基于机器学习的物体识别
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摘要
计算机视觉是人工智能领域的核心问题之一,它的目标是让计算机拥有人的视觉能力,也就是让机算计像人一样理解现实世界中的图像。计算机视觉在医学、工业、军事、航天等领域拥有广泛的应用。但是,根据人的视觉占用至少60%的人脑资源这个事实,计算机视觉在学术界被认为是“人工智能完全”问题,或者至少是“人工智能困难”问题。在众多计算机视觉的问题中,广义的物体识别,即在任意环境下识别任意物体,又是最核心的问题之一。总的来说,物体识别是让计算机自动地把图像中的物体分类。这是个非常具有挑战性的问题,它也是很多应用问题的最紧要瓶颈所在,比如图片搜索问题。虽然世界上诸如麻省理工、斯坦福、耶鲁、剑桥、普林斯顿等众多非常有实力的研究机构已经研究这个问题多年,广义的物体识别问题还远远没有得到很好的解决。但是,从机器学习的角度来说,物体识别的问题至少在一定程度上是可行的。准确的说,只要能合适地抽取图像特征、合适地描述物体和找到合适的分类模型,实现一个能满足实际应用的物体识别系统是可行的。
     在这篇论文里,我们将介绍一个基于机器学习的物体识别系统原型。这个原型系统包括三个部分:物体分割子系统、物体描述子系统和一个分类器。在这三个要点上,我们创造性地提出了自己的方法:一个基于混合图模型(HGM)的物体分割算法、一个基于拉多表示的物体描述算法(RRFD)和一个称为神经编码分类器(NCC)的分类算法。随后,我们对这个基本原型系统做一些改进工作:包括基于低秩描述(LRR)的图像聚类算法、基于局部线性转换(LLT)的多标签分类算法和基于反馈嵌入(FE)的大规模相似图像查找技术。具体来说,本文的创新点有:
     我们提出了用于一般半指导分类的HGM (Hybrid Graph Model,混合图模型),并建立了一个有效的物体自动分割方法。根据我们所知,我们是第一个将混合图引入机器学习的人。不同于传统的物体分割方法,我们的基于HGM的方法是自动的,即不需要手动分割好的训练数据。这使得我们的物体识别系统更加实用。
     我们提出了基于Radon变换的物体描述算法,称为RRFD (Radon Repre-sentation Based Feature Description,基于拉多表示的特征描述)。在物体已经从图像中分割出来后,RRFD可以把物体的形状、颜色、纹理等信息综合地集成到一个维度比较低的特征向量中去,并由此而实现精确的物体识别。除此之外,RRFD也可以作为一个一般的特征描述算法,它可以描述任意一个图像区域。
     物体识别中的最后一个步骤是对特征向量进行分类。我们提出了基于神经编码的分类器,称为NCC(Neural Coding Classifier,神经编码分类器)。和传统的诸如SVM的分类算法相比,NCC不仅能够很好地处理测试数据与训练数据同分布的情况,也能更好地处理测试数据与训练数据概率分布不同的情况。实验结果表明,在测试数据和训练数据概率分布相同的情况下,NCC的分类精度度略微超过SVM;在测试数据和训练数据概率分布不同的情况下,NCC可以显著地超过SVM。
     当一张图像中可能含有多个类的物体时,物体识别中对应的分类问题就是一个MLC(Multi-Label Classification,多标签分类)问题。多标签分类问题可以用MOR(Multi Output Regression,多输出回归)模型来处理。我们提出了用于定义回归分析中损失函数的LLT(LocallyLinear Transformation,局部线性转换)机制,并在SVR(Support VectorRegression,支持向量回归)框架下提出了一种结合LLT和SVR的多输出回归算法,即所谓的LLT-SVR。LLT-SVR即提供了一种很好的多输出回归分析工具,又为我们的物体识别系统提供了一种有效的多标签分类器。
     为了提高物体识别系统的实用性,我们需要一种有效的图像聚类机制。我们首次提出了用于处理矩阵数据信号的LRR(Low-Rank Representation,低秩表示)。LRR是一种新的压缩传感(Compressed Sensor)技术,和传统的SR(Sparse Representation,稀疏表示)相比,LRR能更好的描述数据的整体结构,从而在诸如图像聚类之类的数据聚类问题中,LRR有明显的优势。基于LRR,我们提出了一种有效的图像聚类算法。除图像聚类外,LRR子空间分割算法也是一种基本的数据聚类法。更重要的是,LRR首次提出了“低秩”(Low Rank)准则。LRR不但在机器学习领域产生巨大的理论影响,而且在计算机视觉和图像处理领域有着广泛的应用。
     为了提高物体识别系统的运行速度,我们需要一种高速的相似图像查找技术。我们提出了称为FE(Feedback Embedding,反馈嵌入)的数据降维算法。基于FE,我们可以设计出一种有效的语义哈希算法,进而实现在大规模物体识别系统中的快速相似图像查找。除研究物体识别和一些相关的机器学习问题(比如分类、聚类和降维等)外,本文也对一些根本的科学问题进行了讨论。比如我们探究大脑是如何处理视觉信号的,并提出了一个新颖的神经编码假设,即大脑是基于信号重构来处理信号的。
Computer vision is one of the core problems of artificial intelligence. Its ultimategoal is to make computers own the visual ability of human, i.e., to see and interpret thevisual scenes in the way of human. Computer vision has wide applications in medi-cal, industry, military and aerospace etc. However, as it has been known that humanvision occupies at least60percentage of human brain, it is generally accepted that com-puter vision may be an “AI-complete” problem, or is at least an “AI-difcult” problem.Among the various vision problems, the problem of classifying the objects picturedby images into classes, so called as object recognition, is one of the most fundamentalproblems. It is a very challenge problem and is also one crucial bottleneck that blocksthe advance of many important applications such as image search. Although this prob-lem have being explored for many years by the world’s most competitive academiessuch as MIT, Stanford, Yale, Cambridge and Princeton, the problem is still not wellsolved. However, with the viewpoint of machine learning, object recognition is feasi-ble, at least to some extend. Namely, it is possible to implement an practicable objectrecognition system that fits the requirements of real applications, provided that onecould appropriately extract the features from images, appropriately represent the ob-jects, appropriately represent the object class, and establish an appropriate mechanismto classify the objects.
