基于不变性特征的三维人脸识别研究
|
摘要
作为生物特征识别领域的一个重要研究课题,人脸识别因其深厚的学术背景和广泛的市场应用前景,正在成为国内外顶级研究机构和学者关注的焦点。随着图像处理、模式识别、计算机视觉、统计学习、认知学及心理学等众多相关学科领域研究发展地不断深入,人脸识别技术将成为可以广泛应用于国家安全和公共安全的重要技术支撑手段。尽管以人脸图像的表观特征为基础的二维人脸识别技术已有十余年的研究历史,但是仍存在许多悬而未决的问题,制约了识别准确率的有效提高,尤其是存在大的光照、姿态和表情变化时,二维人脸识别算法准确率的下降更为显著。
随着三维数字获取设备的不断发展,越来越多的研究组织和机构致力于使用三维数据辅助人脸识别,取得了较好的效果,尤其是有较大的姿态、光照和表情变化影响时,基于形状特征的三维人脸识别技术有望从根本上解决这些变化数据的影响。高效地提取三维人脸表面不变性特征是人脸识别准确率提高的核心和关键。一个“好”的辨别特征能够有效地描述某个个体面部区别于大众的细节特征,为实现准确高效的人脸识别打下基础。本文在对三维人脸数据进行细致深入分析的基础上,对三维人脸表面特征描述进行深入地研究和探讨,结合基于三维人脸图像的表面形状特征及统计学习理论提取具有不变性的辨别特征,取得了较好的效果。本文的主要研究内容和创新性工作如下：
1.提出了一种三维人脸预处理及区域分割方法
首先通过二维图像和三维图像的对应关系粗略地提取人脸表面区域,运用三维人脸模型的对称轮廓线检测鼻尖点,去除人脸区域之外的杂乱数据。姿态校正和基于轴角描述的匹配对齐将三维人脸表面数据置于统一的坐标框架中。形状索引描述结合面部几何约束分割人脸表面主要器官区域。本文提出的三维人脸自动预处理方法有助于后续特征提取和分类识别算法的实现,既提高了算法的计算效率,又改善了原始输入的三维人脸数据的质量。
2.提出了三种三维人脸表面特征描述方法
1)提出了一种基于弯曲不变量的三维人脸表面描述子,用于包含表情变化的三维人脸识别。人脸表面的表情变换视为非刚性变换,经验研究显示面部表情可视为等距形变。因此引入弯曲不变量用来构建一个人脸表面的签名。此法在采样点集上使用等距映射算法(ISOMAP)将由表情引起的非刚性形变变换为刚性形变,再在全集点上进行内插。实验结果显示基于弯曲不变量的三维人脸表面特征描述方法有效地提高了包含大表情变化的三维人脸数据的识别性能,克服面部存在表情变化造成的人脸表面变形问题；
2)提出了一种基于边界球的三维人脸表面描述子,对于包含姿态变化的三维人脸数据具有较好的识别效果。为了更好地反映人脸表面形状信息增加辨别性,一个边界球表面描述子用于对齐的三维人脸点云数据。该描述子投影一个面部点云相对位置到以人脸质心点为中心的边界球上。它可以保留较低的描述性,对比其它描述子可以更有效地在一个旋转球域上反映面部特征,使其对大的表情和姿态不敏感。实验结果表明基于边界球的三维人脸表面描述子可以保留尽可能多的几何信息,提取与姿态无关的特征描述子,克服因存在姿态变化而造成的自遮挡对三维人脸识别算法性能的影响；
3)提出一种三维尺度不变特征变换的三维人脸表面描述子,可以克服遮挡和扭曲对三维人脸识别效果的影响。该描述子具有仿射、旋转和尺度不变性,它可以有效地检测关键点,编码三维人脸表面形状信息来描述关键点的辨别信息。加入深度信息的动机是关键点周围深度值的改变可以为其提供更多辨别能力,但对于实际存在差异的对象识别上具有视觉表观相似性。实验结果表明基于三维尺度不变特征变换的三维人脸特征描述方法可以有效地表征扭曲和变形图像,恢复三维人脸表面上的本质特征,提取辨别信息,提高三维人脸识别算法性能。
3.提出了一种鲁棒的区域稀疏回归模型用于辨别特征提取
表情、姿态、遮挡和噪声是影响三维人脸识别准确率提高的主要因素。引入低秩和区域稀疏描述理论来分析前文所提出的特征描述子。结合带噪声的非线性约束和有监督的谱回归约束,基于优化模型的本征低维特征矢量被提取。头发遮挡和噪声被同时分块处理。提取的低维特征具有更多的辨别性、鲁棒性和通用性。实验结果表明基于区域稀疏回归模型所提取的三维人脸本征低维特征向量,具有良好的三维数据表达能力,与国际通用的三维人脸识别算法进行性能对比时,显示出了优越的性能。
4.设计并实现了一个三维人脸识别系统
为了实现有效地三维人脸数据采集并验证前文所提算法的通用性,本文构建了相应的三维人脸识别系统,主要由基于双目视觉的三维人脸识别系统和基于结构光的三维人脸识别系统组成。首先介绍了基于双目视觉的三维人脸深度信息的获取方法。然后介绍并演示了系统中的主要软件功能模块包括图像采集、摄像机标定、三维人脸模型生成、三维人脸模型平滑、三维人脸模型预处理、三维人脸特征描述和三维人脸特征提取,这些为进一步开发和研究三维人脸数据处理和识别奠定了良好的基础。
Face recognition is a key subject of the research on biometrics. Due to the strong academic background and broad application prospects, it has become the focus of domestic and international top research institutions and scholars. With the rapid development of the huge number of related disciplines, such as image processing, pattern recognition, computer vision, statistical learning, cognitive science and psychology, face recognition has been in great need and necessary of national security and public safety, and becomes one of the hottest issues in that field. However, face recognition based on2D face images is still challenged by the large change of illumination, pose and expression after received more than10year's research and its recognition rate is still far away from satisfaction under the change of the above three factors.
With recent progress in3D sensors, more and more organizations have committed to using the three-dimensional data-aided face recognition and made a good result.3D face recognition has potential to overcome the difficulties of the image-based face recognition caused by the variations of illumination, facial posture and expression etc. Effective feature extraction of3D facial surface is one of the core technologies for3D face recognition. To extract the most distinctive3D facial features of the same individual, which is different from the general public, is the first and crucial phase for a highly efficient face recognition algorithm. In this dissertation, based on the detailed and in-depth analysis,3D facial feature descriptors for3D face recognition has been studied and discussed. Combined with the surface shape characteristics of3D facial images and statistical learning theory, we can extract the discriminant features with invariance. The main research content and innovative work are as follows:
1. Proposed an automatic pre-process technique and regional segmentation approach
Based on the correspondence between the2D texture channel and3D data, we first roughly extract the facial area. The facial central stripe is used to detect the nose tip and remove some clutters. Pose correction and registration based on Axis-angle representation can be fixed and the facial pose is estimated and put into a canonical framework. Shape index and facial geometrical constraint are introduced to segment the main organ regions. The proposed3D face automatic pre-process method can contribute to the realization of the subsequent feature extraction and classification algorithms. It can not only improve the computational efficiency, but also improve the quality of the3D face data in the original input.
2. Proposed three kinds of3D facial feature descriptors
1) Bending Invariant is proposed for describing the3D facial information. The transformations of expression on a facial surface can be considered as non-rigid transformations, and empirical observations show that facial expressions can be modeled as isometric transformations. Bending Invariant can be used to construct a signature for facial surfaces. This descriptor can transform the non-rigid deformation caused by expression into the rigid transformation by performing an ISOMAP on a reduced set of points and interpolating on the full set of points. Experimental results show that Bending Invariant can effectively improve the recognition performance of3D face data with large changes in the expression and overcome facial existence of the surface deformation caused by the facial expressions.
2) Bounding sphere representation (BSR) is proposed as3D facial descriptor for3D face recognition with pose variations. In order to better reflect the facial surface shape and increase the discrimination, BSR is used for the aligned3D point cloud data and has been justified as effective on3D information description. The descriptor is imaged as the projection of the relative position of a facial point cloud into bounding spheres centered as the centroid point of the face. The BSR can preserve the lower descriptiveness, and reflect the facial characteristics on a rotational spherical domain intuitively compared with the other descriptors, which makes it insensitive to large expression and pose variations. Experimental results show that BSR can retain more geometrical information, extract the descriptor with posture-related characteristics, and overcome the influence of self-occlusion.
