Non-rigid motion analysis in medical images: A physically based approach

Abstract

We present a physically-based deformable model which can be used to track and to analyze non-rigid motion of dynamic structures in time sequences of 2D or 3D medical images. The model considers an object undergoing an elastic deformation as a set of masses linked by springs, where the classical natural lengths of the springs is set equal to zero, and is replaced by a set of constant equilibrium forces, which characterize the shape of the elastic structure in the absence of external forces. This model has the extremely nice property of yielding dynamic equations which are linear and decoupled for each coordinate, whatever the amplitude of the deformation. Compared to the former work of Terzopoulos and his colleagues [12, 27, 26, 15] and Pentland and his colleagues [22, 21, 23, i0], our model can be viewed as a continuation and unification; it provides a reduced algorithmic complexity, and a sound framework for modal analysis, which allows a compact representation of a general deformation by a reduced number of parameters. The power of the approach to segment, track and analyze 2-D and 3-D images is demonstrated by a set of experimental results on various complex medical images (ultrasound and magnetic resonance images).