     In this thesis, we firstly introduce a prototype of a machine learning based ob-ject recognition system, which is consisting of an object segmentation sub-system, anobject representation sub-system and a classifier. We devise novel algorithms to es-tablish these sub-systems, including an HGM-based object segmentation method, anobject representation approach named RRFD and a classifier named NCC. In order toimprove the performance of the object recognition system, we propose the models ofLRR, LLT and Feedback Embedding for image clustering, multi-label classificationand fast similarity search, respectively. To be precise, the innovations of this paper include:
     We propose HGM (hybrid graph model) for semi-supervised data clustering. Tothe best of our knowledge, we are the first to introduce the hybrid graph intomachine learning. Based on HGM, we devise an efcient and efective systemfor automatically segment objects without annotated training images. This au-tomatic object segmentation approach makes our object recognition system bemore appealing.
     We propose a new feature descriptor based on the Radon transform, called as theRRFD. Given the images with objects being separated from backgrounds, RRFDconverts the objects to a feature vector that encodes the shape, texture and colorof the objects. Moreover, RRFD can be also taken as a general feature descriptorto generate feature vectors for an arbitrary image region.
     To recognize object categories, we need to classify the feature vectors into theirrespective classes. Based on a neural coding hypothesis, we devise a new classi-fication algorithm, called as the NCC. In comparison with the widely used SVMmethod, NCC performs much better in handling the data with diferent training-testing distributions. While the testing data is sampled from the same distributionas the training data, NCC also slightly outperforms SVM.
     When a single image can contain objects of multiple classes, the classificationproblem becomes a MLC (Multi-Label Classification) problem. We propose anovel mechanism, called as the LLT, for defining the loss functions in regressionframeworks. Based on the well established SVR framework, we implement anefective MOR (Multi-Output Regression) algorithm, called as the LLT-SVR.LLT-SVR also provides an efective way for multi-label classification. So it canextend our system from single object class to multiple ones.
     In order to improve the practicability of the object recognition system, we needa mechanism to group images into their respective topics. We establish the cri-terion of low rankness and propose a new method named LRR (Low-Rank Rep-resentation). To the best of our knowledge, we are the first to introduce thelow-rank criterion into machine learning. Based on LRR, we have established an efective algorithm for image clustering.
     In order to achieve fast recognition in large-scale database, we devised a new se-mantic hashing indexing structure. The core of this structure is a new dimension-ality reduction algorithm, called as the FE (Feedback Embedding). Comparingto previous methods such as LLE (Locally Linear Embedding), FE provides amore convincing mechanism for dimensionality reduction.
     Besides the object recognition and some corresponding machine learning problems, inthis article we also explore some essential issues of science. For example, we try toanswer the question of how human brains process visual signals. Namely, we makea new neural coding hypothesis that reveals the reconstruction mechanism in humanbrain.
引文
[1] Azad P, Gockel T, Dillmann R. Computer Vision-Principles and Practice.2008.
    [2] Cortes C, Vapnik V. Support-Vector Networks. Mach. Learn.,1995,20(3):273–297.
