A Unified Framework for Detecting Groups and Application to Shape Recognition

A unified a contrario detection method is proposed to solve three classical problems in clustering analysis. The first one is to evaluate the validity of a cluster candidate. The second problem is that meaningful clusters can contain or be contained in other meaningful clusters. A rule is needed to define locally optimal clusters by inclusion. The third problem is the definition of a correct merging rule between meaningful clusters, permitting to decide whether they should stay separate or unite. The motivation of this theory is shape recognition. Matching algorithms usually compute correspondences between more or less local features (called shape elements) between images to be compared. Each pair of matching shape elements leads to a unique transformation (similarity or affine map.) The present theory is used to group these shape elements into shapes by detecting clusters in the transformation space.

[1]  Wolfgang Gaul,et al.  From Data to Knowledge: Theoretical and Practical Aspects of Classification, Data Analysis, and Knowledge Organization , 1996 .

[2]  Josef Kittler,et al.  Pattern recognition : a statistical approach , 1982 .

[3]  Frédéric Sur,et al.  Extracting Meaningful Curves from Images , 2005, Journal of Mathematical Imaging and Vision.

[4]  Refractor.  Vision , 2000, The Lancet.

[5]  Yann Gousseau,et al.  An A Contrario Decision Method for Shape Element Recognition , 2006, International Journal of Computer Vision.

[6]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[7]  Lionel Moisan,et al.  Edge Detection by Helmholtz Principle , 2001, Journal of Mathematical Imaging and Vision.

[8]  J. William Ahwood,et al.  CLASSIFICATION , 1931, Foundations of Familiar Language.

[9]  H. Bock.  On some significance tests in cluster analysis , 1985 .

[10]  M. Wertheimer.  Untersuchungen zur Lehre von der Gestalt. II , 1923 .

[11]  W. Eric L. Grimson,et al.  On the Verification of Hypothesized Matches in Model-Based Recognition , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Haim J. Wolfson,et al.  Geometric hashing: an overview , 1997 .

[13]  Dana H. Ballard,et al.  Generalizing the Hough transform to detect arbitrary shapes , 1981, Pattern Recognit..

[14]  Lionel Moisan,et al.  Meaningful Alignments , 2000, International Journal of Computer Vision.

[15]  RICHARD C. DUBES,et al.  How many clusters are best? - An experiment , 1987, Pattern Recognit..

[16]  A. Yuille,et al.  A Theoretical Framework for Visual Motion , 1996 .

[17]  Wendy R. Fox,et al.  Finding Groups in Data: An Introduction to Cluster Analysis , 1991 .

[18]  A. D. Gordon.  Null Models in Cluster Validation , 1996 .

[19]  Mi-Suen Lee,et al.  A Computational Framework for Segmentation and Grouping , 2000 .

[20]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[21]  Vipin Kumar,et al.  Introduction to Data Mining, (First Edition) , 2005 .

[22]  M. Wertheimer.  Laws of organization in perceptual forms. , 1938 .

[23]  Susan A. Murphy,et al.  Monographs on statistics and applied probability , 1990 .

[24]  M. Wertheimer,et al.  A source book of Gestalt psychology. , 1939 .

[25]  George C. Stockman,et al.  Matching Images to Models for Registration and Object Detection via Clustering , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Yehezkel Lamdan,et al.  Geometric Hashing: A General And Efficient Model-based Recognition Scheme , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[27]  Lionel Moisan,et al.  A Grouping Principle and Four Applications , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Lionel Moisan,et al.  On the Theory of Planar Shape , 2003, Multiscale Model. Simul..

[29]  Josep Lluís Lisani Roca.  Shape based automatic image comparison , 2001 .

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

[31]  Anil K. Jain,et al.  Statistical Pattern Recognition: A Review , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

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

[33]  X. Pennec.  Toward a generic framework for recognition based on uncertain geometric features , 1998 .

[34]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .

[35]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[36]  David G. Lowe,et al.  Perceptual Organization and Visual Recognition , 2012 .

[37]  Pascal Monasse,et al.  Fast computation of a contrast-invariant image representation , 2000, IEEE Trans. Image Process..

[38]  W. Eric L. Grimson,et al.  On the Sensitivity of the Hough Transform for Object Recognition , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[39]  André Hardy,et al.  An examination of procedures for determining the number of clusters in a data set , 1994 .

[40]  K. Joag-dev,et al.  Negative Association of Random Variables with Applications , 1983 .