Research Of Facial Animation Based On Partial Differential Equation

Along with the three dimensional animation advertisements frequently broadcast on TV screen, computer animation has quietly into the People's Daily life. About human body animation of computer animation, facial expression animation is the most difficult and most challenging problems. Facial expression animation involving multiple organ of facial motion coordination, the face modelling of highly realistic requirement, has its own characteristics. The development of the computer animation for people's communication, culture and recreational bring great convenience and fun. Whether film and television, and virtual teaching or network video game, or a meeting, facial expression animation techniques are applied among them, become an indispensable component parts.In view of face rich expression, simple geometric muscle model certainly cannot be really emersion rich expression details. Therefore, the traditional simple mathematical model generated facial expressions tend to appear very inflexible, has the obvious artificial trace. In recent years, many researchers use facial image to drive the deformation of the 3d face geometry model, and combining texture mapping technology to achieve the change of facial expressions and realistic rendering. This paper studied the change of the facial expressions based on partial differential surface, mainly includes three parts:the structures of the face geometry model, textured drawing of face models and the formation of facial animation. Taking advantage of the boundary-value approach inherent to PDE method, by applying different mathematical transformations to the affected facial boundary curves according to acquire the corresponding facial expression.Done the research work includes the following aspects:1) Two methods were studyed on the structure of surfaces based on Partial Differential Equation:analytic solutions and numerical solution. Geometrical modelling has a very important role in computer animation production process.It is one of the indispensable module in computer animation system. Compared with the traditional surface geometrical modelling technology, tectonic surface using Partial Eifferential Equation method only needed control a few parameters, activating a group of parametric surface, without using any other insert algorithm of the traditional surface, using this method is fast and easy to use. This paper mainly studies the principle and construction method of tectonic face models using elliptic partial differential equation method, and finally fitting out a neutral 3d face models.2) Studied the technique based on the radial basis function with binding face models texture mapping. Compared with the traditional texture mapping technique, based on RBF function of texture mapping technology is more convenient, simple, and can better mapping complex mapping work, mapping results is more realistic. This method extracted a set of characteristic constraint points from the given 2d image, and corresponding to features constraint points extracted from 3d face modules constructed based on PDE method. According to these known texture coordinates of texture graphics constraint points and the corresponding constraints points in 3d face model. Using radial basis function (RBF) ask out all the texture coordinates of the constraint points. Eventually completed the textured drawing of face models.3) After completing face models texture mapping, studied using the mathematical way to control deformation and forming different facial expression, eventually simulate the lifelike expression of happy, fear, disgust, surprised, they are corresponded with the smile, mouthopen, curl lip, raise eyebrow. in the paper also realized innovativly the expression of eyesclose, stiff and eyesclose combined with stiff, eyesclose combined with curl lip, eyesclose combined with smill etc, finally, given the expression formula.4) Finally summarized the full text, pointed out the existing limitations and future research direction.