    [3] Tsoumakas G, Katakis I. Multi Label Classification: An Overview. International Journal ofData Warehousing and Mining,2007,3(3):1–13.
    [4] Haralick R. Statistical and structural approaches to texture. Proceedings of the IEEE,1979,67(5):786–804.
    [5] Jain A K, Farrokhnia F. Unsupervised texture segmentation using Gabor filters. PatternRecogn.,1991,24(12):1167–1186.
    [6] Randen T, Husoy J H. Filtering for Texture Classification: A Comparative Study. IEEETrans. Pattern Anal. Mach. Intell.,1999,21(4):291–310.
    [7] Unser M. Texture classification and segmentation using wavelet frames. Image Processing,IEEE Transactions on,1995,4(11):1549–1560.
    [8] Charalampidis D, Kasparis T. Wavelet-based rotational invariant roughness features fortexture classification and segmentation. IEEE Transactions on Image Processing,2002,11(8):825–837.
    [9] Cula O, Dana K. Compact representation of bidirectional texture functions. ComputerVision and Pattern Recognition,2001. CVPR2001. Proceedings of the2001IEEE ComputerSociety Conference on,2001,1:I–1041–I–1047vol.1.
    [10] Cula O G, Dana K J.3D Texture Recognition Using Bidirectional Feature Histograms. Int.J. Comput. Vision,2004,59(1):33–60.
    [11] Harwood D, Ojala T, Pietika¨inen M, et al. Texture classification by center-symmetric auto-correlation, using Kullback discrimination of distributions. Pattern Recogn. Lett.,1995,16(1):1–10.
    [12] Ojala T, Pietika¨inen M, Harwood D. A comparative study of texture measures with classifi-cation based on featured distributions. Patteron Recognition,1996..
    [13] Zhao G, Pietikainen M. Local Binary Pattern Descriptors for Dynamic Texture Recogni-tion. Proceedings of ICPR’06: Proceedings of the18th International Conference on PatternRecognition, Washington, DC, USA: IEEE Computer Society,2006.211–214.
    [14] Cross G R. Markov random field texture models[D]. East Lansing, MI, USA,1980.
    [15] Caputo B, Hayman E, Mallikarjuna P. Class-Specific Material Categorisation. Proceedingsof ICCV’05: Proceedings of the Tenth IEEE International Conference on Computer Vision,Washington, DC, USA: IEEE Computer Society,2005.1597–1604.
    [16] Leung T, Malik J. Representing and Recognizing the Visual Appearance of Materials usingThree-dimensional Textons. Int. J. Comput. Vision,2001,43(1):29–44.
    [17] Schmid C. Weakly Supervised Learning of Visual Models and Its Application to Content-Based Retrieval. Int. J. Comput. Vision,2004,56(1-2):7–16.
    [18] Schafalitzky F, Zisserman A. Viewpoint invariant texture matching and wide baselinestereo. Computer Vision,2001. ICCV2001. Proceedings. Eighth IEEE International Con-ference on,2001,2:636–643vol.2.
    [19] Varma M, Zisserman A. A Statistical Approach to Texture Classification from Single Im-ages. International Journal of Computer Vision,2005,62(1-2):61–81.
    [20] Falconer K. Techniques in Fractal Geometry.1997.
    [21] Harris C, Stephens M. A Combined Corner and Edge Detection. Proceedings of Proceedingsof The Fourth Alvey Vision Conference,1988.147–151.
    [22] Lowe D. Object recognition from local scale-invariant features. Computer Vision,1999. TheProceedings of the Seventh IEEE International Conference on,1999,2:1150–1157vol.2.
    [23] Zhang J, Marsza M, Lazebnik S, et al. Local Features and Kernels for Classification ofTexture and Object Categories: A Comprehensive Study. Int. J. Comput. Vision,2007,73(2):213–238.
    [24] Bay H, Tuytelaars T, Gool L V. Surf: Speeded up robust features. Proceedings of In ECCV,2006.404–417.
    [25] Mikolajczyk K, Schmid C. A Performance Evaluation of Local Descriptors. IEEE Trans.Pattern Anal. Mach. Intell.,2005,27(10):1615–1630.
    [26] Sarfraz M S, Hellwich O. Head Pose Estimation in Face Recognition Across Pose Scenarios.Proceedings of VISAPP,2008.235–242.
    [27] Agarwal S, Roth D. Learning a Sparse Representation for Object Detection. Proceedings ofECCV: Proceedings of the7th European Conference on Computer Vision-Part IV, London,UK: Springer-Verlag,2002.113–130.
    [28] Li F F, Perona P. A Bayesian Hierarchical Model for Learning Natural Scene Categories.Proceedings of CVPR’05: Proceedings of the2005IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR’05)-Volume2, Washington, DC, USA:IEEE Computer Society,2005.524–531.
