Plot of measured bellow values vs. time for two couch positions. The small black dots show when CT scans are taken and the corresponding bellow values. There are 25 scans at each couch position. The durations of a couch position are indicated by the big dashed lines.
Comparison of image downsampling uses the maxfilter and the Laplacian pyramid filter: (a) the original image, (b), (c), and (d) are images sequentially downsampled by 2, 4, and 8 using the Laplacian filter; (e), (f), and (g) are images sequentially downsampled by 2, 4, and 8 using the maxfilter.
The artificially deformed CT images: (a) the original image; (b) the image deformed with synthesized motion field, the dashed lines mark the 16-slice partitions, (c) the difference image with the motion vectors, (d) the difference image in the axial view.
Comparison of final registration results for using the maxfilter and the Laplacian pyramid filter for image downsampling in the multigrid approach. Dashed lines mark the areas where the most incorrect registration happens in this example: (a) the ground truth target slice, (b) the result by using the maxfilter, (c) the result by using the Laplacian pyramid filter.
Example of the a priori alignment (APA) procedure: (a) the reference volume section, (b) a CT segment, (c) the difference image that the CT segment is aligned with the reference volume according to the couch table position, (d) the reference volume section shifted by APA, (e) the difference image for the CT segment aligned to the reference volume by APA, (f) the final registration difference image, (g) the target slice in transverse view, (h) the registration result achieved without using APA, (i) the registration result achieved using APA. Regions with most apparent improved results by APA are circled by dashed lines.
Example of the inverse motion field fitting for a point selected in the left-inferior lung of a patient. All motion values are in voxels: (a) the tidal volume vs time for the selected point, where the numbered circles mark the time of the CT scan, (b) the SI motion fitting where the circles are the original motion values and the squares are the fitted values, (c) the LR motion fitting, (d) the AP motion fitting, (e) the AP motion vs the LR motion, (f) the SI motion vs the LR motion, (g) the SI motion vs the AP motion, (h) the motion fitting presented in 3D.
Examples of the forward motion field fitting for the same point as used for Fig. 6. All motion values are in voxels: (a) SI motion fitting, (b) LR motion fitting, (c) AP motion fitting, (d) the motion fitting presented in 3D.
Examples of the reference volume being deformed to generate 3D-CT volumes for different breathing phases. Columns 1, 2, and 3 are for the exhaling phases of tidal volumes equal to 30, 60, and 90% of the 90th percentile tidal volume. Row (a) is the 3D-CT volume reconstructed by using the amplitude sorting method. Row (b) is the 3D-CT volume generated by deforming the reference volume by the motion fields that are predicted by the inverse 5D motion model. Row (c) is the difference between row (b) and the reference volume. Row (d) is the difference between row (a) and row (b).
Slice views of the estimated fitting parameters of the forward 5D motion model for patient 2. Column (1) is the coronal view of the parameter [Eq. (9)] vector field, units are in mm/L. Column (2) is the coronal view of the parameter , units are in mm/L/s. Column (3) is the view of parameter , units are in mm. Row (a) is the parameter vector field projection in the AP direction. Row (b) is the LR projection. Row (c) is the SI projection. Row (d) is the magnitude of the vector fields.
Preliminary comparison of four deformable image registration algorithms using the landmarks. In addition, we show results of Horn–Schunck optical flow algorithm without CT number truncation for comparison with the CT number truncation case.
Registration error comparison between using the maxfilter and the Laplacian pyramid filter for image downsampling. Reported values are the mean and the standard deviation of the absolute magnitude of registration errors.
Registration error tested with the artificially deformed CT (Sect. ???) with and without using a priori alignment (APA) procedure. The reported registration error values are the mean and the standard deviation of the absolute magnitudes.
Validation of registration errors using landmarks. For patients 1 to 3, the landmarks were manually selected in the CT segments and the reference volume. The CT segments used in the validation were randomly selected from the middle to inferior lung and with higher corresponding tidal volumes so that image motions were the largest with respect to the reference volume.
Number of landmark pairs (LPs) used to compute target modeling errors (TME), modeling error (ME), modeling prediction error (MPE), and boundary discontinuity (BD). Values enclosed in braces are the maximum error values.
Average computation time of important tasks.
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