Decomposition of Longitudinal Deformations via Beltrami Descriptors
This work addresses the detection of subtle abnormalities in periodic motions, such as in medical image analysis, but appears incremental as it builds on existing quasiconformal theories and decomposition methods.
The authors tackled the problem of decomposing longitudinal deformations into normal and abnormal components to detect subtle quivers in periodic motions from video sequences, with results demonstrating the efficacy of their model on synthetic and real data.
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.