Probabilistic Modeling for Image Registration Using Radial Basis Functions: Application to Cardiac Motion Estimation

Cardiovascular diseases (CVDs) are the leading cause of death, affecting the cardiac dynamics over the cardiac cycle. Estimation of cardiac motion plays an essential role in many medical clinical tasks. This article proposes a probabilistic framework for image registration using compact support radial basis functions (CSRBFs) to estimate cardiac motion. A variational inference-based generative model with convolutional neural networks (CNNs) is proposed to learn the probabilistic coefficients of CSRBFs used in image deformation. We designed two networks to estimate the deformation coefficients of CSRBFs: the first one solves the spatial transformation using given control points, and the second one models the transformation using drifting control points. The given-point-based network estimates the probabilistic coefficients of control points. In contrast, the drifting-point-based model predicts the probabilistic coefficients and spatial distribution of control points simultaneously. To regularize these coefficients, we derive the bending energy (BE) in the variational bound by defining the covariance of coefficients. The proposed framework has been evaluated on the cardiac motion estimation and the calculation of the myocardial strain. In the experiments, 1409 slice pairs of end-diastolic (ED) and end-systolic (ES) phase in 4-D cardiac magnetic resonance (MR) images selected from three public datasets are employed to evaluate our networks. The experimental results show that our framework outperforms the state-of-the-art registration methods concerning the deformation smoothness and registration accuracy.