  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.

Computer Vision and Pattern Recognition