Deformable object tracking using the boundary element method

Abstract

This paper presents a method to perform 2D (two-dimensional) deformable object tracking using the boundary element method (BEM). BEM, like the finite element method (FEM), is a technique to model an elastic solid. BEM differs from FEM in that only the contour of an object needs to be meshed for BEM, making this method attractive for computer vision problems. For FEM, the interior of the object must be meshed also. In order to track deformable objects, a deformable template is defined that uses BEM to model displacements. The template is registered to the image by applying a force field that deforms the template to match the image. This force field is found using an energy minimization approach. Even though the deformable template uses a linear elastic model, it can be used to track the deformations of objects with nonlinear material properties or in cases where there are large deformations. We demonstrate the performance of this method on objects with linear and nonlinear elastic properties. In addition, it is discussed how this method can be readily extended to 3D (three-dimensional) deformable object tracking.