Projective and illumination invariant representation of disjoint shapes

A projectively invariant representation for groups of planar disjoint contours is proposed as a simultaneous polar reparametrization of multiple curves. Its origin is an invariant point and for each ray orientation, the cross-ratio of the intersections with its closest curves is taken as a value associated to the radius. The sequence of cross-ratio values for all orientations represents a signature. With respect to other methods this representation is less reliant on single curve properties, both for the construction of the projective basis and for calculating the signature. The proposed representation has been originally developed for planar shapes, but an extension is proposed and validated for trihedral corners. Illumination invariant measures are introduced into the representation to increase it discrimination capability. The whole approach is applied to shape-based retrieval from image databases. Experiments are reported on a database of real trademarks.

[1]  Thierry Pun,et al.  Statistical structuring of pictorial databases for content-based image retrieval systems , 1996, Pattern Recognit. Lett..

[2]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[3]  David F. Rogers,et al.  Mathematical elements for computer graphics , 1976 .

[4]  T. Pun,et al.  Recognition of planar objects over complex backgrounds using line invariants and relevance measures , 1995 .

[5]  Fernand S. Cohen,et al.  Part I: Modeling Image Curves Using Invariant 3-D Object Curve Models-A Path to 3-D Recognition and Shape Estimation from Image Contours , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Arnold W. M. Smeulders,et al.  Image Databases and Multi-Media Search , 1998, Image Databases and Multi-Media Search.

[7]  Alex Pentland,et al.  Photobook: tools for content-based manipulation of image databases , 1994, Electronic Imaging.

[8]  Graham D. Finlayson,et al.  Color constancy in diagonal chromaticity space , 1995, Proceedings of IEEE International Conference on Computer Vision.

[9]  Thierry Pun,et al.  Planar Shape Databases with Affine Invariant Search , 1998, Image Databases and Multi-Media Search.

[10]  Sunil Arya,et al.  An optimal algorithm for approximate nearest neighbor searching fixed dimensions , 1998, JACM.

[11]  Thomas H. Reiss,et al.  Recognizing Planar Objects Using Invariant Image Features , 1993, Lecture Notes in Computer Science.

[12]  Richard I. Hartley,et al.  Projective Reconstruction and Invariants from Multiple Images , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Ehud Rivlin,et al.  Local Invariants For Recognition , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Kenichi Kanatani.  Computational cross ratio for computer vision , 1994 .

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

[16]  Sudhir P. Mudur,et al.  Mathematical Elements for Computer Graphics , 1985, Advances in Computer Graphics.

[17]  Patrick Gros,et al.  Geometric interpretation of joint conic invariants , 1992 .

[18]  Toshikazu Kato,et al.  Query by Visual Example - Content based Image Retrieval , 1992, EDBT.

[19]  Andrew Zisserman,et al.  Recognizing general curved objects efficiently , 1992 .

[20]  Dragutin Petkovic,et al.  Query by Image and Video Content: The QBIC System , 1995, Computer.

[21]  Thierry Pun,et al.  Correspondence analysis and hierarchical indexing for content-based image retrieval , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[22]  Emanuele Trucco,et al.  Geometric Invariance in Computer Vision , 1995 .

[23]  Aaron Heller,et al.  An experimental evaluation of projective invariants , 1992 .

[24]  Arnold W. M. Smeulders,et al.  A comparative study of several color models for color image invariant retrieval , 1996 .

[25]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.