## Aj xx

expl 2 2

The calculation of the Wj's implies an "external" computational loop where p- is decreased and an internal loop where the Wj's are calculated by iteration of (43) for each given p. In detail, this works as follows: In a first step, the number tmax of the "external" iteration steps, the initial p(t = 0), and final value p(tmax) of the widths pj of the receptive fields are defined, and the codebook vector positions are initialized at the center of the data distribution X. While keeping pj = p(t = 0) constant, the "internal" loop is iterated according to (43) until the codebook vectors have reached stationary positions or a maximal number of iteration steps (e.g., 50) have been performed. Subsequently, the widths pj of the receptive fields are reduced according to an exponential decay scheme p(t) = p(0) W te [0, tmax], (45)

and the procedure is repeated. The computation is stopped at the iteration step tmax of the "external" loop.

As a result, we obtain a fuzzy tesselation of the feature space X. According to Eq. (23), the codebook vectors Wj represent the

The data set X = {x} is now presented as the input to a vector quantizer according to Section 3.1. By uĀ«supervised clusteri"g, a set C of codebook vectors Wj with C = {Wj e IR" | j e {1,..., N}} is computed that represent the data set X. Here, the number N of codebook vectors is much smaller than the number of feature vectors. The codebook vector positions are

FIGURE 8 Manual labeling of tissue classes for supervised learning. The labeled regions (medium gray = "gray matter,'' light gray = "white matter,'' dark gray = "CSF") provide the training data set for supervised learning of the output weights Sj of the GRBF network.

Value

FIGURE 9 Comparison of the segmentation results for a frontal coronal cross-section of data set 2. (a) T1 weighted image. (b) Segmentation by vector quantization and subsequent manual interactive assignment of codebook vectors. (c) Segmentation by a GRBF classifier.

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