Deformable B-Solids and Implicit Snakes for 3D Localization and Tracking of SPAMM MRI Data

Abstract

To date, MRI–SPAMM data from different image slices have been analyzed independently. In this paper, we propose an approach for 3D tag localization and tracking of SPAMM data by a novel deformable B-solid. The solid is defined in terms of a 3D tensor product B-spline. The isoparametric curves of the B-spline solid have special importance. These are termed implicit snakes as they deform under image forces from tag lines in different image slices. The localization and tracking of tag lines is performed under constraints of continuity and smoothness of the B-solid. To track motion from boundaries and restrict image forces to the myocardium, a volumetric model is employed as a pair of coupled endocardial and epicardial B-spline surfaces. To recover deformations of the left ventricle (LV), an energy-minimization problem is posed where both tag and LV boundary data are used. The framework has been implemented on tag data from short axis (SA) cardiac images, as well as SA LV boundaries, and is currently being extended to include long axis data.