Mixture of principal axes registration for change analysis in computer-aided diagnosis

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 nonlinear interpolation methods such as the thin-plate-spline approach. However, it is a difficulty task to establish an exact point correspondence due to the high complexity of the nonlinear deformation existing 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 an 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 (MLP) neural network to recover the nonlinear deformation. The neural computation for registration used a committee machine to obtain a mixture of piecewise rigid registrations, which gives a reliable point correspondence using multiple extracted objects in a finite mixture scheme. Then the MLP was 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 from 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.