We present a physically based deformable model which can be used to track and to analyze the non-rigid motion of dynamic structures in time sequences of 2-D or 3-D medical images. The model considers an object undergoing an elastic deformation as a set of masses linked by springs, where the 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. 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.
"Physically based analysis of deformations in 3D images", Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); doi: 10.1117/12.146624; https://doi.org/10.1117/12.146624