3)3D scale invariant feature transform (3D SIFT), with affine, rotation and scale invariance, is proposed for describing3D facial surface, which can effectively detect key points based on the3D facial surface information and encode the facial surface information to describe the key points. The intuition to add depth is that the changing of the depth value of the key points may give us more information to discriminate the subjects, which are visually similar to each other but are different because they are in different level of depth. Experimental results show that3D SIFT descriptor can effectively characterize the distorted and deformed images, restore the essential characteristics of the3D facial surface, extract the discriminant information and improve the recognition result.
3. Proposed a robust group sparse regression model for discriminant feature extraction
Expression, poses, occlusions and corruptions are common problems that significantly influence the accuracy gain of the3D system. We introduce the theory of low rank and group sparse representation to analysis our feature representation. Combined with nonlinear corruption constraint and a supervised Spectral Regression constraint, a lower intrinsic dimensional feature vector can be extracted based on a novel optimization model. Hair occlusion and data corruptions can be patched handled simultaneously. The extracted low-dimensional features are more discriminative, robust and generative. Experimental results show that3D facial intrinsic feature vector based on RGSRM has a good dimensional data representation capability and show superior performance.
4. Designed and implemented a3D face recognition system
For the purpose of3D face data acquisition and proving the generality of these algorithms proposed upon, the3D face recognition system is based on the stereo vision and structured light. The software function modules are composed of image capturing, camera calibration,3D face model generation,3D face model smoothing,3D face model pre-processing,3D face description and feature extraction. All work lays a good foundation of further research and development of3D face processing and recognition.
随着三维数字获取设备的不断发展,越来越多的研究组织和机构致力于使用三维数据辅助人脸识别,取得了较好的效果,尤其是有较大的姿态、光照和表情变化影响时,基于形状特征的三维人脸识别技术有望从根本上解决这些变化数据的影响。高效地提取三维人脸表面不变性特征是人脸识别准确率提高的核心和关键。一个“好”的辨别特征能够有效地描述某个个体面部区别于大众的细节特征,为实现准确高效的人脸识别打下基础。本文在对三维人脸数据进行细致深入分析的基础上,对三维人脸表面特征描述进行深入地研究和探讨,结合基于三维人脸图像的表面形状特征及统计学习理论提取具有不变性的辨别特征,取得了较好的效果。本文的主要研究内容和创新性工作如下：
1.提出了一种三维人脸预处理及区域分割方法
首先通过二维图像和三维图像的对应关系粗略地提取人脸表面区域,运用三维人脸模型的对称轮廓线检测鼻尖点,去除人脸区域之外的杂乱数据。姿态校正和基于轴角描述的匹配对齐将三维人脸表面数据置于统一的坐标框架中。形状索引描述结合面部几何约束分割人脸表面主要器官区域。本文提出的三维人脸自动预处理方法有助于后续特征提取和分类识别算法的实现,既提高了算法的计算效率,又改善了原始输入的三维人脸数据的质量。
2.提出了三种三维人脸表面特征描述方法
1)提出了一种基于弯曲不变量的三维人脸表面描述子,用于包含表情变化的三维人脸识别。人脸表面的表情变换视为非刚性变换,经验研究显示面部表情可视为等距形变。因此引入弯曲不变量用来构建一个人脸表面的签名。此法在采样点集上使用等距映射算法(ISOMAP)将由表情引起的非刚性形变变换为刚性形变,再在全集点上进行内插。实验结果显示基于弯曲不变量的三维人脸表面特征描述方法有效地提高了包含大表情变化的三维人脸数据的识别性能,克服面部存在表情变化造成的人脸表面变形问题；
2)提出了一种基于边界球的三维人脸表面描述子,对于包含姿态变化的三维人脸数据具有较好的识别效果。为了更好地反映人脸表面形状信息增加辨别性,一个边界球表面描述子用于对齐的三维人脸点云数据。该描述子投影一个面部点云相对位置到以人脸质心点为中心的边界球上。它可以保留较低的描述性,对比其它描述子可以更有效地在一个旋转球域上反映面部特征,使其对大的表情和姿态不敏感。实验结果表明基于边界球的三维人脸表面描述子可以保留尽可能多的几何信息,提取与姿态无关的特征描述子,克服因存在姿态变化而造成的自遮挡对三维人脸识别算法性能的影响；
3)提出一种三维尺度不变特征变换的三维人脸表面描述子,可以克服遮挡和扭曲对三维人脸识别效果的影响。该描述子具有仿射、旋转和尺度不变性,它可以有效地检测关键点,编码三维人脸表面形状信息来描述关键点的辨别信息。加入深度信息的动机是关键点周围深度值的改变可以为其提供更多辨别能力,但对于实际存在差异的对象识别上具有视觉表观相似性。实验结果表明基于三维尺度不变特征变换的三维人脸特征描述方法可以有效地表征扭曲和变形图像,恢复三维人脸表面上的本质特征,提取辨别信息,提高三维人脸识别算法性能。
3.提出了一种鲁棒的区域稀疏回归模型用于辨别特征提取
表情、姿态、遮挡和噪声是影响三维人脸识别准确率提高的主要因素。引入低秩和区域稀疏描述理论来分析前文所提出的特征描述子。结合带噪声的非线性约束和有监督的谱回归约束,基于优化模型的本征低维特征矢量被提取。头发遮挡和噪声被同时分块处理。提取的低维特征具有更多的辨别性、鲁棒性和通用性。实验结果表明基于区域稀疏回归模型所提取的三维人脸本征低维特征向量,具有良好的三维数据表达能力,与国际通用的三维人脸识别算法进行性能对比时,显示出了优越的性能。
4.设计并实现了一个三维人脸识别系统
为了实现有效地三维人脸数据采集并验证前文所提算法的通用性,本文构建了相应的三维人脸识别系统,主要由基于双目视觉的三维人脸识别系统和基于结构光的三维人脸识别系统组成。首先介绍了基于双目视觉的三维人脸深度信息的获取方法。然后介绍并演示了系统中的主要软件功能模块包括图像采集、摄像机标定、三维人脸模型生成、三维人脸模型平滑、三维人脸模型预处理、三维人脸特征描述和三维人脸特征提取,这些为进一步开发和研究三维人脸数据处理和识别奠定了良好的基础。
Face recognition is a key subject of the research on biometrics. Due to the strong academic background and broad application prospects, it has become the focus of domestic and international top research institutions and scholars. With the rapid development of the huge number of related disciplines, such as image processing, pattern recognition, computer vision, statistical learning, cognitive science and psychology, face recognition has been in great need and necessary of national security and public safety, and becomes one of the hottest issues in that field. However, face recognition based on2D face images is still challenged by the large change of illumination, pose and expression after received more than10year's research and its recognition rate is still far away from satisfaction under the change of the above three factors.
With recent progress in3D sensors, more and more organizations have committed to using the three-dimensional data-aided face recognition and made a good result.3D face recognition has potential to overcome the difficulties of the image-based face recognition caused by the variations of illumination, facial posture and expression etc. Effective feature extraction of3D facial surface is one of the core technologies for3D face recognition. To extract the most distinctive3D facial features of the same individual, which is different from the general public, is the first and crucial phase for a highly efficient face recognition algorithm. In this dissertation, based on the detailed and in-depth analysis,3D facial feature descriptors for3D face recognition has been studied and discussed. Combined with the surface shape characteristics of3D facial images and statistical learning theory, we can extract the discriminant features with invariance. The main research content and innovative work are as follows:
1. Proposed an automatic pre-process technique and regional segmentation approach
Based on the correspondence between the2D texture channel and3D data, we first roughly extract the facial area. The facial central stripe is used to detect the nose tip and remove some clutters. Pose correction and registration based on Axis-angle representation can be fixed and the facial pose is estimated and put into a canonical framework. Shape index and facial geometrical constraint are introduced to segment the main organ regions. The proposed3D face automatic pre-process method can contribute to the realization of the subsequent feature extraction and classification algorithms. It can not only improve the computational efficiency, but also improve the quality of the3D face data in the original input.
2. Proposed three kinds of3D facial feature descriptors
1) Bending Invariant is proposed for describing the3D facial information. The transformations of expression on a facial surface can be considered as non-rigid transformations, and empirical observations show that facial expressions can be modeled as isometric transformations. Bending Invariant can be used to construct a signature for facial surfaces. This descriptor can transform the non-rigid deformation caused by expression into the rigid transformation by performing an ISOMAP on a reduced set of points and interpolating on the full set of points. Experimental results show that Bending Invariant can effectively improve the recognition performance of3D face data with large changes in the expression and overcome facial existence of the surface deformation caused by the facial expressions.
