A VARIATIONAL APPROACH TO CARDIAC MOTION ESTIMATION BASED ON COVARIANT DERIVATIVES AND MULTI-SCALE HELMHOLTZ DECOMPOSITION

作者：Duits Remco^*; Janssen Bart; Becciu Alessandro; van Assen Hans

来源：Quarterly of Applied Mathematics, 2013, 71(1): 1-36.

• Covariant derivatives
• fiber bundles
• Helmholtz decomposition
• inverse problems
• optical flow methods in image analysis
• scale space

The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev norm expressed in covariant derivatives. These covariant derivatives are used to express prior knowledge about the velocity field in the variational framework employed. Furthermore, we propose a multi-scale Helmholtz decomposition algorithm that combines diffusion and Helmholtz decomposition in one nonsingular analytic kernel operator in order to decompose the optic flow vector field in a divergence-free and a rotation-free part. Finally, we combine both the multi-scale Helmholtz decomposition and our vector field reconstruction (based on covariant derivatives) in a single algorithm and show the practical benefit of this approach by an experiment on real cardiac images.

• 出版日期2013