Abstract
Recent research has showed that invariant indexing can speed up the recognition process in computer vision. Extraction of invariant features can be done by choosing first a canonical reference frame, and then features in this reference frame. This paper gives methods for extracting invariants for planar curves under affine and projective transformations. The invariants can be used semilocally to recognize occluded objects. For affine transformations, there are methods giving a unique reference frame, with continuity in the Hausdorff metric. This is not possible in the projective case. Continuity can, however, be kept by sacrificing uniqueness.
Keywords
The work has been supported by the Swedish National Board for Technical and Industrial Development (NUTEK). The work is done within the ESPRIT-BRA project VIVA.
Download to read the full chapter text
Chapter PDF
References
Blake, A., Marinos, C.: Shape from Texture: Estimation, Isotropy and Moments. Artificial Intelligence 45 (1990) 332–380
Blake, A., Sinclair, D.: On the projective normalisation of planar shape. Technical Report OUEL Oxford Great Britain (1992)
Brady, M., Yuille, A.: An Extremum Principle for Shape from Contour. PAMI-6 3 (1984) 288–301
Burns J. B., Weiss R. S., Riseman E. M.: The Non-existence of General-case View-Invariants, in Geometrical Invariance in Computer Vision, Mundy, J. L. and Zisserman, A. editors, MIT Press (1992) 120–131
Carlsson S.: Projectively Invariant Decomposition and Recognition of Planar Shapes, Proc. ICCV4, May, Berlin, Germany (1993) 471–475
Duda, R. O. and Hart, P. E.: Pattern Classification and Scene Analysis. Wiley-Interscience (1973)
Van Gool, L., Moons, T., Pauwels, E. and Oosterlinck, A.: Semi-differential Invariants. in Geometrical Invariance in Computer Vision, Mundy, J. L. and Zisserman, A. editors, MIT Press (1992) 157–192
Gårding, J.: Shape from Surface Markings. Ph. D. thesis, Dept. of Numerical Analysis and Computer Science, Royal Institute of Technology, Stockholm, Sweden (1991)
Gros, P., and Quan L.: Projective Invariants for Vision. Technical Report RT 90 IMAG — 15 LIFIA, LIFIA-IRIMAG, Grenoble, France (1992)
Lamdan, Y., Schwartz, J. T., and Wolfson, H. J.: Affine Invariant Model-based Object Recognition. IEEE Journal of Robotics and Automation 6 (1990) 578–589
Mundy, J. L., and Zisserman A. (editors): Geometric invariance in Computer Vision. MIT Press, Cambridge Ma, USA (1990)
Rothwell, C. A., Zisserman, A., Forsyth, D. A. and Mundy J. L.: Canonical Frames for Planar Object Recognition. Proc. ECCV92 Genova Italy (1992) 757–772
Rothwell, C. A.: Hierarchical Object Description Using Invariants. Proc. Second ARPA/NSF-ESPRIT Workshop on Invariance, Ponta Delgada, Azores (1993) 287–302
Weiss, I.: Noise-resistant Invariants of Curves. in Geometrical Invariance in Computer Vision, Mundy, J. L. and Zisserman, A. editors, MIT Press (1992) 135–156
Witkin, A. P.: Recovering Surface Shape and Orientation from Texture. J. of Artificial Intelligence 17 (1981) 17–45
åström, K.: A Correspondence Problem in Laser-Guided Navigation. Proc. Swedish Society for Automated Image Analysis, Uppsala, Sweden (1992) 141–144
åström, K.: Affine Invariants of Planar Sets. Proc. SCIA8, Tromsö, Norway (1993) 769–776
åström, K.: Fundamental Difficulties with Projective Normalization of Planar Curves. Proc. Second ARPA/NSF-ESPRIT Workshop on Invariance, Ponta Delgada, Azores (1993) 377–389
åström, K.: Object Recognition using Affine and Projective Invariants of Planar Sets. CODEN:LUFTD2/TFMA-3002/5002-SE, Lund, Sweden (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
åström, K. (1994). Affine and projective normalization of planar curves and regions. In: Eklundh, JO. (eds) Computer Vision — ECCV '94. ECCV 1994. Lecture Notes in Computer Science, vol 801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028375
Download citation
DOI: https://doi.org/10.1007/BFb0028375
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57957-1
Online ISBN: 978-3-540-48400-4
eBook Packages: Springer Book Archive