Abstract
Geometric regularities have often been used for grouping. Nonetheless, their foundations have typically been rather ad hoc - with “regular” or “non-accidental” features being listed according to intuition or based on application-specific considerations. This paper describes a more systematic line of thought towards such visual grouping. Based on an earlier observation that fixed structures in images are directly related to object regularities and grouping specific invariants, fixed structures are propounded as a theoretical glue. Moreover, grouping strategies with less than combinatorial complexity are difficult to develop. The propounded approach is also intended to keep grouping complexity under control. To that end, it combines the use of invariants with a Cascaded Hough Transform to efficiently extract candidate fixed structures.
Preview
Unable to display preview. Download preview PDF.
References
S. Carlsson, R. Mohr, T. Moons, L. Morin, C. Rothwell, M. Van Diest, L. Van Gool, F. Veillon, and A. Zisserman, Semi-local projective invariants for the recognition of smooth plane curves, to appear in Int. Journal of Computer Vision
R. Glachet, J. Lapreste, M. Dhome, Locating and modelling a flat symmetric object from a single projective image, Computer Vision, Graphics, and Image Processing: Image Understanding, Vo1.57, pp.219–226, 1993
T. Kanade, Recovery of the 3-dimensional shape of an object from a single view, Artificial Intelligence, Vol.17, pp.75–116, 1981
D. Lowe, Perceptual Organization and Visual Recognition Stanford University technical report STAN-CS-84-1020, 1984
D. Lowe, The Viewpopint Consistency Constraint, International Journal of Computer Vision, pp.57–72, Voll, 1987
D. Lowe, Perceptual organisation and visual recognition, Kluwer Academic Publishers, 1985
J. Mundy and A. Zisserman (eds.), Geometric invariance in computer vision, MIT Press, Cambridge, 1992
J. Ponce, On characterizing ribbons and finding skewed symmetries, Proc. Int. Conf. on Robotics and Automation, pp. 49–54, 1989
C. Rothwell, Recognition using perspective invariance, PhD Thesis, Univ. of Oxford, 1993
C. Rothwell, D. Forsyth, A. Zisserman, and J. Mundy, Extracting projective structure from single perspective views of 3D points sets, Proc. 3rd Int. Conf. Computer Vision, Belin, pp. 573–582, 1993
C. Rothwell and J. Stern, Understanding the shape properties of trihedral polyhedra, Eur. Conf. Computer Vision, pp. 175–185, Cambridge, UK, 1996
J. Semple and G. Kneebone, Algebraic projective geometry, Clarendon, 1979
D. Sinclair, H. Christensen, and C. Rothwell, Using the relation between a plane projectivity and the fundamental matrix, Britsh Machine Vision Conference
C. Springer, Geometry and analysis of projective spaces, Freeman, 1964
T. Tuytelaars, M. Proesmans, and L. Van Gool, The Cascaded Hough Transform as support for grouping and finding vanishing points and lines, published in these proceedings.
L. Van Gool, T. Moons, E. Pauwels, and A. Oosterlinck, Semi-differential invariants, in Applications of invariance in vision, J. Mundy and A. Zisserman (eds.), pp. 157–192, MIT Press, Boston, 1992
L. Van Gool, M. Proesmans, and A. Zisserman, Grouping and invariants using planar homologies, Proc. Europe-China Workshop on Geometrical Modeling and Invariants for Computer Vision, pp. 182–189, 1995
L. Van Gool, T. Moons, D. Ungureanu, and A. Oosterlinck, The characterisation and detection of skewed symmetry, Computer Vision and Image Understanding (previously CVGIP), Vol. 61, No. 1, pp. 138–150, 1995
L. Van Gool, T. Moons, and M. Proesmans, Groups for grouping: a strategy for the exploitation of geometrical constraints, Proc. 6th Int. Conf. on Computer Analysis of Images and Patterns, Prague, pp. 1–8, sept. 1995
L. Van Gool, T. Moons, and M. Proesmans, Mirror and point symmetry under perspective skewing, IEEE Conf. Computer Vision and Pattern Recognition, pp. 285–292, San Francisco, june 1996
M. Wertheimer, Laws of organization in perceptual forms, in A source-book of Gestalt Psychology, ed. D. Ellis, Harcourt, Brace and Co., pp.71–88, 1938
A. Zisserman, J. Mundy, D. Forsyth, and J. Liu, Class-based grouping in perspective images, Proc. Int. Conf. Computer Vision, pp.183–188, 1995
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Van Gool, L. (1997). A systematic approach to geometry-based grouping and non-accidentalness. In: Sommer, G., Koenderink, J.J. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 1997. Lecture Notes in Computer Science, vol 1315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017864
Download citation
DOI: https://doi.org/10.1007/BFb0017864
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63517-8
Online ISBN: 978-3-540-69589-9
eBook Packages: Springer Book Archive