Context-dependent kernel design for object matching and recognition

The success of kernel methods including support vector networks (SVMs) strongly depends on the design of appropriate kernels. While initially kernels were designed in order to handle fixed-length data, their extension to unordered, variable-length data became more than necessary for real pattern recognition problems such as object recognition and bioinformatics. We focus in this paper on object recognition using a new type of kernel referred to as ldquocontext-dependentrdquo. Objects, seen as constellations of local features (interest points, regions, etc.), are matched by minimizing an energy function mixing (1) a fidelity term which measures the quality of feature matching, (2) a neighborhood criteria which captures the object geometry and (3) a regularization term. We will show that the fixed-point of this energy is a ldquocontext-dependentrdquo kernel (ldquoCDKrdquo) which also satisfies the Mercer condition. Experiments conducted on object recognition show that when plugging our kernel in SVMs, we clearly outperform SVMs with ldquocontext-freerdquo kernels.

[1]  Luc Van Gool,et al.  The 2005 PASCAL Visual Object Classes Challenge , 2005, MLCW.

[2]  David Haussler,et al.  Convolution kernels on discrete structures , 1999 .

[3]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[4]  Cordelia Schmid,et al.  Local Grayvalue Invariants for Image Retrieval , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Claus Bahlmann,et al.  Online handwriting recognition with support vector machines - a kernel approach , 2002, Proceedings Eighth International Workshop on Frontiers in Handwriting Recognition.

[6]  Jianguo Zhang,et al.  The PASCAL Visual Object Classes Challenge , 2006 .

[7]  Siwei Lyu,et al.  Mercer kernels for object recognition with local features , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[8]  Vladimir Vapnik,et al.  An overview of statistical learning theory , 1999, IEEE Trans. Neural Networks.

[9]  Jian-Yun Nie,et al.  Cross-language information retrieval based on parallel texts and automatic mining of parallel texts from the Web , 1999, SIGIR '99.

[10]  Vapnik,et al.  SVMs for Histogram Based Image Classification , 1999 .

[11]  Tony Jebara,et al.  A Kernel Between Sets of Vectors , 2003, ICML.

[12]  Bernhard Schölkopf,et al.  Kernel Methods in Computational Biology , 2005 .

[13]  N. Boujemaa,et al.  The intermediate matching kernel for image local features , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[14]  Barbara Caputo,et al.  Recognition with local features: the kernel recipe , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[15]  Linda G. Shapiro,et al.  A SIFT descriptor with global context , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[16]  Cordelia Schmid,et al.  Semi-Local Affine Parts for Object Recognition , 2004, BMVC.

[17]  Francesca Odone,et al.  Hausdorff Kernel for 3D Object Acquisition and Detection , 2002, ECCV.

[18]  Christopher G. Harris,et al.  A Combined Corner and Edge Detector , 1988, Alvey Vision Conference.

[19]  GärtnerThomas.  A survey of kernels for structured data , 2003 .

[20]  Trevor Darrell,et al.  The Pyramid Match Kernel: Efficient Learning with Sets of Features , 2007, J. Mach. Learn. Res..

[21]  Lior Wolf,et al.  Learning over Sets using Kernel Principal Angles , 2003, J. Mach. Learn. Res..

[22]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[23]  Jitendra Malik,et al.  Shape matching and object recognition using shape contexts , 2010, 2010 3rd International Conference on Computer Science and Information Technology.

[24]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[25]  Thomas Gärtner,et al.  A survey of kernels for structured data , 2003, SKDD.

[26]  Tamir Hazan,et al.  Algebraic Set Kernels with Application to Inference Over Local Image Representations , 2004, NIPS.

[27]  Nuno Vasconcelos,et al.  A Kullback-Leibler Divergence Based Kernel for SVM Classification in Multimedia Applications , 2003, NIPS.

[28]  Nicu Sebe,et al.  Fast spatial pattern discovery integrating boosting with constellations of contextual descriptors , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[29]  Paul A. Viola,et al.  Rapid object detection using a boosted cascade of simple features , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[30]  Patrick Haffner,et al.  Support vector machines for histogram-based image classification , 1999, IEEE Trans. Neural Networks.

[31]  Daniel Marcu,et al.  Statistical Phrase-Based Translation , 2003, NAACL.

[32]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[33]  Michael J. Swain,et al.  Color indexing , 1991, International Journal of Computer Vision.

[34]  David Haussler,et al.  Using the Fisher Kernel Method to Detect Remote Protein Homologies , 1999, ISMB.

[35]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[36]  Marco Cuturi.  Etude de noyaux de semigroupe pour objets structurés dans le cadre de l'apprentissage statistique , 2005 .

[37]  Jitendra Malik,et al.  Shape Context: A New Descriptor for Shape Matching and Object Recognition , 2000, NIPS.

[38]  Hichem Sahbi,et al.  Consensus Network Decoding for Statistical Machine Translation System Combination , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.