    [29] H B, RN N. Shape description using weighted symmetric axis features. Pattern Recognition,1978,10:167–180.
    [30] Leibe B, Leonardis A, Schiele B. Combined Object Categorization and Segmentation withan Implicit Shape Model. Proceedings of ECCV Workshop on Statistical Learning in Com-puter Vision, Prague, Czech Republic,2004.17–32.
    [31] Agarwal S, Awan A, Roth D. Learning to Detect Objects in Images via a Sparse, Part-BasedRepresentation. IEEE Trans. Pattern Anal. Mach. Intell.,2004,26(11):1475–1490.
    [32] Fergus R, Perona P, Zisserman A. A Sparse Object Category Model for Efcient Learningand Exhaustive Recognition. Proceedings of CVPR’05: Proceedings of the2005IEEEComputer Society Conference on Computer Vision and Pattern Recognition (CVPR’05)-Volume1, Washington, DC, USA: IEEE Computer Society,2005.380–387.
    [33] Opelt A, Pinz A, Fussenegger M, et al. Generic Object Recognition with Boosting. IEEETrans. Pattern Anal. Mach. Intell.,2006,28(3):416–431.
    [34] Fergus R, Perona P, Zisserman A. Weakly Supervised Scale-Invariant Learning of Modelsfor Visual Recognition. Int. J. Comput. Vision,2007,71(3):273–303.
    [35] Bar-Hillel A, Weinshall D. Efcient Learning of Relational Object Class Models. Int. J.Comput. Vision,2008,77(1-3):175–198.
    [36] Kokkinos I, Yuille A. HOP: Hierarchical Object Parsing. Proceedings of Proceedings ofIEEE Conference on Computer Vision and Pattern Recognition,2009.
    [37] Grauman K, Darrell T. The pyramid match kernel: discriminative classification with sets ofimage features. Proceedings of Proceedings of IEEE International Conference on ComputerVision, volume2,2005.1458–1465.
    [38] Chin R T, Dyer C R. Model-based recognition in robot vision. ACM Comput. Surv.,1986,18(1):67–108.
    [39] Kass M, Witkin A, Terzopoulos D. Snakes: Active contour models. International Journal ofComputer Vision,1988,1(4):321–331.
    [40] Hinton G R E, Williams C K I, Revow M. Adaptive elastic models for hand-printed characterrecognition. Proceedings of Advances in Neural Information Processing Systems4. MorganKaufmann,1992.512–519.
    [41] Yuille A L, Hallinan P W, Cohen D S. Feature extraction from faces using deformabletemplates. Int. J. Comput. Vision,1992,8(2):99–111.
    [42] Lipson P, Yuille A L, O’Keefe D, et al. Deformable Templates for Feature Extraction fromMedical Images. Proceedings of ECCV’90: Proceedings of the First European Conferenceon Computer Vision, London, UK: Springer-Verlag,1990.413–417.
    [43] Hill A, Taylor C J. Model-based image interpretation using genetic algorithms. ImageVision Comput.,1992,10(5):295–300.
    [44] Figueiredo M, Leit J M N, Jain A K. Adaptive Parametrically Deformable Contours. Pro-ceedings of EMMCVPR’97: Proceedings of the First International Workshop on EnergyMinimization Methods in Computer Vision and Pattern Recognition, London, UK: Springer-Verlag,1997.35–50.
    [45] Bozma I, Duncan J S. Model-Based Recognition of Multiple Deformable Objects Usinga Game-Theoretic Framework. Proceedings of IPMI’91: Proceedings of the12th Interna-tional Conference on Information Processing in Medical Imaging, London, UK: Springer-Verlag,1991.358–372.
    [46] Goodall C. Procrustes Methods in the Statistical Analysis of Shape. Journal of the RoyalStatistical Society. Series B (Methodological),1991,53(2):285–339.
    [47] Pentland A, Sclarof S. Closed-Form Solutions for Physically Based Shape Modeling andRecognition. IEEE Trans. Pattern Anal. Mach. Intell.,1991,13(7):715–729.
    [48] Cootes T F, Taylor C J, Cooper D H, et al. Active shape models, their training and applica-tion. Comput. Vis. Image Underst.,1995,61(1):38–59.
    [49] Sharon E, Brandt A, Basri R. Segmentation and Boundary Detection Using MultiscaleIntensity Measurements. Proceedings of CVPR (1),2001.469–476.
    [50] Galun M, Sharon E, Basri R, et al. Texture Segmentation by Multiscale Aggregation ofFilter Responses and Shape Elements. Proceedings of ICCV,2003.716–723.
