Metric-topological approach to shape representation and recognition

Visual shape can be represented by means of certain integer valued functions of two real variables called size functions. This paper presents the theory of size functions in detail and discusses several useful properties of size functions, like stability to small shape changes and invariance to transformations of increasing generality. Then, a scheme for shape recognition based on size functions is described and tested on a study case. It is concluded that size functions can be very useful for shape representation and recognition.

[1]  Stephen M. Pizer,et al.  Hierarchical Shape Description Via the Multiresolution Symmetric Axis Transform , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  A. Peter Blicher,et al.  A Shape Representation Based on Geometric Topology: Bumps, Gaussian Curvature, and the Topological Zodiac , 1987, IJCAI.

[3]  Alessandro Verri,et al.  Studying Shape Through Size Functions , 1994 .

[4]  Patrizio Frosini,et al.  Measuring shapes by size functions , 1992, Other Conferences.

[5]  Olivier D. Faugeras,et al.  HYPER: A New Approach for the Recognition and Positioning of Two-Dimensional Objects , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  P. Frosini,et al.  A distance for similarity classes of submanifolds of a Euclidean space , 1990, Bulletin of the Australian Mathematical Society.

[7]  David G. Lowe,et al.  Three-Dimensional Object Recognition from Single Two-Dimensional Images , 1987, Artif. Intell..

[8]  J. Koenderink,et al.  The structure of two-dimensional scalar fields with applications to vision , 1979, Biological Cybernetics.

[9]  I. H. Öğüş,et al.  NATO ASI Series , 1997 .

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

[11]  Alessandro Verri,et al.  Invariant Size Functions , 1993, Applications of Invariance in Computer Vision.

[12]  D. Huttenlocher.  Three-Dimensional Recognition of Solid Objects from a Two- Dimensional Image , 1988 .

[13]  P. Frosini,et al.  Connections between Size Functions and Critical Points , 1996 .

[14]  Donald D. Hoffman,et al.  Codon constraints on closed 2D shapes , 1986 .

[15]  W. Eric L. Grimson,et al.  Localizing Overlapping Parts by Searching the Interpretation Tree , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Oscar Firschein,et al.  Readings in computer vision: issues, problems, principles, and paradigms , 1987 .

[17]  Shimon Ullman,et al.  An Approach to Object Recognition: Aligning Pictorial Descriptions , 1986 .

[18]  Lee R. Nackman,et al.  Three-Dimensional Shape Description Using the Symmetric Axis Transform I: Theory , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  David A. Forsyth,et al.  Invariant Descriptors for 3D Object Recognition and Pose , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Farzin Mokhtarian,et al.  A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  W. Grimson,et al.  Model-Based Recognition and Localization from Sparse Range or Tactile Data , 1984 .

[22]  Russell H. Taylor,et al.  Automatic Synthesis of Fine-Motion Strategies for Robots , 1984 .

[23]  James L. Crowley,et al.  A Representation for Shape Based on Peaks and Ridges in the Difference of Low-Pass Transform , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  David A. Forsyth,et al.  Extracting projective structure from single perspective views of 3D point sets , 1993, 1993 (4th) International Conference on Computer Vision.

[25]  Alessandro Verri,et al.  On the recognition of the alphabet of the sign language through size functions , 1994, Proceedings of the 12th IAPR International Conference on Pattern Recognition, Vol. 3 - Conference C: Signal Processing (Cat. No.94CH3440-5).