Unsupervised thresholds for shape matching

Shape recognition systems usually order a fixed number of best matches to each query, but do not address or answer the two following questions: Is a query shape in a given database? How can we be sure that a match is correct? This communication deals with these two key points. A database being given, with each shape S and each distance /spl delta/, we associate its number of false alarms NFA(S, /spl delta/), namely the expectation of the number of shapes at distance /spl delta/ in the database. Assume that NFA(S, /spl delta/) is very small with respect to 1, and that a shape S' is found at distance /spl delta/ from S in the database. This match could not occur just by chance and is therefore a meaningful detection. Its explanation is usually the common origin of both shapes. Experimental evidence will show that NFA(S, /spl delta/) can be predicted accurately.

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

[2]  Lionel Moisan,et al.  Affine plane curve evolution: a fully consistent scheme , 1998, IEEE Trans. Image Process..

[3]  Agnès Desolneux,et al.  Vanishing Point Detection without Any A Priori Information , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

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

[5]  Charles V. Stewart,et al.  MINPRAN: A New Robust Estimator for Computer Vision , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

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

[7]  Jitendra Malik,et al.  Blobworld: A System for Region-Based Image Indexing and Retrieval , 1999, VISUAL.

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

[9]  Clark F. Olson,et al.  Automatic target recognition by matching oriented edge pixels , 1997, IEEE Trans. Image Process..

[10]  Guillermo Sapiro,et al.  Affine invariant scale-space , 1993, International Journal of Computer Vision.

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

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

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