Numerical integration methods for simulation of mass-spring-damper systems

The dynamics of a face are often implemented as a system of connected particles with various forces acting upon them. Animation of such a system requires the approximation of velocity and position of each particle through numerical integration. There are many numerical integrators that are commonly used in the literature. We conducted experiments to determine the suitability of numerical integration methods in approximating the particular dynamics of mass-spring-damper systems. Among Euler, semi-implicit Euler, Runge-Kutta and Leapfrog, we found that simulation with Leapfrog numerical integration characterizes a mass-spring-damper system best in terms of the energy loss of the overall system.This research is part of project "Expression Recognition based on Facial Anatomy", grant number 109E061, supported by The Support Programme for Scientific and Technological Research Projects (1001) of The Scientific and Technological Research Council of Turkey (TUBITAK)Publisher's Versio

Semi-automatic adaptation of high-polygon wireframe face models through inverse perspective projection

Precise registration of a generic 3D face model with a subject's face is a critical stage for model based analysis of facial expressions. In this study we propose a semi-automatic model fitting algorithm to fit a high-polygon wireframe model to a single image of a face. We manually mark important landmark points both on the wireframe model and the face image. We carry out an initial alignment by translating and scaling the wireframe model. We then translate the landmark vertices in the 3D wireframe model so that they coincide with inverse perspective projections of image landmark points. The vertices that are not manually labeled as landmark are translated with a weighted sum of vectorial displacement of k neighboring landmark vertices, inversely weighted by their 3D distances to the vertex under consideration. Our experiments indicate that we can fit a high-polygon model to the subject's face with modest computational complexity.This research is part of project "Expression Recognition based on Facial Anatomy", grant number 109E061, supported by The Support Programme for Scientific and Technological Research Projects (1001) of The Scientific and Technological Research Council of Turkey (TUBITAK)Publisher's Versio