Non-Rigid Image Registration by Neural Computation

Non-rigid image registration is a prerequisite for many medical image analysis applications such as image fusion of multimodality 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. However, it may be very difficult to establish such correspondence at an initial stage when confronted with large and complex deformation. 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 the alignment of two point sets without the need of establishing 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 two steps: (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 uses 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 control points. We have applied our mPAR method to register synthetic data sets, surgical prostate models, and 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.