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We propose an optical navigation system that acquires the 3-D position in real space from 2-D values given by multiple CCD images and discuss the ill-posedness of the problem arising in nonlinear transformation of the positional information with a neural network, using fewer tutorial data. Regularization of the network output can be achieved by minimization of the second derivative norm of the network output and construction of a segmented network that approximates cubic splines with power units. We confirm the effectiveness of the proposed method by comparing the network outputs to those of a nonregularized network and a network with a Gaussian regularizer. ã 1998 Scripta Technica, Syst Comp Jpn, 29(10): 3645, 1998

Ill-posed problems arising in image-guided navigation systems and a network realization based on spline interpolation