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6.4 Structural Matching 273

The probabilities are then updated, as:

As a result of this updating process, it is expected that the probabilities
corresponding to a match will be close to one, while the other values will be close
to zero. In practice, one may stop the iterative process when a sufficient
discrimination of values above or below 0.5 is reached.

Figure 6.21. An image registration example, where the goal is to establish a
correspondence of centroids of A regions with centroids of B regions.

We exemplify this method using the regions shown in Figure 6.21, where there
are two types of regions (white and grey) with areas and distances among the
centroids as indicated. Table 6.4 shows the probability matrix from the initial phase
up to the second iteration. Initially, the probabilities depend only on the region
size, and in this particular case, all non-zero values are initially close to one. In the
following iterations, the compatibility factors play their role so that in the second
iteration it is already clear that there is only one valid match: (AI,B3), (A2,B2).

Table 6.4. Estimates of centroid matching probabilities for the image registration
example.