Detection of abnormal deformations from normal motions via RPCA of Beltrami coefficients

Detection of abnormal deformations from normal motions is crucial in image analysis, especially for medical image analysis. For instance, accurate extraction of abnormal cardiac motions is a necessary procedure for cardiac disease analysis. The combination of nomral motion and abnormal deformations bring challenges to extract abnormalities. In this work, we propose a novel method to extract abnormal deformation from normal (periodic) motions by using the Beltrami coefficients (BC). BCs are used to represent a sequence of deformations over a sequence of images capturing an object of interest in motion. RPCA is then performed on the BCs to decompose the overall motion into nomral motion and abnormal deformation. Experiments have been carried out on both synthetic and real medical image sequence, which demonstrate the efficacy of our proposed method.

Example 1:

(First) Original deformation; (Second) Extracted normal deformation; (Third) Extracted abnormal deformation.

Example 2:

(First) Original deformation; (Second) Extracted normal deformation; (Third) Extracted abnormal deformation.