Biomedical Engineering Reference
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Figure 24. Segmentation using shape prior active contour. The first column includes the
original noisy images for segmentation. The second column shows the images overlapped
with initial average shape. The third column are the images with the final segmentation
results. See attached CD for color version.
(see Figure 25). This method will automatically deal with the topological changes
during training and segmentation that is due to the level set representation method.
There are many methods that can be utilized to adjust parameters for the
model-based segmentation. Artificial neural networks, like Multi-Layer Percep-
trons (MLPs), have become standard tools for regression. In general, an MLP
with fixed structure defines a differentiable mapping from a parameter space to the
space of functions. In the case where an MLP is with a fixed structure, a regres-
sion problem enters into the adaptation of parameters: the weights of the network
given the sample data. This procedure is often referred to as learning. Because
MLPs are differentiable, gradient-based adaptation techniques are typically ap-
plied to determine the weights. The earliest and most straightforward adaptation
rule, ordinary gradient descent, adapts weights proportional to the partial deriva-
tives of the error functional. Several improvements on this basic adaptation rule
have been proposed, some based on elaborated heuristics, others on theoretical
reconsideration of gradient-based learning. Resilient backpropagation (Rprop) is
a well-established modification of the ordinary gradient descent. The basic idea is
to adjust individual step size for each parameter to be optimized. These step sizes
are not proportional to the partial derivatives but are themselves adapted based on
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