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The measurement of three-dimension surface by scanning usually
generates huge amount of data occupying very large space of
storage. In stead of saving the dimensional data directly, this
paper proposes to approximate the surface by learning the
measured data with a neural network and then simply saves the
weights of the neural network in the storage. This approach is
found to be able to achieve simultaneously the results of
approximation, smoothing and, more importantly, compression of
the surface data. The Radial Basis Function (RBF) Neura Network
is chosen to be the approximator due to its performance in
accuracy. The learning algorithm is developed on the basis of
Recursive Least Square Method (RLSM) so that incremental
learning of the surface can be achieved. The capability of
incremental learning allows the approximation by the Neural
Network to be improved along with the addition of new
measurements of the surface. Since the accuracy of
approximating a surface by the Neural Network with fixed
numbers of layers and nodes is closely related to the
complexity or order of the target surface. An algorithm of
adaptive segmentation is developed to split the surface data
into segments each with suitable complexity for approximation.
Given the desired accuracy of approximation, it is shown that
the RBF Neural Network based approximator can obtain large
ratio of data compression. Several numerical examples are
demonstrated.
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