Meshfree particle method

Many of the computer vision algorithms have been posed in various forms of differential equations, derived from minimization of specific energy functionals, and the finite element representation and computation have become the de facto numerical strategies for solving these problems. However, for cases where domain mappings between numerical iterations or image frames involve large geometrical shape changes, such as deformable models for object segmentation and nonrigid motion tracking, these strategies may exhibit considerable loss of accuracy when the mesh elements become extremely skewed or compressed. We present a new computational paradigm, the meshfree particle method, where the object representation and the numerical calculation are purely based on the nodal points and do not require the meshing of the analysis domain. This meshfree strategy can naturally handle large deformation and domain discontinuity issues and achieve desired numerical accuracy through adaptive node and polynomial shape function refinement. We discuss in detail the element-free Galerkin method, including the shape function construction using the moving least square approximation and the Galerkin weak form formulation, and we demonstrate its applications to deformable model based segmentation and mechanically motivated left ventricular motion analysis.