2) Bounding sphere representation (BSR) is proposed as3D facial descriptor for3D face recognition with pose variations. In order to better reflect the facial surface shape and increase the discrimination, BSR is used for the aligned3D point cloud data and has been justified as effective on3D information description. The descriptor is imaged as the projection of the relative position of a facial point cloud into bounding spheres centered as the centroid point of the face. The BSR can preserve the lower descriptiveness, and reflect the facial characteristics on a rotational spherical domain intuitively compared with the other descriptors, which makes it insensitive to large expression and pose variations. Experimental results show that BSR can retain more geometrical information, extract the descriptor with posture-related characteristics, and overcome the influence of self-occlusion.
3)3D scale invariant feature transform (3D SIFT), with affine, rotation and scale invariance, is proposed for describing3D facial surface, which can effectively detect key points based on the3D facial surface information and encode the facial surface information to describe the key points. The intuition to add depth is that the changing of the depth value of the key points may give us more information to discriminate the subjects, which are visually similar to each other but are different because they are in different level of depth. Experimental results show that3D SIFT descriptor can effectively characterize the distorted and deformed images, restore the essential characteristics of the3D facial surface, extract the discriminant information and improve the recognition result.
3. Proposed a robust group sparse regression model for discriminant feature extraction
Expression, poses, occlusions and corruptions are common problems that significantly influence the accuracy gain of the3D system. We introduce the theory of low rank and group sparse representation to analysis our feature representation. Combined with nonlinear corruption constraint and a supervised Spectral Regression constraint, a lower intrinsic dimensional feature vector can be extracted based on a novel optimization model. Hair occlusion and data corruptions can be patched handled simultaneously. The extracted low-dimensional features are more discriminative, robust and generative. Experimental results show that3D facial intrinsic feature vector based on RGSRM has a good dimensional data representation capability and show superior performance.
4. Designed and implemented a3D face recognition system
For the purpose of3D face data acquisition and proving the generality of these algorithms proposed upon, the3D face recognition system is based on the stereo vision and structured light. The software function modules are composed of image capturing, camera calibration,3D face model generation,3D face model smoothing,3D face model pre-processing,3D face description and feature extraction. All work lays a good foundation of further research and development of3D face processing and recognition.
引文
[1]A.K. Jain, A. Ross, S. Prabhakar, An introduction to biometric recognition. IEEE Transaction on Circuits and Systems for Video Technology,2004,14(1):4-20.
[2]S. Pankanti, R.M. Bolle, A. Jain, Biometrics:The Future of Identification. Computer,2000,33(2): 46-49.
[3]金一,人脸识别中若干算法的研究,北京交通大学博士论文,2009.
[4]W. Zhao, R. Chellappa, A. Rosenfeld, P.J. Phillips, Face recognition:A Literature Survey. ACM Computing Surveys,2003, pp.399-458.
[5]FRVT, Face Recognition Vendor Test, http://www.frvt.org/,2002.
[6]P.J. Phillips, P.J. Flynn, T. Scruggs, K.W. Bowyer, Jin Chang, K. Hoffman, J. Marques, Jaesik Min, and W. Worek, Overview of the Face Recognition Grand Challenge, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, June 2005, pp.947-954.
[7]王跃明,表情不变的三维人脸识别研究,浙江大学博士论文,2007.
[8]Yueming Wang, Gang Pan, Zhaohui Wu, and Yigang Wang, Exploring facial expression effects in 3D face recognition using partial ICP. in Proc. of Asian Confernece on Computer Vision,2006, pp.581-590.
[9]Xiaoguang Lu, A.K. Jain, and D. Colbry, Matching 2.5D face scans to 3D models. IEEE Transactions on Pattern Recognition and Machine Intelligence,2006,28(1):31-43.
[10]F. Tsalakanidou, S. Malassiotis, M.G. Strintzis, Face localization and authentication using color and depth images. IEEE Transactions on Image Processing,2005,14(2):152-168.
[11]O. Ocegueda, S. Shah, I. Kakadiaris, Which parts of the face give out your identity? in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2011, pp.641-648.
[12]Lijun Yin, Xiaozhou Wei, Yi Sun, Jun Wang, M.J. Rosato, A 3D facial expression database for facial behavior research, in Proc. of the 7th International Conference on Automatic Face and Gesture Recognition,2006, pp.211-216.
[13]Kevin W. Bowyer, Kyong Chang, Patrick Flynn, A survey of approaches and challenges in 3D and multi-modal 3D + 2D face recognition. Computer Vision and Image Understanding,2006, 101(1):1-15.
[14]Andrea F. Abate, Michele Nappi, Daniel Ricco, and Gabriele Sabatino,2D and 3D face recognition:A survey. Pattern Recognition Letters,2007,28(14):1885-1906.
[15]G. Passalis, P. Perakis, T. Theoharis, and I.A. Kakadiaris, Using facial symmetry to handle pose variations in real-world 3D face recognition. IEEE Transactions on Pattern Recognition and Machine Intelligence,2011,33(10):1938-1951.
[16]G. Medioni and R. Waupotitsch, Face modeling and recognition in 3D, Proc. IEEE Int'1 Workshop Analysis and Modeling of Faces and Gestures, pp.232-233,2003.
[17]K. Chang, K. W. Bowyer, and P. Flynn, Effects on facial expression in 3D face recognition, Proc. SPIE Conf. Biometric Technology for Human Identification, pp.132-143,2005.
[18]T. Maurer, D. Guigonis, I. Maslov, B. Pesenti, A. Tsaregorodtsev, D. West, and G. Medioni, Performance of Geometrix ActiveID 3D face recognition engine on the FRGC data, in Proc. of IEEE Workshops on Computer Vision and Pattern Recognition,2005, pp.154.
[19]Yueming Wang, Jianzhuang Liu, and Xiaoou Tang, Robust 3D face recognition by local shape difference boosting. IEEE Transactions on Pattern Recognition and Machine Intelligence,2010, 32(10):1858-1870.
[20]K.I. Chang, K.W. Bowyer, and P.J. Flynn, Multiple nose region matching for 3D face recognition under varying facial expression. IEEE Transactions on Pattern Recognition and Machine Intelligence,2006,28(10):1695-1700.
[21]R. Tyrrell Rockafellar, Roger J-B Wets, Variational Analysis, Springer-Verlag,2005, ISBN 3-540-62772-3, ISBN 978-3-540-62772-2, pp.117.
[22]Gang Pan, Yijun Wu, Zhaohui Wu, and Wenyao Liu,3D face recognition by profile and surface matching, in Proc. of IEEE International Joint Conference on Neutral Networks,2003, pp. 2169-2174.
[23]B. Achermann, and H. Bunke, Classifying range images of human faces with Hausdorff distance, in Proc. of International Conference on Pattern Recognition,2000, pp.809-813.
[24]Chin-Seng Chua, Feng Han, and Yeong-Khing Ho,3D human face recognition using point signature, in Proc. of International Conference on Automatic Face and Gesture Recognition,2000, pp.233-238.
[25]Zhaohui Wu, Yueming Wang, and Gang Pan,3D face recognition using local shape map. in Proc. of IEEE Interational Conference on Image Processing,2004, pp.2003-2006.
[26]Chris Boehnen, Tanya Peters, and Patrick J. Flynn,3D signatures for fast 3D face recognition, Proc. of IAPR/IEEE International Conference on Biometrics,2009, pp.12-21.
[27]J. Cook, V. Chandran, and C. Fookes,3D face recognition using Log-Gabor templates, Proc. British Machine Vision Conf., pp.83-83,2006.
[28]T. Nagamine, T. Uemura, and I. Masuda,3D facial image analysis for human identification, in Proc. of International Confonference on Pattern Analysis and Machine Intelligence, vol.28, no.11, pp.1858-1863, Nov.2006.
[29]C. Beumier and M. Acheroy, Automatic 3D face authenntication. Image Vision Computing, 2000,18(4):315-321.
[30]C. Samir, A. Srivastava, and M. Daoudi, Three-dimensional face recognition using shapes of facial curves, IEEE Transactions on Pattern Recognition and Machine Intelligence,2006,28(11): 1858-1863.
[31]S. Berretti, A. Del Bimbo, and P. Pala,3D face recognition using Isogeodesic Stripes. IEEE Transactions on Pattern Recognition and Machine Intelligence,2010,32(12):2162-2177.
