Automated 2D-3D registration of a radiograph and a cone beam CT using line-segment enhancementa)
This figure depicts the patient coordinate system employed. The three principal axes, ML, SI, and AP, and their orientation with respect to the , , and axes are displayed.
(a) and (b) show a DRR obtained by taking a projection through the kV CBCT and a kV radiograph acquired with the phantom at its reference position, respectively. Shading artifacts in the CBCT gave rise to darker regions of lower contrast in the central part of the DRRs as compared to the kV radiographs. (c) and (d) show the line-enhanced DRR and kV radiograph obtained by filtering images (a) and (b) with “sticks,” short line segments varied in orientation, and which have the form of a matched filter. Filtering the images with the “sticks” operator improves the contrast of linear features to background.
2D objective function obtained by computing the correlation coefficient between the downsampled feature-enhanced DRR and radiograph as a function of translation along the SI and ML axes for pose at optimization level 4. A Gaussian kernel of width and a subsampling factor of 3 were employed when downsampling the images. The objective function is smooth with a single peak at the global maximum. Such an objective function allows easy optimization. The value of the correlation coefficient at alignment, as given by the global peak of the objective function, was 0.9572 indicating a strong linear relationship between the images being matched.
The multiresolution optimization strategy employed in 2D is illustrated by means of contour plots of the correlation coefficient as a function of translation along the SI and ML axes. The contour plots show slices of constant correlation coefficient values through the corresponding 2D objective functions. The optimization was performed over eight levels. Contour plots for levels 8, 6, 4, and 1 are shown here. The position of the peak of the objective function for each of the four levels is indicated with a dot and the value of the true displacement is indicated with an . The starting point was at (0, 0) and is also indicated with a dot. Note how the objective functions become narrower and steeper as the optimization proceeds from level 8 to level 1. Note also the stability of the global peak. The optimization algorithm reaches the peak at level 8 and moves only marginally after that at higher resolutions. Although the global peak was reached at level 8 in this instance, this is not necessarily the case for all poses and for all transformation parameters. The peak value of the objective function at level 1 was 0.9483.
(Color) Example of superimposed feature-enhanced DRRs and feature-enhanced radiographs prior to registration (a) and after registration (b). In these images, red and green represent linear features in the DRR and kV radiograph, respectively. At alignment red and green features overlap to maximize the amount of yellow present in the fused image. In this experiment, the radiograph was obtained with the phantom rotated by around the SI axis and shifted along the SI axis (pose ).
This figure illustrates the maximum total error in determining setup deviations against the magnitude of the setup deviations for poses through . The error and displacements were calculated for points on the surface of a sphere of radius . Poses that have in-plane displacements only are labeled with a diamond. Poses that contain an out-of-plane rotation and/or an out-of-plane translation are labeled with a circle. For the displacements tested, the overall error in recovering setup deviations did not increase with the presence of out-of-plane rotational or translational displacements. Furthermore, there was no observable trend in the overall error.
Error in recovering setup deviation (with and without the error in determining translations along the AP axis) as a function of displacement. This figure illustrates the maximum error in determining setup deviations for poses through . The error and displacements were calculated for points on the surface of a sphere of radius . Diamonds denote the total registration error and circles denote the registration error excluding errors in the estimation of out-of-plane translations along the AP axis. Note that registration inaccuracies stem mainly from errors in estimating translations along the AP axis.
(Color) Examples of superimposed feature-enhanced kV DRRs and portal images for two sets of patient data [week 1, (a)–(d) and week 2,(g)–(h)]. Red represents features in the DRRs and green, features in the portal images. The left column shows the unaligned AP and lateral images and the right column shows the corresponding images after registration of the AP portal images to the planning CT. The lateral images were used to visually verify alignment along the AP axis and around the ML axis. Both sets of data were correctly aligned despite the presence of air cavities and deformable soft tissue structures.
Table of displacements and residual errors. through denote the different poses tested. The true pose, estimated pose, and residual errors in estimating the true pose are presented for each of the six transformations parameters. The correlation coefficient, , obtained at the estimated pose, total distance moved, , and total registration error, are also shown. The offset present at the start of the experiment, computed from the mean of the estimated pose for and , was subtracted from the estimated poses reported here.
Table of residual errors. The mean, standard deviation, minimum, and maximum value of the absolute value of the residual errors for poses through .
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