    [51] Sharon E, Galun M, Sharon D, et al. Hierarchy and adaptivity in segmenting visual scenes.Nature,2006,442(7104):810–813.
    [52] Shi J, Malik J. Normalized Cuts and Image Segmentation. IEEE Transactions on PatternAnalysis and Machine Intelligence,2000,22(8):888–905.
    [53] Ma Y, Derksen H, Hong W, et al. Segmentation of Multivariate Mixed Data via Lossy DataCoding and Compression. IEEE Trans. Pattern Anal. Mach. Intell.,2007,29(9):1546–1562.
    [54] Agarwal S, Roth D. Learning a Sparse Representation for Object Detection. Proceedings ofECCV: Proceedings of the7th European Conference on Computer Vision-Part IV, London,UK: Springer-Verlag,2002.113–130.
    [55] Leibe B, Leonardis A, Schiele B. Combined Object Categorization and Segmentation withan Implicit Shape Model. Proceedings of ECCV Workshop on Statistical Learning in Com-puter Vision, Prague, Czech Republic,2004.17–32.
    [56] Tu Z, Chen X, Yuille A L, et al. Image Parsing: Unifying Segmentation, Detection, andRecognition. Proceedings of Toward Category-Level Object Recognition. Springer,2006.545–576.
    [57] Yu S X, Shi J. Object-Specific Figure-Ground Segregation. Proceedings of CVPR: IEEEComputer Society Conference on Computer Vision and Pattern Recognition. IEEE Com-puter Society,2003.39–45.
    [58] Munim H E A E, Farag A A. A Shape-Based Segmentation Approach: An Improved Tech-nique Using Level Sets. Proceedings of ICCV:10th IEEE International Conference onComputer Vision,2005.930–935.
    [59] Yuille A L, Hallinan P W, Cohen D S. Feature extraction from faces using deformabletemplates. Int. J. Comput. Vision,1992,8(2):99–111.
    [60] Zhao L, Davis L S. Closely Coupled Object Detection and Segmentation. Proceedingsof ICCV: Proceedings of the Tenth IEEE International Conference on Computer Vision(ICCV’05) Volume1, Washington, DC, USA: IEEE Computer Society,2005.454–461.
    [61] Yu S X, Gross R, Shi J. Concurrent Object Recognition and Segmentation by Graph Par-titioning. Proceedings of NIPS: Neural Information Processing Systems. MIT Press,2002.1383–1390.
    [62] Borenstein E, Ullman S. Class-Specific, Top-Down Segmentation. Proceedings of ECCV:Proceedings of the7th European Conference on Computer Vision-Part II, London, UK:Springer-Verlag,2002.109–124.
    [63] Cour T, Shi J. Recognizing objects by piecing together the Segmentation Puzzle.2007.
    [64] Borenstein E, Ullman S. Learning to Segment. Proceedings of ECCV:8th European Con-ference on Computer Vision. Springer,2004.315–328.
    [65] Winn J M, Jojic N. LOCUS: Learning Object Classes with Unsupervised Segmentation.Proceedings of ICCV:10th IEEE International Conference on Computer Vision. IEEE Com-puter Society,2005.756–763.
    [66] Rother C, Minka T, Blake A, et al. Cosegmentation of Image Pairs by Histogram Matching-Incorporating a Global Constraint into MRFs. Proceedings of CVPR: Proceedings of the2006IEEE Computer Society Conference on Computer Vision and Pattern Recognition,Washington, DC, USA: IEEE Computer Society,2006.993–1000.
    [67] Levin A, Weiss Y. Learning to Combine Bottom-Up and Top-Down Segmentation. Pro-ceedings of ECCV: Proceedings of the9th European Conference on Computer Vision-PartIV,2006.581–594.
    [68] Mori G. Guiding Model Search Using Segmentation. Proceedings of ICCV: Proceedingsof the Tenth IEEE International Conference on Computer Vision, Washington, DC, USA:IEEE Computer Society,2005.1417–1423.
    [69] Cao L, Fei-Fei L. Spatially Coherent Latent Topic Model for Concurrent Segmentationand Classification of Objects and Scenes. Computer Vision,2007. ICCV2007. IEEE11thInternational Conference on,14-21Oct.2007.1–8.
    [70] Belkin M, Niyogi P, Sindhwani V. Manifold Regularization: A Geometric Framework forLearning from Labeled and Unlabeled Examples. J. Mach. Learn. Res.,2006,7:2399–2434.
    [71] Zhou D, Huang J, Scho¨lkopf B. Learning from labeled and unlabeled data on a directedgraph. Proceedings of ICML: Proceedings of the22nd international conference on Machinelearning, New York, NY, USA: ACM Press,2005.1036–1043.
