Non-rigid image registration is a prerequisite for many medical image analysis applications such as image fusion of multi-modality images and quantitative change analysis of a temporal sequence in computer-aided diagnosis. By establishing the point correspondence of the extracted feature points, it is possible to recover the deformation using non-linear interpolation methods such as the thin-plate-spline approach. However, it is a difficulty task to establish exact point correspondence due to the high complexity of nonlinear deformation existed in medical images. In this paper, a mixture of principal axes registration (mPAR) method is proposed to resolve the correspondence problem through a neural computational approach. The novel feature of mPAR is to align two point sets without needing to establish explicit point correspondence. Instead, it aligns the two point sets by minimizing the relative entropy between their probability distributions resulting in a maximum likelihood estimate of the transformation matrix. The registration process consists of: (1) a finite mixture scheme to establish an improved point correspondence and (2) a multilayer perceptron neural network (MLP) to recover the nonlinear deformation. The neural computation for registration used a committee machine to obtain a mixture of piece-wise rigid registrations, which gives a reliable point correspondence using multiple extracted objects in a finite mixture scheme. Then the MLP is used to determine the coefficients of a polynomial transform using extracted cross points of elongated structures as control points. We have applied our mPAR method to a temporal sequence of mammograms of a single patient. The experimental results show that mPAR not only improves the accuracy of the point correspondence but also results in a desirable error-resilience property for control point selection errors.