Various real-time applications such as Human–Computer Interactions, Psychometric analysis, etc. use facial expressions as one of the important parameters. The researchers have used Action Units (AU) of the face as feature points and its deformation is compared with the reference points on the face to estimate the facial expressions. Among many parts of the face, features from the mouth contribute largely to all the well-known emotions. In this paper, the parabola theory is used to identify and mark various points on the lips. These points are considered as feature points to construct feature vectors. The Latus Rectum, Focal Point, Directrix, Vertex, etc. are also considered to identify the feature points of the lower lips and upper lips. The proposed approach is evaluated on benchmark datasets such as JAFFEE and Cohn–Kanade dataset and it is found that the performance is encouraging in understanding the facial expressions. The results are compared with contemporary methods and found that the proposed approach has given good classification accuracy in recognizing facial expressions.

各种实时应用程序，例如人机交互、心理测量分析等，都将面部表情作为重要参数之一。研究人员使用人脸的动作单元（AU）作为特征点，并将其变形与人脸的参考点进行比较，以估计人脸表情。在面部的许多部分中，嘴巴的特征在很大程度上促成了所有众所周知的情绪。在本文中，抛物线理论用于识别和标记嘴唇上的各个点。这些点被认为是构造特征向量的特征点。Latus Rectum、Focal Point、Directrix、Vertex等也被认为是识别下唇和上唇的特征点。所提出的方法在 JAFFEE 和 Cohn-Kanade 数据集等基准数据集上进行了评估，发现在理解面部表情方面的表现令人鼓舞。将结果与当代方法进行比较，发现所提出的方法在识别面部表情方面具有良好的分类精度。