[32]G. G. Gordon, Face recognition based on depth and curvature features, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,1992, pp.808-810.
[33]Ana Belen Moreno, Angel Sanchez, Jose Fco Velez, and Fco Javier Diaz, Face recognition using 3D surface-extraced descriptors, in Proc. of Irish Machine Vision and Image Processing Conference,2003.
[34]S. Gupta, J.K. Aggarwal, M.K. Markey, and A.C. Bovik,3D face recognition founded on the structural diversity of human face, in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2007, pp.1-7.
[35]Chenghua Xu, Tieniu Tan, Stan Li, Yunhong Wang, and Cheng Zhong, Learning effective intrinsic features to boost 3D-based face recognition, in Proc. of European Conference on Computer Vision,2006, pp.416-427.
[36]Cheng Zhong, Zhenan Sun, and Tieniu Tan, Robust 3D face recognition using learned visual codebook. in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2007, pp.1-6.
[37]T.C. Faltemier, K.W. Bowyer, and P.J. Flynn, A region ensemble for 3D face recognition. IEEE transactions on Information Forensics and Security,2008,3(1):62-73.
[38]B. Achermann, X. Jiang, and H. Bunke, Face recognition using range images, in Proc. of International Conference on Virtual Systems and Multimedia,1997, pp.129-136.
[39]Alexander M. Bronstein, Michael M. Bronstein, and Ron Kimmel, Expression-invariant 3D face recognition, in Proc. of International Conference on Audio- and Video-Based Biometric Person Authentication,2003, pp.62-70.
[40]C. Hesher, A. Srivastava, and G. Erlebacher, A novel technique for face recognition using range imaging, in Proc. of International Symposium on Signal Processing and Its Applications,2003, pp. 201-204.
[41]T. Russ, C. Boehnen, and T. Peters,3D face recognition using 3D alignment for PCA, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2006, pp. 1391-1398.
[42]C.C. Queirolo, L. Silva, O.R.P. Bellon, and M.P. Segundo,3D face recognition using simulated annealing and the surface interpenetration measure. IEEE Transactions on Pattern Recognition and Machine Intelligence,2010,32(2):206-219.
[43]H.T. Tanaka, M. Ikeda, and H. Chiaki, Curvature-based face surface recognition using spherical correlation-principal directions for curved object recogntion. in Proc. of International Conference on Automatic Face and Gesture Recognition,1998, pp.372-377.
[44]Alexander M. Bronstein, Michael M. Bronstein, and Ron Kimmel, Three diensional face recognition. International Journal of Computer Vision,2005,64(1):5-30.
[45]Xiaoguang Lu, and A.K. Jain, Deformation modeling for robust 3D face matching, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2006, pp. 1377-1383.
[46]Yueming Wang, Gang Pan, and Zhaohui Wu,3D face recognition in the presence of expression: A guidance-based constraint deformation approach, in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2007, pp.1-7.
[47]I.A. Kakadiaris, G. Passalis, G. Toderici, M.N. Murtuza, Yunliang Lu, N. Karampatziakis, and T. Theoharis, Three-dimensional face recognition in the presence of facial expressions:An annotated deformable model approach. IEEE Transactions on Pattern Recognition and Machine Intelligence, 2007,29(4):640-649.
[48]Yingjie Wang, Chin-Seng Chua, and Yeong-Khing Ho, Face recognition from 2D and 3D images, in Proc. of International Audio- and Video-based Person Authentication,2001, pp.26-31.
[49]A.M. Bronstein, M.M. Bronstein, E. Gordon, R. Kimmel, Fusion of 2D and 3D data in three-dimensional face recognition. in Proc. of IEEE International Conference on Image Processing, 2004, pp.87-90.
[50]T. Papatheodorou, D. Rueckert, Evaluation of automatic 4D face recognition using surface and texture registration, in Proc. of IEEE International Conference on Automatic Face and Gesture Recognition,2004, pp.321-326.
[51]Chiraz BenAbdelkader, Paul A. Griffin, Comparing and combining depth and texture cues for face recognition, Image and Vision Computing,2005,23(3):339-352.
[52]A. Samani, J. Winkler, M. Niranjan, Automatic face recognition using stereo images. in Proc. of IEEE International Conference on Acoustics, Speech and Signal Processing,2006.
[53]Yi Sun, Lijun Yin,3D Spatio-Temporal face recognition using dynamic range model sequences, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops,2008, pp.1-7.
[54]F. Tsalakanidou, D. Tzovaras, M.G. Strintzis, Use of depth and color eigenfaces for face recognition, Pattern Recognition Letters,2003,24(9):1427-1435.
[55]Kyong I. Chang, Kevin W. Bowyer, and Patrick J. Flynn, Face recognition using 2D and 3D facial data, in Proc. of ACM Workshops on Multimodal User Authentication,2003.
[56]F. Tsalakanidou, S. Malassiotis, M.G. Strintzis, Integration of 2D and 3D images for enhanced face authentication, in Proc. of IEEE International Conference on Automatic Face and Gesture Recognition,2004.
[57]M. Husken, M. Brauckmann, S. Gehlen, Von der C. Malsburg, Strategies and benefits of fusion of 2D and 3D face recognition, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshop,2005.
[58]Xiaoguang Lu, and A. K. Jain, Integrating Range and Texture Information for 3D Face Recognition, in Proc. of IEEE Workshops on Application of Computer Vision,2005, pp.156-163.
[59]Xin Chen, T. Faltemier, P. Flynn, and K. Bowyer, Human face modeling and recognition through multi-view high resolution stereopsis, in Proc. of IEEE International Conference on Computer Vision and Pattern Recognition Workshop,2006.
[60]Loris Nanni, Alessandra Lumini, RegionBoost learning for 2D+3D based face recognition. Pattern Recognition Letters,2007,28(15):2063-2070.
[61]A.S. Mian, M. Bennamoun, and R. Owens, An efficient multimodal 2D-3D hybrid approach to automatic face recognition, IEEE Transactions on Pattern Recognition and Machine Intelligence, 2007,29(11):1927-1943.
[62]Daniel Riccio, Jean-Luc Dugelay, Geometric invariants for 2D/3D face recognition. Pattern Recognition Letters,2007,28(14):1907-1914.
[63]Jian-Gang Wang, Eng Thiam Lim, Xiang Chen, and Ronda Venkateswarlu, Real-time stereo face recognition by fusing appearance and depth fisherfaces. Journal of VLSI Signal Processing, 2007,49(3):409-423.
[64]http://my.icxo.com/276388/viewspace-70594.html.
[65]http://szjyl2010.b2b.youboy.com/show0sp54560101.html.
[66]http://www.genewell.net/?page_id=271.
[67]P Paul J. Besl, and Neil D. Mckay, A method of registration of 3D shapes, IEEE Transactions on Pattern Recognition and Machine Intelligence,1992,14(2):239-256.
[68]Geof Givens, J. Ross Beveridge, Bruce A. Draper, David Bolme, A statistical assessment of subject factors in the PCA recognition of human faces, in Proc. of IEEE International Conference Computer Vision and Pattern Recognition Workshop,2003.
[69]J. Wright, A.Y. Yang, A. Ganesh, S.S. Sastry, and Yi Ma, Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(2): 210-227.
[70]Peyre Gabriel, Numerical Mesh Processing. Chapter 4.
[71]Dong Chen-shi, and Wang Guo-zhao, Curvature estimation on triangular mesh, J Zhejiang Univ SCI.2005 6A(Suppl.1):128-136.
[72]Xin Chen, Francis Schmitt, Intrinsic surface poperties from surface triangulation. in Proc. of the European Conference on Computer Vision,1992, pp.739-743.
[73]J. A. Sethian. Level Sets Methods and Fast Marching Methods. Cambridge University Press, 2nd edition,1999.
[74]T. H. Cormen, C. E. Leiserson, and R. R. Rivest, Introduction to Algorithms. MIT Press, Cambridge, Massachusetts,1990.
[75]R. Kimmel and J. A. Sethian. Computing Geodesic Paths on Manifolds. Proc. Natl. Acad. Sci., 1998,95(15):8431-8435.
[76]Y. Eldar, M. Lindenbaum, M. Porat, and Y. Y. Zeevi. The farthest point strategy for progressive image sampling. IEEE transactions on image processing,1997,6(9):1305-1315.
[77]G. Peyre and L. D. Cohen. Geodesic remeshing using front propagation. International Journal of Computer Vision.2006,69(1):145-156.
[78]Deng Cai, Xiaofei He, and Jiawei Han, Spectral regression for efficient regularized subspace learning, in Proc. of IEEE International Conference on Computer Vision,2007.
