Mathematical Representations of Blended Facial Expressions towards Facial Expression Modeling

The paper mainly aims to create a mapping between facial expression and its corresponding facial muscle contractions along with their movement directions. This mapping is illustrated in terms of mathematical symbolic representations. The paper proposes a set of mathematical representations of basic as well as blended facial expressions. These symbolic representations of facial expressions are evaluated from different normalized facial features and 2D spatial coordinates of a face. They offer a simple generalization of 18 facial expressions and will be used as a background formulation for generating expressive face image from a given neutral face. The facial expression modeling and synthesis is a widely useful application for man-machine interaction.