

Fig. 2

Imaging scenario depicting (a) X-ray images, (b) X-ray source, (c) projection lines, (d) background objects, and (e) foreground object.

Fig. 3

(a) Metasphere phantom with (b) corresponding silhouette, (c) SxMAC reconstruction, and (d), (e) DRRs (12).

Fig. 4

SxMAC reconstruction of a torus acquired from a [(a), (e)] 90° arc, [(b), (f)] 30° arc, and wobbled [(c), (g)] 30° arc. X-ray projection images are depicted in their proper pose relative to the reconstructed object. Reconstructions shown in (a), (b), and (c) are juxtaposed to (d) ground truth in (e), (f), and (g).

Fig. 5

(a) Dragon phantom ground truth, (b) visual hull initialization, (c) SxMAC reconstruction, and (d) X-ray images shown in their relative pose.

Fig. 6

Synthesized (a) pre-operative X-ray image of dry femur and (b) postoperative X-ray image with cement attenuation of 1900 HU.

Fig. 7

Error between ground truth and SxMAC reconstruction for varying bone cement attenuation. Error bars indicate one standard deviation from the mean.

Fig. 8

Error between ground truth and SxMAC reconstruction for different numbers of synthetic X-ray images.

Fig. 9

Error between ground truth and SxMAC reconstruction from eight images for different sweep angles.

Fig. 10

Error between ground truth and SxMAC reconstruction from four images and different magnitude translation errors.

Fig. 11

Error between ground truth and SxMAC reconstruction from four images and different magnitude rotation errors.

Fig. 12

(a) Ground truth segmentation and (b) silhouette reconstruction from 8 images with cement attenuation of 1900 HU. SxMAC reconstruction from 8 images with cement attenuation of (c) 1730 HU with soft tissue; (d) 1900 HU with soft tissue.

Fig. 13

(a) Post-injection X-ray image and (b) Pre/Post-injection difference image.

Fig. 14

Error between ground truth and SxMAC reconstruction from for different numbers of real X-ray images.

Fig. 15

Error between ground truth and SxMAC reconstruction from four real X-ray images and different sweep angles.

Fig. 16

(a) Ground truth cement segmentation, (b) silhouette reconstruction from four images, (c) silhouette reconstruction from eight images, (d) SxMAC reconstruction from four images, (e) SxMAC reconstruction from 8 images.