[79]贾贝贝,基于双目视觉的三维人脸重建,北京交通大学硕士学位论文,2009.
[80]S. Malassiotis, M.G. Strintzis, Real-time head tracking and 3D pose estimation from range data, in Proc. of IEEE International Conference on Image Processing,2003.
[81]Gabriel Taubin, A signal processing approach to fair surface design, in Proc. of the 22nd Annual Conference on Computer Graphics and interactive techniques,1995, pp.351-358.
[82]Mathieu Desbrun, Mark Meyer, Peter Schroder, Alan H. Barr, Anisotropic feature-preserving denoising of height fields and bivariate data, in Proc. of Graphics interface,2000, pp.145-152.
[83]轴角描述,http://en.wikipedia.org/wiki/Axis-angle_representation.
[84]王晶,三维人脸识别,西北工业大学硕士学位论文,2005.
[85]CS277-Geometric Modeling in Computer Graphics_Discrete Differential Geometry.
[86]S. J. Kim, W. K. Jeong, C. H. Kim. LOD Generation with Discrete Curvature Error Metric.
[87]C. Dorai, A.K. Jain, COSMOS-A representation scheme for 3D free-form objects, IEEE Transactions on Pattern Analysis and Machine Intelligence,1997,19(10):1115-1130.
[88]N. Alyuz, B. Gokberk, L. Akarun, Regional registration for expression resistant 3D face recognition.IEEE Transactions on Information Forensics and Security,2010,5(3):425-440.
[89]Xi Zhao, Emmanuel Dellandrea, and Liming Chen, A 3D statistical facial feature model and its application on locating facial landmarks. Advanced Concepts for Intelligent Vision Systems,2009, 5807:686-697.
[90]M. Romero and N. Pears, Landmark localisation in 3D face data, in Proc. of IEEE International Conference on Advanced Video and Signal Based Surveillance,2009, pp.73-78.
[91]H. Dibeklioglu, A.A. Salah, and L. Akarun,3D facial landmarking under expression, pose, and occlusion variations, in Proc. of IEEE International Conference on Biometrics:Theory, Applications and Systems,2008, pp.1-6.
[92]M.P. Segundo, C. Queirolo, O.R.P. Bellon, and L. Silva, Automatic 3D facial segmentation and landmark detection, in Proc. of 14th International Conference on Image Analysis and Processing, 2007, pp.431-436.
[93]J.D. Hose, J. Colineau, C. Bichon, and B. Dorizzi, Precise localization of landmarks on 3D faces using Gabor Wavelets, in Proc. of IEEE International Conference on Biometrics:Theory, Applications and Systems,2007, pp.1-6.
[94]Albert Ali Salah and Lale Akarun,3D facial feature localization for registration, in Proc. of International Workshop on Multimedia Content Rpresentation, Claasification and Security,2006, pp. 338-345.
[95]Hatice Cinar Akakin, Albert Ali Salah, Lale Akarun, and Bulent Sankur,2D/3D facial feature extraction, in Proc. of SPIE:Image Processing:Algorithms and Systems, Neutral Networks, and Machine Learning, vol.6064, no.1,2006, Article 60641D.
[96]Xiaoguang Lu and A.K. Jain, Automatic feature extraction for multiview 3D face recognition, in Proc. of 7th International Conference on Automatic Face and Gesture Recognition,2006, pp. 585-590.
[97]E.L. Schwatz, A. Shaw, E. Wolfson, A numerical solution to the generalized mapmaker's problem:flattening nonconvex polyhedral sufaces. IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(9):1005-1008.
[98]G. Zigelman, R. Kimmel, N. Kiryati, Texture mapping using surface flattening via multidimensional scaling. IEEE Transaction on Visualization and Computer Graphics,2002,8(2): 198-207.
[99]R. Grossmann, N. Kiryati, and R. Kimmel, Compuational surface flattening:a voxel-based approach. IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(4):433-441.
[100]A. Elad, R. Kimmel, Bendng invariant representations for surfaces, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2001.
[101]M. Balasubramanian, E.L. Shwartz, J.B. Tenenbaum, V. de Silva, J.C. Langford, The ISOMAP algorithm and Topological Stability, Science,2002,295(5552):9-11.
[102]Jau-Ling Shih, Chang-Hsing Lee, Jian Tang Wang. A new 3D model retrieval approach based on the elevation descriptor. Pattern Recognition,2007,40(1):283-295.
[103]D.V. Vranic, An improvement of rotation invariant 3D-shape descriptor based on functions on concentric spheres, in Proc. of IEEE International Conference on Image Processing,2003, pp.757-760.
[104]Yue Gao, Qionghai Dai, Naiyao Zhang,3D model comparison using spatial structure circular descriptor. Pattern Recognition,2010,43(3):1142-1151.
[105]D. G. Lowe, Distinctive Image Features from Scale-Invariant Keypoints, International Journal of Computer Vision,2004,60(2):91-110.
[106]K.I. Chang, K.W. Bowyer, and P.J. Flynn, An evaluation of multimodal 2D+3D face biometrics. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,28(4):619-624.
[107]Chenghua Xu, Stan Li, Tieniu Tan, and Long Quan, Automatic 3D face recognition from depth and intensity Gabor features. Patter recognition,2009,42(9):1895-1905.
[108]John Wright, Arvind Ganesh, Shankar Rao, Peng, Y., and Y. Ma. Robust principle component analysis:Exact recovery of corrputed low-rank matrices via convex optimization, in Proc. Advances in Neural Information Processing Systems,2009.
[109]Berk Gokberk, Helin Dutagaci, Aydin Ulas, Lale Akarun, and Bulent Sankur, Representation plurality and fusion for 3D face recognition. IEEE Transactions on Systems, Man, and Cybernetics (B),2008,38(1):155-173.
[110]A. Savran, B. Sankur, M. T. Bilge, Comparative Evaluation of 3D versus 2D modality for automatic detection of facial action units. Pattern Recognition,2012,45 (2):767-782.
[111]CASIA-3D FaceVl, http://biometrics.idealtest.org/.
[112]D.L. Swets and J.J. Weng, Using discriminant eigenfeatures for image retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence,1996,18(8):831-836.
[113]P. Howland and H. Park, Generalizing discriminant analysis using the generalized singular value decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence,2004,26(8): 995-1006.
[114]I.T. Jolliffe, Principle component analysis. Springer-Verlag,1986.
[115]P.N. Belhumeur, J.P. Hespanha, and D.J. Kriegman, Eigenfaces versus Fisherfaces:recognition using class specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence,1997,19(7):711-720.
[116]Xiaofei He and Partha Niyogi, Locality preserving projections. Advances In Neural Information Processing Systems,2004.
[117]Xiaofei He, Shuicheng Yan, Yuxiao Hu, P. Niyogi, and Hong-Jiang Zhang, Face recognition using laplacianfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(3): 328-340.
[118]Deli Zhao, Zhouchen Lin, Rong Xiao, and Xiaoou Tang, Linear laplacian discrimination for feature extraction, in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2007.
[119]Risheng Liu, Zhouchen Lin, Zhixun Su, and Kewei Tang, Feature extraction by learning Lorentzian metric tensor and its extensions. Pattern Recognition,2010,43(10):3298-3306.
[120]Shuicheng Yan, Dong Xu, Benyu Zhang, Hong-Jiang Zhang, Qiang Yang, and S. Lin, Graph embedding and extensions:A general framework for dimensionality reduction. IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(1):40-51.
[121]David Freedman, Statistical Models:Theory and Practice,2005.
[122]Elazar j. Pedhazur, Multiple regression in behavioral research:Explanation and prediction (2nd edition), New York:Holt, Rinehart and Winston,1982.
[123]http://cseweb.ucsd.edu/-saul/teaching/cse291s07/Llnorm.pdf.
[124]Yigang Peng, Arvind Ganesh, John Wright, Wenli Xu, and Yi Ma, RASL:Robust alignment by sparse and low-rank decomposition for linearly correlated images. IEEE Transactions on Pattern Analysis and Machine Intelligence,2010, In Press.
[125]Xi Chen, Bing Bai, Yanjun Qi, Qihang Lin and Jaime G. Carbonell, Sparse Latent Semantic Analysis, in Proc. of SIAM International Conference on Data Mining,2011.
[126]Ming Yuan, Yi Lin, Model selection and estimation in regression with grouped variables. Journal of the royal statistics society:Series B,2006,68(1):49-67.
