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Methods
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details can be matched refines the registration. At this stage, the computational effort is much
higher than before.
The computation can be terminated at any point if the results seem to be sufficient. Also,
the user can later compare the results of the low-resolution matching with the high-resolution
matching results. Matching on lower resolution images with fewer control points sometimes
has advantages because the matching is not as prone to noise. On the other hand, fine details
cannot be matched. Therefore, as a rule of thumb it can be stated that the number of control
points and the image resolution should be increased if the data is better, i.e., less noisy. At
each step of the hierarchical matching procedure, the aim of the optimization procedure is to
find the displacement field that minimizes the total energy (weighted sum of the explained
energy components).
The hierarchical approach has two main advantages over performing all operations at the
highest resolution with many control points. First, the speed of calculation is increased be-
cause the algorithm is able to find a good early fit fast. Second, local minima are avoided be-
cause the algorithm matches at first blurred images so that gross structures drive the fit at this
stage. Then, the result of the previous step is used as a starting point for the next step, where
the matching is done with less blurred data to process finer details. In [Evans, et al., 1996
#48], a similar procedure is described for the case where two volumes are to be registered.
5.2.9 Advantages of Atlas Matching
Functional flat maps can contain a lot of noise (see Figure 45). In many cases, it is even for
experienced human users difficult to find boundaries between adjacent retinotopic visual ar-
eas. This makes the automatic segmentation extremely difficult. Approaches that only use lo-
cal phase data in an image have the disadvantage that they are prone to noise. It was therefore
decided to take the whole region of interest (the area in a phase image that corresponds to the
atlas area) into account, i.e., calculating a global energy based on the difference between de-
formed atlas and corresponding measured image. The representation of the displacement field
(displacement values are only assigned to control points) and an energy component that in-
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