    [72] Puzicha J, Hofmann T, Buhmann J M. Non-parametric Similarity Measures for Unsuper-vised Texture Segmentation and Image Retrieval. Proceedings of CVPR: Conference onComputer Vision and Pattern Recognition, Los Alamitos, CA, USA: IEEE Computer Soci-ety,1997.267–272.
    [73] Fei-Fei L, Fergus R, Perona P. Learning generative visual models from few training ex-amples: an incremental Bayesian approach tested on101object categories. Proceedings ofCVPR: IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2004.
    [74] Mao J, Jain A K. Texture classification and segmentation using multiresolution simultaneousautoregressive models. Pattern Recogn.,1992,25(2):173–188.
    [75] Tuytelaars T, Gool L J V. Wide Baseline Stereo Matching based on Local, Afnely InvariantRegions. Proceedings of BMVC,2000.
    [76] Lazebnik S, Schmid S M C, Ponce F J. A Sparse Texture Representation Using Local AfneRegions. IEEE Trans. Pattern Anal. Mach. Intell.,2005,27(8):1265–1278.
    [77] Levy Vehel J, Mignot P, Berroir J P. Multifractals, texture, and image analysis. IEEEComputer Society Conference on Computer Vision and Pattern Recognition,1992..
    [78] Kaplan L. Extended fractal analysis for texture classification and segmentation. IEEE Trans-actions on Image Processing,1999,8(11):1572–1585.
    [79] Xu Y, Ji H, Fermuller C. A Projective Invariant for Textures. Proceedings of CVPR’06: Pro-ceedings of the2006IEEE Computer Society Conference on Computer Vision and PatternRecognition, Washington, DC, USA: IEEE Computer Society,2006.1932–1939.
    [80] Varma M, Garg R. Locally Invariant Fractal Features for Statistical Texture Classification.Proceedings of Proceedings of the IEEE International Conference on Computer Vision, Riode Janeiro, Brazil,2007.
    [81] Khotanzad A, Hong Y H. Invariant Image Recognition by Zernike Moments. IEEE Trans.Pattern Anal. Mach. Intell.,1990,12(5):489–497.
    [82] Yao J, Chin L. Power-adjusted fractional power radial harmonic filters for shift-and scale-invariant pattern recognition with improved noise robustness and discrimination. OpticsCommunications.,1999,162(5):26–30.
    [83] Chetverikov D, Fo¨ldva′ri Z. Afne-Invariant Texture Classification. Proceedings of ICPR,2000.3901–3904.
    [84] Zhang J, Tan T. Afne invariant classification and retrieval of texture images. PatternRecognition,2003,36(3):657–664.
    [85] Ballester C, Gonza′lez M. Afne Invariant Texture Segmentation and Shape from Texture byVariational Methods. J. Math. Imaging Vis.,1998,9(2):141–171.
    [86] Tan T N. Rotation Invariant Texture Features and Their Use in Automatic Script Identifica-tion. IEEE Trans. Pattern Anal. Mach. Intell.,1998,20(7):751–756.
    [87] Radon J. The Radon Transform and Some of its Applications (”Translation of Radon’s1917paper”),1983.
    [88] Hejazi M R, Ho Y S. Texture Analysis Using Modified Discrete Radon Transform. IEICE-Trans. Inf. Syst.,2007, E90-D(2):517–525.
    [89] Cui P, Li J, Pan Q, et al. Rotation and scaling invariant texture classification based on Radontransform and multiscale analysis. Pattern Recogn. Lett.,2006,27(5):408–413.
    [90] Hayman E, Caputo B, Fritz M, et al. On the Significance of Real-World Conditions forMaterial Classification. Proceedings of ECCV,2004.
    [91] Agarwal S, Roth D. Learning a Sparse Representation for Object Detection. Proceedings ofECCV,2002.113–130.
    [92] Al-Yousefi H, Udpa S S. Recognition of Arabic Characters. IEEE Trans. Pattern Anal.Mach. Intell.,1992,14(8):853–857.
    [93] Jain A K. Fundamentals of digital image processing. Upper Saddle River, NJ, USA:Prentice-Hall, Inc.,1989.
    [94] Sanz J L C, Hinkle E B, Jain A K. Radon and projection transform-based computer vi-sion: algorithms, a pipeline architecture, and industrial applications. New York, NY, USA:Springer-Verlag New York, Inc.,1988.
    [95] Al-Shaykh O, Doherty J. Invariant image analysis based on Radon transform and SVD.Circuits and Systems II: Analog and Digital Signal Processing,1996,43(2):123–133.
    [96] Burges C J C. A Tutorial on Support Vector Machines for Pattern Recognition. DMKD,1998..
