Various methods o f surface fitting outlined in the literature can be characterized by differences in the type and level o f description at which the matching was attempted. Accordingly, some new approaches are used in the current work to facilitate the surface fitting algorithm and reduce its previous deficiencies.
a) The matching performed by most o f the previous workers was based on the surface patches delineated between a number o f selected points on the contours o f 2-D slices. In this work, the fitted surfaces are characterized by voxels in 3-D geometrical space. Since the surfaces are represented at the voxel level, a good accuracy can be expected in presentation o f fine structures and surface details.
With respect to that, any hole which is likely to be due to presence of tumour or cold regions in the surface o f ECT (Emission Computerized Tomography) data, can be interpolated. As discussed in section 4.5, extrapolating over such holes can reform the defective parts o f surfaces, and thus facilitate the application of the surface fitting method for registration o f SPECT data.
c) A new approach, based the shape interpolation (see section 4.4.4), for reconstruction o f the surface between the adjacent slices is used. It is believed (Herman 1991) that a better approximation (than the one o f trilinear interpolation) is obtained between the contours o f thick slices or in the gaps between them. In this method, the geometrical form o f the surface is represented by the locations o f the (binary) voxels, and grey scale values are not used.
d) Unlike some o f previous methods, only rotations and translations are applied as 3-D rigid transformation. In this work, no attempt is made to scale the data during the routine registration process. The scaling is applied only at the preprocessing stage based on the knowledge of imaging parameters. However, if the statistic o f the individual distance errors confirms an uncertainty in image size, an attempt is made to scale the registering data set. This uncertainty is due to segmentation errors for example a possible sub-optimal choice o f threshold in surface detection process. In this respect, the variance o f distance errors are evaluated as well as the distance errors (e.g. MSD value). Special attention is paid, then, to a high MSD value which has a low variance. These are counted as behaviour o f two images being registered at different wrong geometrical scaling.
e) In the current method, after each stage in which a promising transformation is detected, the coordinates o f the transforming surface are updated. The sample points are then reselected from the transformed surface. This updating and re-sampling strategy minimizes the error introduced due to sub-optimal choice o f the point-correspondence (as described in section 3.2.4).
f) Due to the inherent type o f surface representation, the method o f ray tracing and 3-D intersection used in the current work is based on a line drawing algorithm in 3-D geometrical space. Although this intersection method ought to be slower than those based on intersection of a ray with surface patches (tiles), some efficient modifications, such as tracing o f a small line segment around the surface points (instead o f a line through 3-D volume data), make the algorithm fast enough to be applicable in the surface fitting process. The efficiency becomes
consistently higher with reducing the size o f intersection line across the surfaces.
g) Viewing and visual inspection play a major and important role in registration process. Three orthogonal contours (on the 3 orthogonal planes) o f cross sectional images are displayed before starting an automatic registration and also between some stages o f the registration. This visualization makes the manual interaction and operator modifications applied during the registration easier. The superimposed 3-D registering points (from hat) and the surface data (head) are also illustrated in one comer o f the same contour-viewing screen.
h) The surface fitting technique was augmented in order to preclude undesirable local minima obtained by previous methods, thereby allowing it to be used on SPECT imaging. A multi dimensional symmetric space o f geometric transformations is globally searched, in a novel approach, for the global transformation parameters (at the true match location). Using a cumulative distance error instead of a mean distance error provides a sequential process which can be terminated at certain mismatch locations. An alternative type of algorithm which uses a multi-grid (known as multi-resolution) coarse-to-fine search space to speed up the registration process is suggested. Using these two strategies greatly reduces the search effort and makes the global search applicable for registration o f the medical images, at a reasonable computing time. These are the main originalities o f the project, being set forth in chapters 6 and 7.
i) Finally, display methods o f the registered images and superimposition routine were developed which are new in their own approach. The implementation was mostly based on the requirements of clinicians in the hospital where the work was performed. In chapter 9, different display methods as well as some examples o f superimposed images are outlined.