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Yayın Numerical integration methods for simulation of mass-spring-damper systems(Springer-Verlag, 2012) Özgüz, Mete; Eskil, Mustafa TanerThe 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.Yayın An observation based muscle model for simulation of facial expressions(Elsevier Science BV, 2018-05) Erkoç, Tuğba; Ağdoğan, Didem; Eskil, Mustafa TanerThis study presents a novel facial muscle model for coding of facial expressions. We derive this model from unintrusive observation of human subjects in the progress of the surprise expression. We use a generic and single-layered face model which embeds major muscles of the human face. This model is customized onto the human subject's face on the first frame of the video. The last frame of the video is used to project a set of manually marked feature points to estimate the 3 dimensional displacements of vertices due to facial expression. Vertex displacements are used in a mass spring model to estimate the external forces, i.e. the muscle forces on the skin. We observed that the distribution of muscle forces resemble sigmoid or hyperbolic tangent functions. We chose hyperbolic tangent function as our base model and parameterized it using least squares. We compared the proposed muscle model with frequently used models in the literature.
