3D image matching using a finite element based elastic deformation model

Abstract

We present a new approach for the computation of the deformation field between three dimensional (3D) images. The deformation field minimizes the sum of the squared differences between the images to be matched and is constrained by the physical properties of the different objects represented by the image. The objects are modeled as elastic bodies. Compared to optical flow methods, this approach distinguishes itself by three main characteristics: it can account for the actual physical properties of the objects to be deformed, it can provide us with physical properties of the deformed objects (i.e. stress tensors), and computes a global solution to the deformation instead of a set of local solutions. This latter characteristic is achieved through a finite-element based scheme. The finite element approach requires the different objects in the images to be meshed. Therefore, a tetrahedral mesh generator using a precomputed case table and specifically suited for segmented images has been developed. Preliminary experiments on simulated data as well as on medical data have been carried out successfully. Tested medical applications included muscle exercise imaging and ventricular deformation in multiple sclerosis.