An Incompressible Log-Domain Demons Algorithm for Tracking Heart Tissue

We describe an application of the previously proposed iLogDemons algorithm to the STACOM motion-tracking challenge data. The iLogDemons algorithm is a consistent and efficient framework for tracking left-ventricle heart tissue using an elastic incompressible non-linear registration algorithm based on the LogDemons algorithm. This method has shown promising results when applied to previous data-sets. Along with having the advantages of the LogDemons algorithm such as computing deformations that are invertible with smooth inverse, the method has the added advantage of allowing physiological constraints to be added to the deformation model. The registration is entirely performed in the log-domain with the incompressibility constraint strongly ensured and applied directly in the demons minimisation space. Strong incompressibility is ensured by constraining the stationary velocity fields that parameterise the transformations to be divergence-free in the myocardium. The method is applied to a data-set of 15 volunteers and one phantom, each with echocardiography, cine-MR and tagged-MR images. We are able to obtain reasonable results for each modality and good results for echocardiography images with respect to quality of the registration and computed strain curves.