CNN-Driven Quasiconformal Model for Large Deformation Image Registration

We present a novel way to perform image registration, which is not limited to a specific kind, between image pairs with very large deformation, while preserving Quasiconformal property without tedious manual landmark labeling that conventional mathematical registration methods require. Alongside the practical function of our algorithm, one just-as-important underlying message is that the integration between typical CNN and existing Mathematical model is successful as will be pointed out by our paper, meaning that machine learning and mathematical model could coexist, cover for each other and significantly improve registration result. This paper will demonstrate an unprecedented idea of making use of both robustness of CNNs and rigorousness of mathematical model to obtain meaningful registration maps between 2D images under the aforementioned strict constraints for the sake of well-posedness.

Decomposition of Longitudinal Deformations via Beltrami Descriptors

We present a mathematical model to decompose a longitudinal deformation into normal and abnormal components. The goal is to detect and extract subtle quivers from periodic motions in a video sequence. It has important applications in medical image analysis. To achieve this goal, we consider a representation of the longitudinal deformation, called the Beltrami descriptor, based on quasiconformal theories. The Beltrami descriptor is a complex-valued matrix. Each longitudinal deformation is associated to a Beltrami descriptor and vice versa. To decompose the longitudinal deformation, we propose to carry out the low rank and sparse decomposition of the Beltrami descriptor. The low rank component corresponds to the periodic motions, whereas the sparse part corresponds to the abnormal motions of a longitudinal deformation. Experiments have been carried out on both synthetic and real video sequences. Results demonstrate the efficacy of our proposed model to decompose a longitudinal deformation into regular and irregular components.