[127]Zhouchen Lin, Minming Chen, and Yi Ma, The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrix. Technical Report UILU-ENG-09-2215, UIUC,2009.
[128]Guangcan Liu, Zhouchen Lin, and Yong Yu, Robust subspace segmentation by low-rank representation, in Proc. IEEE International Conference on Machine Learning,2010.
[129]Xiaofei He, Deng Cai, Shuicheng Yan, and Hong-Jiang Zhang, Neighborhood Preserving Embedding, in Proc. of IEEE International Conference on Computer Vision,2005.
[130]Deng Cai, Xiaofei He, Kun Zhou, Jiawei Han and Hujun Bao, Locality Sensitive Discriminant Analysis. IJCAI'2007.
[131]T. Ahonen, A. Hadid, M. Pietikainen, Face description with local binary patterns:application to face recognition. IEEE Trasactions on Pattern Analysis and Machine Intelligence,2008,28(12): 2037-2041.
[132]郑颖,基于图像的三维人脸建模研究,中国科学技术大学博士学位论文,2009.
[133]Z. Zhang, A flexible new technique for camera calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence,2000,22(11):1330-1334.
[134]http://www.vision.caltech.edu/bouguetj/calib_doc/.
[2]S. Pankanti, R.M. Bolle, A. Jain, Biometrics:The Future of Identification. Computer,2000,33(2): 46-49.
[3]金一,人脸识别中若干算法的研究,北京交通大学博士论文,2009.
[4]W. Zhao, R. Chellappa, A. Rosenfeld, P.J. Phillips, Face recognition:A Literature Survey. ACM Computing Surveys,2003, pp.399-458.
[5]FRVT, Face Recognition Vendor Test, http://www.frvt.org/,2002.
[6]P.J. Phillips, P.J. Flynn, T. Scruggs, K.W. Bowyer, Jin Chang, K. Hoffman, J. Marques, Jaesik Min, and W. Worek, Overview of the Face Recognition Grand Challenge, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, June 2005, pp.947-954.
[7]王跃明,表情不变的三维人脸识别研究,浙江大学博士论文,2007.
[8]Yueming Wang, Gang Pan, Zhaohui Wu, and Yigang Wang, Exploring facial expression effects in 3D face recognition using partial ICP. in Proc. of Asian Confernece on Computer Vision,2006, pp.581-590.
[9]Xiaoguang Lu, A.K. Jain, and D. Colbry, Matching 2.5D face scans to 3D models. IEEE Transactions on Pattern Recognition and Machine Intelligence,2006,28(1):31-43.
[10]F. Tsalakanidou, S. Malassiotis, M.G. Strintzis, Face localization and authentication using color and depth images. IEEE Transactions on Image Processing,2005,14(2):152-168.
[11]O. Ocegueda, S. Shah, I. Kakadiaris, Which parts of the face give out your identity? in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2011, pp.641-648.
[12]Lijun Yin, Xiaozhou Wei, Yi Sun, Jun Wang, M.J. Rosato, A 3D facial expression database for facial behavior research, in Proc. of the 7th International Conference on Automatic Face and Gesture Recognition,2006, pp.211-216.
[13]Kevin W. Bowyer, Kyong Chang, Patrick Flynn, A survey of approaches and challenges in 3D and multi-modal 3D + 2D face recognition. Computer Vision and Image Understanding,2006, 101(1):1-15.
[14]Andrea F. Abate, Michele Nappi, Daniel Ricco, and Gabriele Sabatino,2D and 3D face recognition:A survey. Pattern Recognition Letters,2007,28(14):1885-1906.
[15]G. Passalis, P. Perakis, T. Theoharis, and I.A. Kakadiaris, Using facial symmetry to handle pose variations in real-world 3D face recognition. IEEE Transactions on Pattern Recognition and Machine Intelligence,2011,33(10):1938-1951.
[16]G. Medioni and R. Waupotitsch, Face modeling and recognition in 3D, Proc. IEEE Int'1 Workshop Analysis and Modeling of Faces and Gestures, pp.232-233,2003.
[17]K. Chang, K. W. Bowyer, and P. Flynn, Effects on facial expression in 3D face recognition, Proc. SPIE Conf. Biometric Technology for Human Identification, pp.132-143,2005.
[18]T. Maurer, D. Guigonis, I. Maslov, B. Pesenti, A. Tsaregorodtsev, D. West, and G. Medioni, Performance of Geometrix ActiveID 3D face recognition engine on the FRGC data, in Proc. of IEEE Workshops on Computer Vision and Pattern Recognition,2005, pp.154.
[19]Yueming Wang, Jianzhuang Liu, and Xiaoou Tang, Robust 3D face recognition by local shape difference boosting. IEEE Transactions on Pattern Recognition and Machine Intelligence,2010, 32(10):1858-1870.
[20]K.I. Chang, K.W. Bowyer, and P.J. Flynn, Multiple nose region matching for 3D face recognition under varying facial expression. IEEE Transactions on Pattern Recognition and Machine Intelligence,2006,28(10):1695-1700.
[21]R. Tyrrell Rockafellar, Roger J-B Wets, Variational Analysis, Springer-Verlag,2005, ISBN 3-540-62772-3, ISBN 978-3-540-62772-2, pp.117.
[22]Gang Pan, Yijun Wu, Zhaohui Wu, and Wenyao Liu,3D face recognition by profile and surface matching, in Proc. of IEEE International Joint Conference on Neutral Networks,2003, pp. 2169-2174.
[23]B. Achermann, and H. Bunke, Classifying range images of human faces with Hausdorff distance, in Proc. of International Conference on Pattern Recognition,2000, pp.809-813.
[24]Chin-Seng Chua, Feng Han, and Yeong-Khing Ho,3D human face recognition using point signature, in Proc. of International Conference on Automatic Face and Gesture Recognition,2000, pp.233-238.
[25]Zhaohui Wu, Yueming Wang, and Gang Pan,3D face recognition using local shape map. in Proc. of IEEE Interational Conference on Image Processing,2004, pp.2003-2006.
[26]Chris Boehnen, Tanya Peters, and Patrick J. Flynn,3D signatures for fast 3D face recognition, Proc. of IAPR/IEEE International Conference on Biometrics,2009, pp.12-21.
[27]J. Cook, V. Chandran, and C. Fookes,3D face recognition using Log-Gabor templates, Proc. British Machine Vision Conf., pp.83-83,2006.
[28]T. Nagamine, T. Uemura, and I. Masuda,3D facial image analysis for human identification, in Proc. of International Confonference on Pattern Analysis and Machine Intelligence, vol.28, no.11, pp.1858-1863, Nov.2006.
[29]C. Beumier and M. Acheroy, Automatic 3D face authenntication. Image Vision Computing, 2000,18(4):315-321.
[30]C. Samir, A. Srivastava, and M. Daoudi, Three-dimensional face recognition using shapes of facial curves, IEEE Transactions on Pattern Recognition and Machine Intelligence,2006,28(11): 1858-1863.
[31]S. Berretti, A. Del Bimbo, and P. Pala,3D face recognition using Isogeodesic Stripes. IEEE Transactions on Pattern Recognition and Machine Intelligence,2010,32(12):2162-2177.
[32]G. G. Gordon, Face recognition based on depth and curvature features, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,1992, pp.808-810.
[33]Ana Belen Moreno, Angel Sanchez, Jose Fco Velez, and Fco Javier Diaz, Face recognition using 3D surface-extraced descriptors, in Proc. of Irish Machine Vision and Image Processing Conference,2003.
[34]S. Gupta, J.K. Aggarwal, M.K. Markey, and A.C. Bovik,3D face recognition founded on the structural diversity of human face, in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2007, pp.1-7.
[35]Chenghua Xu, Tieniu Tan, Stan Li, Yunhong Wang, and Cheng Zhong, Learning effective intrinsic features to boost 3D-based face recognition, in Proc. of European Conference on Computer Vision,2006, pp.416-427.
[36]Cheng Zhong, Zhenan Sun, and Tieniu Tan, Robust 3D face recognition using learned visual codebook. in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2007, pp.1-6.
[37]T.C. Faltemier, K.W. Bowyer, and P.J. Flynn, A region ensemble for 3D face recognition. IEEE transactions on Information Forensics and Security,2008,3(1):62-73.
[38]B. Achermann, X. Jiang, and H. Bunke, Face recognition using range images, in Proc. of International Conference on Virtual Systems and Multimedia,1997, pp.129-136.
