Decomposition of Longitudinal Deformations via Beltrami Descriptors

TL;DR

This paper introduces a mathematical model using Beltrami descriptors to decompose longitudinal deformations in videos into normal and abnormal parts, aiding in medical image analysis.

Contribution

It proposes a novel decomposition method based on quasiconformal theory and low rank-sparse separation of Beltrami descriptors for analyzing longitudinal deformations.

Findings

Effective separation of periodic and abnormal motions demonstrated

Model validated on synthetic and real video sequences

Shows promise for medical image analysis applications

Abstract

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.