BENDING AND STRETCHING MODELS FOR LV WALL MOTION ANALYSIS FROM CURVES AND SURFACES

A unified framework for motion tracking of curves and surfaces with specific applications to the left-ventricular endocardial wall is outlined. The theory considers both two-dimensional curves and three-dimensional surfaces, and in each case uses an elastic model of the object with constraints on the types of motion for tracking the movement. The emphasis of the paper is on surface motion. For surface motion, conformal stretching is measured from a system of coordinates based on the principal direction of a surface patch. In addition, an energy for bending of a 3D surface is defined and used for motion tracking. Membrane smoothing with confidences is used to optimize the initial 3D flow estimates. 4D example data from different imaging modalities of the left ventricle in motion are illustrated. Algorithms are presented, and applications to real and simulated data are included.