    [97] Sugiyama M. Local Fisher discriminant analysis for supervised dimensionality reduction.Proceedings of ICML’06: Proceedings of the23rd international conference on Machinelearning, New York, NY, USA: ACM,2006.905–912.
    [98] Balakrishnama G. Linear Discriminant Analysis-A brief Tutorial,1998.
    [99] Tenenbaum J B, Silva V, Langford J C. A global geometric framework for nonlinear dimen-sionality reduction. Science,2000,290:2319–2323.
    [100] Roweis S T, Saul L K. Nonlinear Dimensionality Reduction by Locally Linear Embedding.Science,2000,290:2323–2326.
    [101] Mercer J. Functions of Positive and Negative Type, and their Connection with the Theoryof Integral Equations. Philosophical Transactions of the Royal Society,1909,209:415–446.
    [102] Borst A, Theunissen F E. Information theory and neural coding. Nat Neurosci,1999,2:947–957.
    [103] Hinton G E, Salakhutdinov R R. Reducing the Dimensionality of Data with Neural Net-works. Science,2006,313:504–507.
    [104] Hebb D O. The organization of behavior. NY, USA: Wiley,1949.
    [105] Georghiades A, Belhumeur P, Kriegman D. From Few to Many: Illumination Cone Modelsfor Face Recognition under Variable Lighting and Pose. IEEE Trans. Pattern Anal. Mach.Intelligence,2001,23:643–660.
    [106] Lee K, Ho J, Kriegman D. Acquiring Linear Subspaces for Face Recognition under VariableLighting. IEEE Trans. Pattern Anal. Mach. Intelligence,2005,27(5):684–698.
    [107] Bingham E, Mannila H. Random projection in dimensionality reduction: applications to im-age and text data. Proceedings of Proceedings of the seventh ACM International Conferenceon Knowledge Discovery and Data mining,2001.245–250.
    [108] Grifn G, Holub A, Perona P. Caltech-256Object Category Dataset. Technical Report7694,California Institute of Technology,2007.
    [109] Serre T, Wolf L, Poggio T. Object Recognition with Features Inspired by Visual Cortex.Proceedings of CVPR’05: Proceedings of the2005IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR’05)-Volume2, Washington, DC, USA:IEEE Computer Society,2005.994–1000.
    [110] Berg A C, Berg T L, Malik J. Shape Matching and Object Recognition Using Low DistortionCorrespondences. Proceedings of CVPR’05: Proceedings of the2005IEEE ComputerSociety Conference on Computer Vision and Pattern Recognition (CVPR’05)-Volume1,Washington, DC, USA: IEEE Computer Society,2005.26–33.
    [111] Holub A D, Welling M, Perona P. Combining Generative Models and Fisher Kernels forObject Recognition. Proceedings of ICCV’05: Proceedings of the Tenth IEEE Interna-tional Conference on Computer Vision (ICCV’05) Volume1, Washington, DC, USA: IEEEComputer Society,2005.136–143.
    [112] Zhang H, Berg A C, Maire M, et al. SVM-KNN: Discriminative Nearest Neighbor Clas-sification for Visual Category Recognition. Proceedings of CVPR’06: Proceedings of the2006IEEE Computer Society Conference on Computer Vision and Pattern Recognition,Washington, DC, USA: IEEE Computer Society,2006.2126–2136.
    [113] Gruber A, Weiss Y. Multibody Factorization with Uncertainty and Missing Data Using theEM Algorithm. Proceedings of CVPR,2004.
    [114] Ho J, Yang M H, Lim J, et al. Clustering Appearances of Objects Under Varying IlluminationConditions. Proceedings of CVPR,2003.
    [115] Fischler M A, Bolles R C. Random sample consensus: a paradigm for model fitting withapplications to image analysis and automated cartography. Commun. ACM,1981..
    [116] Zhang T, Szlam A, Lerman G. Median K-flats for hybrid linear modeling with many outliers.CoRR,2009..
    [117] Yang A Y, Rao S R, Ma Y. Robust Statistical Estimation and Segmentation of MultipleSubspaces. Proceedings of CVPR,2006.
    [118] Ma Y, Derksen H, Wei H, et al. Segmentation of Multivariate Mixed Data via Lossy DataCoding and Compression. CVIU,2008..
    [119] Wright J, Tao Y, Lin Z, et al. Classification via Minimum Incremental Coding Length(MICL). Proceedings of NIPS.2008:.
    [120] Costeira a P, Kanade T. A Multibody Factorization Method for Independently Moving Ob-jects. IJCV,1998..
    [121] Ma Y, Yang A Y, Derksen H, et al. Estimation of Subspace Arrangements with Applicationsin Modeling and Segmenting Mixed Data. SIAM,2008..
