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Mathematical Problems in Engineering
Volume 2016, Article ID 2370919, 14 pages
Research Article

An Improved Surface Simplification Method for Facial Expression Animation Based on Homogeneous Coordinate Transformation Matrix and Maximum Shape Operator

Department of Computer Science and Information Engineering, Minghsin University of Science and Technology, No. 1, Xinxing Road, Xinfeng Township, Hsinchu County 304, Taiwan

Received 28 September 2015; Revised 2 January 2016; Accepted 10 January 2016

Academic Editor: Fazal M. Mahomed

Copyright © 2016 Juin-Ling Tseng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Facial animation is one of the most popular 3D animation topics researched in recent years. However, when using facial animation, a 3D facial animation model has to be stored. This 3D facial animation model requires many triangles to accurately describe and demonstrate facial expression animation because the face often presents a number of different expressions. Consequently, the costs associated with facial animation have increased rapidly. In an effort to reduce storage costs, researchers have sought to simplify 3D animation models using techniques such as Deformation Sensitive Decimation and Feature Edge Quadric. The studies conducted have examined the problems in the homogeneity of the local coordinate system between different expression models and in the retainment of simplified model characteristics. This paper proposes a method that applies Homogeneous Coordinate Transformation Matrix to solve the problem of homogeneity of the local coordinate system and Maximum Shape Operator to detect shape changes in facial animation so as to properly preserve the features of facial expressions. Further, root mean square error and perceived quality error are used to compare the errors generated by different simplification methods in experiments. Experimental results show that, compared with Deformation Sensitive Decimation and Feature Edge Quadric, our method can not only reduce the errors caused by simplification of facial animation, but also retain more facial features.