Optimal feature selection for subspace image matching

Image matching has been a central research topic in computer vision over the last decades. Typical approaches to correspondence involve matching features between images. In this paper, we present a novel problem for establishing correspondences between a sparse set of image features and a previously learned subspace model. We formulate the matching task as an energy minimization, and jointly optimize over all possible feature assignments and parameters of the subspace model. This problem is in general NP-hard. We propose a convex relaxation approximation, and develop two optimization strategies: naive gradient-descent and quadratic programming. Alternatively, we reformulate the optimization criterion as a sparse eigenvalue problem, and solve it using a recently proposed backward greedy algorithm. Experimental results on facial feature detection show that the quadratic programming solution provides better selection mechanism for relevant features.

[1]  Vladimir Kolmogorov,et al.  Feature Correspondence Via Graph Matching: Models and Global Optimization , 2008, ECCV.

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

[3]  Joachim M. Buhmann,et al.  Feature selection for support vector machines , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[4]  Anand Rangarajan,et al.  The Softassign Procrustes Matching Algorithm , 1997, IPMI.

[5]  Marie-Christine Plateau Quadratic convex reformulations for quadratic 0–1 programming , 2008, 4OR.

[6]  Timothy F. Cootes,et al.  Statistical models of appearance for medical image analysis and computer vision , 2001, SPIE Medical Imaging.

[7]  Martial Hebert,et al.  A spectral technique for correspondence problems using pairwise constraints , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[8]  P. Torr Geometric motion segmentation and model selection , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Cordelia Schmid,et al.  A Performance Evaluation of Local Descriptors , 2005, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  R. Fletcher Practical Methods of Optimization , 1988 .

[11]  H. C. Longuet-Higgins,et al.  An algorithm for associating the features of two images , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[12]  Ian T. Jolliffe,et al.  Principal Component Analysis , 2002, International Encyclopedia of Statistical Science.

[13]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Takeo Kanade,et al.  Discriminative cluster analysis , 2006, ICML.

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

[16]  Matthijs C. Dorst Distinctive Image Features from Scale-Invariant Keypoints , 2011 .

[17]  S. Avidan Joint feature-basis subset selection , 2004, CVPR 2004.

[18]  Timothy F. Cootes,et al.  Statistical models of appearance for computer vision , 1999 .

[19]  Qiang Yang,et al.  Feature selection in a kernel space , 2007, ICML '07.

[20]  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.

[21]  J BeslPaul,et al.  A Method for Registration of 3-D Shapes , 1992 .

[22]  B. Moghaddam,et al.  Sparse regression as a sparse eigenvalue problem , 2008, 2008 Information Theory and Applications Workshop.

[23]  Alex Pentland,et al.  Modal Matching for Correspondence and Recognition , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Larry A. Rendell,et al.  The Feature Selection Problem: Traditional Methods and a New Algorithm , 1992, AAAI.