[39]Alexander M. Bronstein, Michael M. Bronstein, and Ron Kimmel, Expression-invariant 3D face recognition, in Proc. of International Conference on Audio- and Video-Based Biometric Person Authentication,2003, pp.62-70.
[40]C. Hesher, A. Srivastava, and G. Erlebacher, A novel technique for face recognition using range imaging, in Proc. of International Symposium on Signal Processing and Its Applications,2003, pp. 201-204.
[41]T. Russ, C. Boehnen, and T. Peters,3D face recognition using 3D alignment for PCA, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2006, pp. 1391-1398.
[42]C.C. Queirolo, L. Silva, O.R.P. Bellon, and M.P. Segundo,3D face recognition using simulated annealing and the surface interpenetration measure. IEEE Transactions on Pattern Recognition and Machine Intelligence,2010,32(2):206-219.
[43]H.T. Tanaka, M. Ikeda, and H. Chiaki, Curvature-based face surface recognition using spherical correlation-principal directions for curved object recogntion. in Proc. of International Conference on Automatic Face and Gesture Recognition,1998, pp.372-377.
[44]Alexander M. Bronstein, Michael M. Bronstein, and Ron Kimmel, Three diensional face recognition. International Journal of Computer Vision,2005,64(1):5-30.
[45]Xiaoguang Lu, and A.K. Jain, Deformation modeling for robust 3D face matching, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2006, pp. 1377-1383.
[46]Yueming Wang, Gang Pan, and Zhaohui Wu,3D face recognition in the presence of expression: A guidance-based constraint deformation approach, in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2007, pp.1-7.
[47]I.A. Kakadiaris, G. Passalis, G. Toderici, M.N. Murtuza, Yunliang Lu, N. Karampatziakis, and T. Theoharis, Three-dimensional face recognition in the presence of facial expressions:An annotated deformable model approach. IEEE Transactions on Pattern Recognition and Machine Intelligence, 2007,29(4):640-649.
[48]Yingjie Wang, Chin-Seng Chua, and Yeong-Khing Ho, Face recognition from 2D and 3D images, in Proc. of International Audio- and Video-based Person Authentication,2001, pp.26-31.
[49]A.M. Bronstein, M.M. Bronstein, E. Gordon, R. Kimmel, Fusion of 2D and 3D data in three-dimensional face recognition. in Proc. of IEEE International Conference on Image Processing, 2004, pp.87-90.
[50]T. Papatheodorou, D. Rueckert, Evaluation of automatic 4D face recognition using surface and texture registration, in Proc. of IEEE International Conference on Automatic Face and Gesture Recognition,2004, pp.321-326.
[51]Chiraz BenAbdelkader, Paul A. Griffin, Comparing and combining depth and texture cues for face recognition, Image and Vision Computing,2005,23(3):339-352.
[52]A. Samani, J. Winkler, M. Niranjan, Automatic face recognition using stereo images. in Proc. of IEEE International Conference on Acoustics, Speech and Signal Processing,2006.
[53]Yi Sun, Lijun Yin,3D Spatio-Temporal face recognition using dynamic range model sequences, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops,2008, pp.1-7.
[54]F. Tsalakanidou, D. Tzovaras, M.G. Strintzis, Use of depth and color eigenfaces for face recognition, Pattern Recognition Letters,2003,24(9):1427-1435.
[55]Kyong I. Chang, Kevin W. Bowyer, and Patrick J. Flynn, Face recognition using 2D and 3D facial data, in Proc. of ACM Workshops on Multimodal User Authentication,2003.
[56]F. Tsalakanidou, S. Malassiotis, M.G. Strintzis, Integration of 2D and 3D images for enhanced face authentication, in Proc. of IEEE International Conference on Automatic Face and Gesture Recognition,2004.
[57]M. Husken, M. Brauckmann, S. Gehlen, Von der C. Malsburg, Strategies and benefits of fusion of 2D and 3D face recognition, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshop,2005.
[58]Xiaoguang Lu, and A. K. Jain, Integrating Range and Texture Information for 3D Face Recognition, in Proc. of IEEE Workshops on Application of Computer Vision,2005, pp.156-163.
[59]Xin Chen, T. Faltemier, P. Flynn, and K. Bowyer, Human face modeling and recognition through multi-view high resolution stereopsis, in Proc. of IEEE International Conference on Computer Vision and Pattern Recognition Workshop,2006.
[60]Loris Nanni, Alessandra Lumini, RegionBoost learning for 2D+3D based face recognition. Pattern Recognition Letters,2007,28(15):2063-2070.
[61]A.S. Mian, M. Bennamoun, and R. Owens, An efficient multimodal 2D-3D hybrid approach to automatic face recognition, IEEE Transactions on Pattern Recognition and Machine Intelligence, 2007,29(11):1927-1943.
[62]Daniel Riccio, Jean-Luc Dugelay, Geometric invariants for 2D/3D face recognition. Pattern Recognition Letters,2007,28(14):1907-1914.
[63]Jian-Gang Wang, Eng Thiam Lim, Xiang Chen, and Ronda Venkateswarlu, Real-time stereo face recognition by fusing appearance and depth fisherfaces. Journal of VLSI Signal Processing, 2007,49(3):409-423.
[64]http://my.icxo.com/276388/viewspace-70594.html.
[65]http://szjyl2010.b2b.youboy.com/show0sp54560101.html.
[66]http://www.genewell.net/?page_id=271.
[67]P Paul J. Besl, and Neil D. Mckay, A method of registration of 3D shapes, IEEE Transactions on Pattern Recognition and Machine Intelligence,1992,14(2):239-256.
[68]Geof Givens, J. Ross Beveridge, Bruce A. Draper, David Bolme, A statistical assessment of subject factors in the PCA recognition of human faces, in Proc. of IEEE International Conference Computer Vision and Pattern Recognition Workshop,2003.
[69]J. Wright, A.Y. Yang, A. Ganesh, S.S. Sastry, and Yi Ma, Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(2): 210-227.
[70]Peyre Gabriel, Numerical Mesh Processing. Chapter 4.
[71]Dong Chen-shi, and Wang Guo-zhao, Curvature estimation on triangular mesh, J Zhejiang Univ SCI.2005 6A(Suppl.1):128-136.
[72]Xin Chen, Francis Schmitt, Intrinsic surface poperties from surface triangulation. in Proc. of the European Conference on Computer Vision,1992, pp.739-743.
[73]J. A. Sethian. Level Sets Methods and Fast Marching Methods. Cambridge University Press, 2nd edition,1999.
[74]T. H. Cormen, C. E. Leiserson, and R. R. Rivest, Introduction to Algorithms. MIT Press, Cambridge, Massachusetts,1990.
[75]R. Kimmel and J. A. Sethian. Computing Geodesic Paths on Manifolds. Proc. Natl. Acad. Sci., 1998,95(15):8431-8435.
[76]Y. Eldar, M. Lindenbaum, M. Porat, and Y. Y. Zeevi. The farthest point strategy for progressive image sampling. IEEE transactions on image processing,1997,6(9):1305-1315.
[77]G. Peyre and L. D. Cohen. Geodesic remeshing using front propagation. International Journal of Computer Vision.2006,69(1):145-156.
[78]Deng Cai, Xiaofei He, and Jiawei Han, Spectral regression for efficient regularized subspace learning, in Proc. of IEEE International Conference on Computer Vision,2007.
[79]贾贝贝,基于双目视觉的三维人脸重建,北京交通大学硕士学位论文,2009.
[80]S. Malassiotis, M.G. Strintzis, Real-time head tracking and 3D pose estimation from range data, in Proc. of IEEE International Conference on Image Processing,2003.
[81]Gabriel Taubin, A signal processing approach to fair surface design, in Proc. of the 22nd Annual Conference on Computer Graphics and interactive techniques,1995, pp.351-358.
[82]Mathieu Desbrun, Mark Meyer, Peter Schroder, Alan H. Barr, Anisotropic feature-preserving denoising of height fields and bivariate data, in Proc. of Graphics interface,2000, pp.145-152.
[83]轴角描述,http://en.wikipedia.org/wiki/Axis-angle_representation.
[84]王晶,三维人脸识别,西北工业大学硕士学位论文,2005.
[85]CS277-Geometric Modeling in Computer Graphics_Discrete Differential Geometry.
[86]S. J. Kim, W. K. Jeong, C. H. Kim. LOD Generation with Discrete Curvature Error Metric.
[87]C. Dorai, A.K. Jain, COSMOS-A representation scheme for 3D free-form objects, IEEE Transactions on Pattern Analysis and Machine Intelligence,1997,19(10):1115-1130.
