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属性，在曲面分析中起着重要的作用。本文将人脸识别问题归结为自由曲面的三维形状识别问题，提出了一种基于最大和最小两种主曲率及其方向分析的方法。该方法基于简单的基于相关性的匹配算法，不需要进行人脸特征提取和曲面分割，将输入图像和模型库中的每个人脸都表示为扩展的高斯图像(EGI)，通过将主(最大和最小)曲率及其方向映射到单位球面上，在每个曲面点进行估计。然后利用Fisher球面相关法进行人脸识别，并对NRCC(National Research Council)3D图像数据文件中的37幅人脸图像进行了简单和稳健性测试。事实证明，这种方法非常简单、高效，而且对眼镜、胡须或发型等干扰很健壮。这代表了与基于传统方法的2D特征(例如眼睛、嘴巴图案)相比的重要优势。结果表明，表面曲率的形状信息为区分和识别人脸等细微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.