目的 人脸2维图像反映出来的纹理并非是3维人脸曲面真实的纹理，并且受光照和妆容的影响很大，因此探索3维局部纹理特征对于人脸识别任务有着重要的意义。为此详细分析了一种新颖的3维局部纹理特征mesh-LBP对于人脸纹理的描述能力。方法 首先，在特征提取和识别任务之前，进行一系列的预处理：人脸分割、离群点移除和孔洞填补；接着，在预处理后的人脸曲面上，提取原始mesh-LBP特征，以及基于阈值化策略的3种改进特征：mesh-tLBP、mesh-MBP和mesh-LTP；然后，对于上述提取的4种特征，采用不同的统计方法，包括整体直方图、局部分块直方图和整体编码图像，用做人脸纹理的特征描述。最后，针对CASIA3D数据集中不同表情和姿态变化的人脸，采用余弦相似度进行人脸的识别任务。结果 通过对比人脸曲面和普通物体曲面的纹理特征，发现人脸纹理完全不同于普通纹理，不规则并且难以描述；通过对比mesh-LBP两种变体，发现mesh-LBP（α₁）适用于姿态变化，而mesh-LBP（α₂）适用于表情变化；通过对比原始mesh-LBP及其3种改进，发现mesh-tLBP对于人脸不同表情变化下的识别准确率最高有0.5%的提升；通过对比3种不同的统计方法，发现采用整体编码图像进行统计的特征尽管弱于局部分块直方图，但相比整体直方图，识别率在不同表情变化下最高有46.8%的提升。结论 mesh-LBP特征是一种优良的3维局部纹理特征，未来将会在3维医学处理、3维地形起伏检测以及3维人脸识别中得到更多的应用。

Objective The texture reflected by 2D facial image is different for a 3D face surface, and this 2D texture is considerably affected by the variations of illumination and make-up. These issues make the investigation on 3D local texture features important for face recognition tasks. The concept of 3D texture is completely different from 2D texture, which reflects the repeatable patterns of a 3D facial surface. Aside from the geometric information, 3D texture preserves the photometric information of the same individual due to the flexibility of 3D mesh. Therefore, two original 3D textures, namely, 3D geometric texture and 3D photometric texture, should be investigated. Method In this study, we investigate a novel framework called mesh-LBP in representing 3D facial texture in detail. Here, we mainly focus on the improvement and statistic of this operator rather than the comparisons on final face recognition rate with state-of-the-art methods. First, a set of general preprocessing operations, including face detection, outlier removal, and hole filling, are performed before feature extraction and classification because raw 3D facial data contain spikes and holes and a large background area. Specifically, a facial surface is initially cropped by using a common scheme, that is, the point sets of a raw face model located on a sphere that are constructed by nose tip and fixed radius, are extracted as the detected facial area. Then, we define the outlier of raw data as the point whose number of neighborhood points are lower than that of a threshold. A mean filter is used to smooth the facial surface when these outliers are detected. The outlier removal operation usually results in holes in 3D facial data. Thus, we adopt bicubic interpolation to solve this problem. Second, the construction procedure of original mesh-LBP operator and three improved operators based on thresholding scheme, which we called mesh-tLBP, mesh-MBP, and mesh-LTP, are developed. For the mesh-tLBP, a small threshold is added to the calculation process of the mesh-LBP. For the mesh-MBP, the value of a center facet on the mesh is replaced by the mean value of its neighborhood. For the mesh-LTP, an additional coding unit is added for the subtle capture of code changes of the mesh-LBP. The first two improvements are designed for the robustness of the mesh-LBP to noise or face changes, whereas the last one improves the power of the mesh-LBP in capturing facial details. Third, different statistical methods, including nave holistic histogram, spatially enhanced histogram, and holistic coded image, are employed to form the final facial representation. For the nave holistic histogram, we do not use any processing method and directly perform frequency statistics on the calculated LBP pattern. For the spatially enhanced histogram, we initially block a 3D facial surface, perform frequency statistics for each block, and concatenate them to form the entire description of the face. For the holistic coded image, we directly use the calculated LBP pattern. However, the number of patterns from different faces is different; thus, we initially normalize them to the same size. Finally, we employ 615 neutral scans under different illumination condition from CASIA3D face database as the training set and evaluate the recognition performance on 615 scans of expression variation and 1 230 scans of pose on the basis of a simple minimum distance classifier. Result Comparison of the texture features of facial surface and common object surface show that the facial texture is completely different from ordinary texture and is irregular and difficult to describe. In addition, the texture variations of 3D faces are smaller than that of 2D faces, and this finding shows the superiority of 3D data. Experiments on the two variants of mesh-LBP show that the mesh-LBP(α₁) is more robust to pose variations, whereas the mesh-LBP(α₂) is more robust to express variations. Experiments on the two variants of mesh-LBP and its three improvements indicate that only mesh-tLBP causes a 0.5% improvement of recognition accuracy on different facial expression variations in the best case. Results of the mesh-LTP are basically the same as those of the mesh-LBP, whereas the results of the mesh-MBP are worse than those of the mesh-LBP. These improvements do not enhance the representation of 3D facial textures, and pre-processing and parameter selection schemes should be conducted to obtain improved results. Comparison of the results of the three statistical methods show that features based on the spatially enhanced histogram obtain the best recognition in two experimental scenarios. The description power of features based on holistic coded image is weaker than that of the spatially enhanced histogram; however, its recognition rate is increased by 46.8% compared with the features based on the naive holistic histogram on different expression variations in the best case. In addition, the results of features based on the holistic coded image on pose variations are the worst among all the statistical methods, which is mainly due to the limitation of the image. Conclusion In comparison with other 3D local feature descriptors, the mesh-LBP is an elegant and efficient framework that allows the direct extraction of 3D local textures from a mesh manifold. The calculated patterns of mesh-LBP can use different statistical methods for the 3D texture analysis of different types of object. For example, the simple mesh-hLBPH is suitable for ordinary 3D objects, whereas the mesh-eLBPH is applicable for 3D face analysis. The mesh-LBP can be used extensively in 3D medical imaging, 3D terrain relief inspection, and 3D face recognition in the near future. Several aspects will be investigated in our next work. First, the fusion of 3D geometry and 3D photometric appearance based on the mesh-LBP framework will be evaluated to improve recognition. Second, the size of the mesh-LBP(α₂) will be optimized, and its discrimination power will be increased. Third, other schemes of 2D LBP, such as neighborhood topology and sampling to mesh-LBP for different applications of 3D texture, will be extended. Finally, the integration of the mesh-LBP with a robust matching algorithm will be investigated.