[88]N. Alyuz, B. Gokberk, L. Akarun, Regional registration for expression resistant 3D face recognition.IEEE Transactions on Information Forensics and Security,2010,5(3):425-440.
[89]Xi Zhao, Emmanuel Dellandrea, and Liming Chen, A 3D statistical facial feature model and its application on locating facial landmarks. Advanced Concepts for Intelligent Vision Systems,2009, 5807:686-697.
[90]M. Romero and N. Pears, Landmark localisation in 3D face data, in Proc. of IEEE International Conference on Advanced Video and Signal Based Surveillance,2009, pp.73-78.
[91]H. Dibeklioglu, A.A. Salah, and L. Akarun,3D facial landmarking under expression, pose, and occlusion variations, in Proc. of IEEE International Conference on Biometrics:Theory, Applications and Systems,2008, pp.1-6.
[92]M.P. Segundo, C. Queirolo, O.R.P. Bellon, and L. Silva, Automatic 3D facial segmentation and landmark detection, in Proc. of 14th International Conference on Image Analysis and Processing, 2007, pp.431-436.
[93]J.D. Hose, J. Colineau, C. Bichon, and B. Dorizzi, Precise localization of landmarks on 3D faces using Gabor Wavelets, in Proc. of IEEE International Conference on Biometrics:Theory, Applications and Systems,2007, pp.1-6.
[94]Albert Ali Salah and Lale Akarun,3D facial feature localization for registration, in Proc. of International Workshop on Multimedia Content Rpresentation, Claasification and Security,2006, pp. 338-345.
[95]Hatice Cinar Akakin, Albert Ali Salah, Lale Akarun, and Bulent Sankur,2D/3D facial feature extraction, in Proc. of SPIE:Image Processing:Algorithms and Systems, Neutral Networks, and Machine Learning, vol.6064, no.1,2006, Article 60641D.
[96]Xiaoguang Lu and A.K. Jain, Automatic feature extraction for multiview 3D face recognition, in Proc. of 7th International Conference on Automatic Face and Gesture Recognition,2006, pp. 585-590.
[97]E.L. Schwatz, A. Shaw, E. Wolfson, A numerical solution to the generalized mapmaker's problem:flattening nonconvex polyhedral sufaces. IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(9):1005-1008.
[98]G. Zigelman, R. Kimmel, N. Kiryati, Texture mapping using surface flattening via multidimensional scaling. IEEE Transaction on Visualization and Computer Graphics,2002,8(2): 198-207.
[99]R. Grossmann, N. Kiryati, and R. Kimmel, Compuational surface flattening:a voxel-based approach. IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(4):433-441.
[100]A. Elad, R. Kimmel, Bendng invariant representations for surfaces, in Proc. of IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2001.
[101]M. Balasubramanian, E.L. Shwartz, J.B. Tenenbaum, V. de Silva, J.C. Langford, The ISOMAP algorithm and Topological Stability, Science,2002,295(5552):9-11.
[102]Jau-Ling Shih, Chang-Hsing Lee, Jian Tang Wang. A new 3D model retrieval approach based on the elevation descriptor. Pattern Recognition,2007,40(1):283-295.
[103]D.V. Vranic, An improvement of rotation invariant 3D-shape descriptor based on functions on concentric spheres, in Proc. of IEEE International Conference on Image Processing,2003, pp.757-760.
[104]Yue Gao, Qionghai Dai, Naiyao Zhang,3D model comparison using spatial structure circular descriptor. Pattern Recognition,2010,43(3):1142-1151.
[105]D. G. Lowe, Distinctive Image Features from Scale-Invariant Keypoints, International Journal of Computer Vision,2004,60(2):91-110.
[106]K.I. Chang, K.W. Bowyer, and P.J. Flynn, An evaluation of multimodal 2D+3D face biometrics. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,28(4):619-624.
[107]Chenghua Xu, Stan Li, Tieniu Tan, and Long Quan, Automatic 3D face recognition from depth and intensity Gabor features. Patter recognition,2009,42(9):1895-1905.
[108]John Wright, Arvind Ganesh, Shankar Rao, Peng, Y., and Y. Ma. Robust principle component analysis:Exact recovery of corrputed low-rank matrices via convex optimization, in Proc. Advances in Neural Information Processing Systems,2009.
[109]Berk Gokberk, Helin Dutagaci, Aydin Ulas, Lale Akarun, and Bulent Sankur, Representation plurality and fusion for 3D face recognition. IEEE Transactions on Systems, Man, and Cybernetics (B),2008,38(1):155-173.
[110]A. Savran, B. Sankur, M. T. Bilge, Comparative Evaluation of 3D versus 2D modality for automatic detection of facial action units. Pattern Recognition,2012,45 (2):767-782.
[111]CASIA-3D FaceVl, http://biometrics.idealtest.org/.
[112]D.L. Swets and J.J. Weng, Using discriminant eigenfeatures for image retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence,1996,18(8):831-836.
[113]P. Howland and H. Park, Generalizing discriminant analysis using the generalized singular value decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence,2004,26(8): 995-1006.
[114]I.T. Jolliffe, Principle component analysis. Springer-Verlag,1986.
[115]P.N. Belhumeur, J.P. Hespanha, and D.J. Kriegman, Eigenfaces versus Fisherfaces:recognition using class specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence,1997,19(7):711-720.
[116]Xiaofei He and Partha Niyogi, Locality preserving projections. Advances In Neural Information Processing Systems,2004.
[117]Xiaofei He, Shuicheng Yan, Yuxiao Hu, P. Niyogi, and Hong-Jiang Zhang, Face recognition using laplacianfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(3): 328-340.
[118]Deli Zhao, Zhouchen Lin, Rong Xiao, and Xiaoou Tang, Linear laplacian discrimination for feature extraction, in Proc. of IEEE Conference on Computer Vision and Pattern Recognition,2007.
[119]Risheng Liu, Zhouchen Lin, Zhixun Su, and Kewei Tang, Feature extraction by learning Lorentzian metric tensor and its extensions. Pattern Recognition,2010,43(10):3298-3306.
[120]Shuicheng Yan, Dong Xu, Benyu Zhang, Hong-Jiang Zhang, Qiang Yang, and S. Lin, Graph embedding and extensions:A general framework for dimensionality reduction. IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(1):40-51.
[121]David Freedman, Statistical Models:Theory and Practice,2005.
[122]Elazar j. Pedhazur, Multiple regression in behavioral research:Explanation and prediction (2nd edition), New York:Holt, Rinehart and Winston,1982.
[123]http://cseweb.ucsd.edu/-saul/teaching/cse291s07/Llnorm.pdf.
[124]Yigang Peng, Arvind Ganesh, John Wright, Wenli Xu, and Yi Ma, RASL:Robust alignment by sparse and low-rank decomposition for linearly correlated images. IEEE Transactions on Pattern Analysis and Machine Intelligence,2010, In Press.
[125]Xi Chen, Bing Bai, Yanjun Qi, Qihang Lin and Jaime G. Carbonell, Sparse Latent Semantic Analysis, in Proc. of SIAM International Conference on Data Mining,2011.
[126]Ming Yuan, Yi Lin, Model selection and estimation in regression with grouped variables. Journal of the royal statistics society:Series B,2006,68(1):49-67.
[127]Zhouchen Lin, Minming Chen, and Yi Ma, The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrix. Technical Report UILU-ENG-09-2215, UIUC,2009.
[128]Guangcan Liu, Zhouchen Lin, and Yong Yu, Robust subspace segmentation by low-rank representation, in Proc. IEEE International Conference on Machine Learning,2010.
[129]Xiaofei He, Deng Cai, Shuicheng Yan, and Hong-Jiang Zhang, Neighborhood Preserving Embedding, in Proc. of IEEE International Conference on Computer Vision,2005.
[130]Deng Cai, Xiaofei He, Kun Zhou, Jiawei Han and Hujun Bao, Locality Sensitive Discriminant Analysis. IJCAI'2007.
[131]T. Ahonen, A. Hadid, M. Pietikainen, Face description with local binary patterns:application to face recognition. IEEE Trasactions on Pattern Analysis and Machine Intelligence,2008,28(12): 2037-2041.
[132]郑颖,基于图像的三维人脸建模研究,中国科学技术大学博士学位论文,2009.
[133]Z. Zhang, A flexible new technique for camera calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence,2000,22(11):1330-1334.
[134]http://www.vision.caltech.edu/bouguetj/calib_doc/.