Flow chart of the proposed calculation procedure for rigid (a) and deformable registration (b). The control volumes are selected by the user only on the model image. A rigid registration algorithm automatically maps the selected control volumes to their corresponding locations on the reference image.
Sagittal, coronal, and axial views of the FLT-PET images (first row) and CT images (second row). The checkerboard of the CT and FLT-PET images after registration is shown in the third row and the left panel of the fourth row. The right panel of the fourth row shows a stereotactic view of the matched PET and CT images after registration.
Metric space of FLT-PET and CT registration when the whole image set is used (a) and when three control volumes on the bony structure are used (b).
Convergence analysis for a rigid registration case with (left column) and without (right column) the use of control volumes. The control volume-based registration converges to the same cost function value and leads to reproducible shift values in the , , and directions, labeled by triangles, squares, and circular dots, respectively. In the standard registration, large variations are observed in the shifts along the , , and directions.
Screenshots of sagittal, coronal, and axial views of the FLT-PET images (first row) and CT images (second row). The checkerboard of the CT and FLT-PET images after registration is shown in the third row. The fourth row shows a stereotactic view of the matched PET and CT images after registration.
Iterative calculation processes for five independent registrations starting from different initial matches for the patient shown in Fig. 5. Some of the curves stop earlier because the convergence criteria is met.
Comparison of the newly proposed control volume-based (left column) and conventional whole image-based algorithms (right column) for rigid image registration. In conventional registration, the metric tries to accommodate all the voxels, which becomes less adequate in the presence of image artifacts or other noises. The control volume-based calculation eliminates the influence of imaging artifacts and produces better registration.
Convergence analyses of a rigid brain CT-MRI registration using the control volume-based and whole image-based algorithms. In the former case, all 50 calculations with different initial transformation parameters converge to the same shift values in the , , and directions, labeled by triangles, squares, and circular dots, respectively. For the latter case, the fluctuation in the final shift values are much larger.
Dependence of registration on the placement of the control volume for three different sized volumes. For each size, the shifts resulting from 20 random placements of the control volume are shown.
Axial slices of the model (a) and reference (b) images for the deformable registration study. Rectangular control volumes, #1 to #5, are placed in the model image and their mappings are shown on the reference image. The anatomy in the regions affected by the respiration does not match initially (c). After the control volume-based deformable registration, the anatomy matches very well, as confirmed by the overlay image (d).
Metric function for the first three control volumes for two different control volume sizes ( for upper row and for the lower row). In both cases, the search spaces are smooth, with a very pronounced ridge. The search space characteristics and the location of the global minima do not depend significantly on the control volume size.
Checkerboard comparison of the model and reference images before (a) and after (b) control volume-based deformable registration. Displacement up to is visible before registration, as marked by the arrows in (a). The control volume-based algorithm yielded the same registration as that of the conventional BSpline calculation, but with a significantly reduced computational time. A checkerboard comparison of the mapped model images from the two algorithms is shown in (c).
Convergence analysis for the first three control volumes shown in Fig. 8. Presented are the shifts of the final transformation as obtained in 100 registration tests starting from different initial transformation parameters. All calculations converged to the same solution to within a range of less than for the (triangles), (squares), and (circular dots) directions.
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