Restoring particle consistency in smoothed particle hydrodynamics
Applied Numerical Mathematics
Discontinuity-preserving moving least squares method
CIS'04 Proceedings of the First international conference on Computational and Information Science
Point-Based geometric deformable models for medical image segmentation
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
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Many of the computer vision algorithms have been posed invariousforms of differential equations, derived from minimization ofspecific energy functionals, and the finite element representationand computation have become the de facto numerical strategies forsolving these problems. However, for cases where domain mappingsbetween numerical iterations or image frames involve largegeometrical shape changes, such as deformable models for objectsegmentation and non rigid motion tracking, these strategies mayexhibit considerable loss of accuracy when themesh elements becomeextremely skewed or compressed. We present a new computationalparadigm, the meshfree particle method, where the objectrepresentation and the numerical calculation are purely based onthe nodal points and do not require the meshing of the analysisdomain. This meshfree strategy can naturally handle largedeformation and domain discontinuity issues and achieve desirednumerical accuracy through adaptive node and polynomial shapefunction refinement. We discuss in detail the element-free Galerkinmethod, including the shape function construction using the movingleast square approximation and the Galerkin weak form formulation,and we demonstrate its applications to deformable model basedsegmentation and mechanically motivated left ventricular motionanalysis.