Face Surface Recognition from Surface Curvature

曲面曲率，如高斯曲率、平均曲率和主曲率是曲面的固有性质，在曲面分析中起着重要的作用。然而，只有它们的符号才能可靠地用于分类和识别表面。本文将人脸识别问题视为自由曲面的三维形状识别问题，提出了一种基于两种主曲率——最大曲率和最小曲率及其方向分析的人脸识别方法。该方法基于简单的基于相关性的匹配算法，既不需要提取人脸特征，也不需要进行表面分割。输入图像和模型数据库中的每个面都表示为扩展高斯图像（EGI），该图像通过将主（最大和最小）曲率及其方向映射到单位球上构建，并在每个表面点上进行估计。然后通过使用Fisher的球面相关来评估其他面孔之间的相似性来识别单个面孔。对该方法的简单性和鲁棒性进行了测试，并对来自加拿大国家研究委员会（NRCC）三维图像数据文件的37张人脸范围图像逐一实现。事实证明，这种方法非常简单、有效，而且不受眼镜、面部毛发或发型等干扰。与传统的基于2D特征的方法（如眼睛、嘴的图案）相比，这代表了重要的优势。结果表明，曲面曲率的形状信息为识别人脸等精细表面结构提供了重要线索。

Surface curvatures such as Gaussian, mean and principal curvatures are intrinsic surface properties and have playd important roles in curved surface analysis. However, only their signs are reliably used in classifying and identifying surfaces.In this paper, we treat face recognition problem as 3D shape recognition problem of free-form curved surfaces and present an approach based on the analysis of two principal curvatures, max and minimum curvatures and their directions. The approach is based on simple correlation-based matching algorithm which does not require either face feature extraction or surface segmentation.Each face in both input images and the model database, is represented as an Extended Gaussian Image(EGI), constructed by mapping principal (max and minimum) curvatures and their directions onto the unit sphere, estimated at each surface points. Individual face is then recognized by evaluating the similarities among others by using Fisher's spherical correlation.The method is tested for its simplicity and robustness and successively implemented for each of 37 face range images from NRCC (National Research Council Canada) 3D image data files. It turned out that the method is quite simple, efficient and robust to distractions such glasses, facial hair or hair style. These represent important advantages over conventional method based 2D features such as eye, mouth patterns. Results shows that shape information from surface curvatures provides vital cues in distinguishing and identifying such fine surface structure as human faces.