Registration of CT Images of the Skull Figure 7 presents an example of the registration of two CT images of the dry skull in a Plexiglas box in two different positions. We used the geometric hashing algorithm on frames (Section 2.3). As the transformation between the two images is close enough to the identity, the ICP algorithm also gives very similar results.

FIGURE 6 Preprocessing: The 6D invariant vector associated with every couple of model frames is computed with its error zone and used as an index for the couple in the hash table. Recognition: For each scene frame couple, we compute the 6D invariant vector and retrieve through the hash table every compatible model frame couple. For each such couple, we tally a vote for the matching of the reference frames (here the match (Fmj, Fsj) scores 2). From A. Gueziec, X. Pennec, and N. Ayache. Medical image registration using geometric hashing. IEEE Computational Science and Engineering, Special issue on Geometric Hashing, 4(4) 29-41, Oct.-Dec. 1997 with permission. © 1997 IEEE.

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FIGURE 6 Preprocessing: The 6D invariant vector associated with every couple of model frames is computed with its error zone and used as an index for the couple in the hash table. Recognition: For each scene frame couple, we compute the 6D invariant vector and retrieve through the hash table every compatible model frame couple. For each such couple, we tally a vote for the matching of the reference frames (here the match (Fmj, Fsj) scores 2). From A. Gueziec, X. Pennec, and N. Ayache. Medical image registration using geometric hashing. IEEE Computational Science and Engineering, Special issue on Geometric Hashing, 4(4) 29-41, Oct.-Dec. 1997 with permission. © 1997 IEEE.

FIGURE 7 Example of registered crest lines between two CT skull images of the same phantom acquired in two different positions. Extremal points are represented by a color change from yellow to blue on the lines. (Left) Front view with all crest lines from the two skulls after registration. (Middle) Left view of the matched crest lines. (Right) Close-up on the occipital foramen on the right. In this last image, the width of a line is a tenth of a voxel, which shows the very precise registration of these extremal points. One can also see that the trihedron part of the matched frames is very well conserved. See also Plate 70. From A. Gueziec, X. Pennec, and N. Ayache. Medical image registration using geometric hashing. IEEE Computational Science and Engineering, Special issue on Geometric Hashing, 4(4) 29-41, Oct.-Dec. 1997, with permission. © 1997 IEEE.

FIGURE 8 Example of registered crest lines between two MR T1 images of the same patient. Only the 240 matched lines are displayed. Extremal points are represented by a color change from yellow to blue on the lines. (Left) View of matched crest lines from the left of the head. (Right) View from the front.

FIGURE 8 Example of registered crest lines between two MR T1 images of the same patient. Only the 240 matched lines are displayed. Extremal points are represented by a color change from yellow to blue on the lines. (Left) View of matched crest lines from the left of the head. (Right) View from the front.

About 75 crest lines are matched with more than 4 extremal points among the 550 lines in each image, leading to a total of 550 matched extremal points (only on the 75 matched lines). Using the techniques described in Section 3.2, we have computed that the typical object accuracy (the expected standard RMS error on image superimposition due to the transformation in the area of the matched features) is 0.04 mm, whereas the typical corner accuracy is 0.1mm. This is to be compared with the voxel size: 1 x 1 x 1.5 mm.

Registration of MR Images of the Head Figure 8 is an example of the registration of two MR T1 images of the same patient. In this case, 240 crest lines are matched among approximately 2100 in each image, for a total of 860 matched extremal points among 3600 in each image (about 25%). We used the zero-crossing of the Laplacian to define the interest surfaces. Thus, there are crest lines all over the head. However, if some of the matched lines are located on the surface of the skin (we can recognize the nose and the eyes), most of them are located on the surface of the brain. The typical object accuracy of the registration is 0.06 mm for a typical corner accuracy of 0.125 mm. Once again, the accuracy is far below the voxel size (0.97 x 0.97 x 1.5 mm).

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