    [122] Rao S, Yang A, Sastry S, et al. Robust Algebraic Segmentation of Mixed Rigid-Body andPlanar Motions in Two Views. IJCV,2009..
    [123] Elhamifar E, Vidal R. Sparse subspace clustering. Proceedings of CVPR,2009.
    [124] Wright J, Yang A Y, Ganesh A, et al. Robust Face Recognition via Sparse Representation.TPAMI,2008..
    [125] Eldar Y C, Mishali M. Robust Recovery of Signals From a Union of Subspaces. CoRR,2008..
    [126] Shi J, Malik J. Normalized Cuts and Image Segmentation. TPAMI,2000..
    [127] Cande`s E J, Recht B. Exact Matrix Completion via Convex Optimization. Foundations ofComputational Mathematics,2009..
    [128] Keshavan R, Montanari A, Oh S. Matrix Completion from Noisy Entries. Proceedings ofNIPS,2009.
    [129] Candes E J, Li X, Ma Y, et al. Robust Principal Component Analysis?,2009.
    [130] Fazel M. Matrix Rank Minimization with Applications. PhD thesis,2002..
    [131] Candes E J, Plan Y. Matrix Completion With Noise. Proceedings of IEEE Proceeding,2009.
    [132] Lin Z, Chen M, Wu L, et al. The Augmented Lagrange Multiplier Method for Exact Re-covery of Corrupted Low-Rank Matrices. Technical report, UIUC Technical Report UILU-ENG-09-2215,2009.
    [133] Chen S. Multi-output regression using a locally regularised orthogonal least-squares algo-rithm. Vision, Image and Signal Processing, IEE Proceedings-, Aug2002,149(4):185–195.
    [134] Vazquez E, Walter E. Multi Output Support Vector Regression.13th IFAC Symposium onSystem Identification, SYSID2003,2003.1820–1825.
    [135] Kobayashi S, Nomizu K. Foundations of diferential geometry.1963.
    [136] Golub G H, Reinsch C. Singular value decomposition and least squares solutions. Nu-merische Mathematik,1970,14:403–420.
    [137] Smola A J, Scho¨lkopf B. A tutorial on support vector regression. Statistics and Computing,2004,14(3):199–222.
    [138] Tsoumakas G, Katakis I. Multi Label Classification: An Overview. International Journal ofData Warehousing and Mining,2007,3(3):1–13.
    [139] Belkin M, Niyogi P. Laplacian Eigenmaps for Dimensionality Reduction and Data Repre-sentation. Neural Computation,2002,15:1373–1396.
    [140] Donoho D L, Grimes C. Hessian Eigenmaps: Locally Linear Embedding Techniquesfor High-Dimensional Data. Proceedings of the National Academy of Sciences,2003,100(10):5591–5596.
    [141] Agrafiotis D K, Xu H. A Self-Organizing Principle for Learning Nonlinear Manifolds.Proceedings of the National Academy of Sciences,2002,99:15869–15872.
    [142] Kybernetik F B, Smola A, Scholkopf B, et al. Nonlinear Component Analysis as a KernelEigenvalue Problem,1998.
    [143] Hastie T. Principal Curves and Surfaces,1984.
    [144] Ke′gl B, Krzyzak A, Linder T, et al. Learning and Design of Principal Curves. IEEE Trans.Pattern Anal. Mach. Intell.,2000,22(3):281–297.
    [145] Meinicke P, Klanke S, Memisevic R, et al. Principal Surfaces from Unsupervised KernelRegression. IEEE Trans. Pattern Anal. Mach. Intell.,2005,27:1379–1391.
    [146] Chang K Y, Ghosh J. A Unified Model for Probabilistic Principal Surfaces. IEEE Trans.Pattern Anal. Mach. Intell.,2001,23(1):22–41.
    [147] Souvenir R, Pless R. Manifold Clustering. Proceedings of ICCV’05: Proceedings of theTenth IEEE International Conference on Computer Vision (ICCV’05) Volume1, Washing-ton, DC, USA: IEEE Computer Society,2005.648–653.
    [148] Tagliarini G A, Christ J F, Page E W. Optimization Using Neural Networks. IEEE Transac-tions on Computers,1991,40(12):1347–1358.
    [149] Riedmiller M, Braun H. RPROP–Description and Implementation Details. TechnicalReport of Universitat Karlsruhe.,1994..
    [150] Nene S, Nayar S K, Murase H. Columbia Object Image Library (COIL-20).1996. Thedataset is available at http://www1.cs.columbia. edu/CAVE/software/softlib/coil-20.php.
    [151] Horn R, Johnson C. Topics in Matrix Analysis.1991.
    [152] Rockafellar R. Convex analysis. Princeton, NJ, USA: Princeton University Press,1970.

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