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Acquisition of the unique solution based on spline network [neuro-surgical navigation system]

As the means for regularization, in providing solution uniqueness, we propose spline networks which evaluate the derivative norm of the network output as well as the mean square error of the network. These networks incorporate the power units in the hidden layer and a gating unit to select the best power unit. We confirm the effectiveness of the proposed method by comparing the network output with those of the non-regularized network and with the Gaussian regularizer. We also consider the application of the network in the medical field. In neuro-surgical operations, the acquisition of an accurate relationship between the patient and the tomogram, e.g. CT or MRI, is important to minimize the damage to the normal tissue and to shorten the surgical time. We propose a navigation system which calculates the 3-D probe position from 2-D values given by CCD images, with the consideration on the ill-posedness of the problem arising in the nonlinear transformation of the positional information with the neural network, using fewer tutorial data.