Abstract
This paper presents a new geometric relation between a solid bounded by a smooth surface and its silhouette in images formed under weak perspective projection. The relation has the potential to be used for recognizing complex 3-D objects from a single image. Objects are modeled by showing them to a camera without any knowledge of their motion. The main idea is to consider the dual of the 3-D surface and the family of dual curves of the silhouettes over all viewing directions. Occluding contours correspond to planar slices of the dual surface. We introduce an affine-invariant representation of this surface that can constructed from a sequence of images and allows an object to be recognized from arbitrary viewing directions. We illustrate the proposed object representation scheme through synthetic examples and image contours detected in real images.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
E. Arbogast and R. Mohr. 3D structure inference from image sequences. Journal of Pattern Recognition and Artificial Intelligence, 5(5), 1991.
E. Boyer and M. Berger. 3d surface reconstruction using occluding contours. Int. J. Computer Vision, 22(3):219–233, 1997.
J. Bruce and P. Giblin. Curves and Singularities. Cambridge University Press, 1992.
R. Cipolla, K. Aström, and P. Giblin. Motion from the frontier of curved surfaces. In Int. Conf. on Computer Vision, pages 269–275, 1995.
R. Cipolla and A. Blake. Surface shape from the deformation of the apparent contour. Int. J. Computer Vision, 9(2):83–112, November 1992.
M. do Carmo. Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, N.J., 1976.
P. Giblin and R. Weiss. Epipolar curves on surfaces. Image and Vision Computing, 13(1):33–44, 1995.
R. Glachet, M. Dhome, and J. Lapersté. Finding the perspective projection of an axis of revolution. Pattern Recognition Letters, 12:693–700, 1991.
D. Huttenlocher and S. Ullman. Recognizing solid objects by alignment with an image. IJCV, 5(2):195–212, November 1990.
T. Joshi, B. Vijayakumar, D. Kriegman, and J. Ponce. HOT curves for modelling and recognition of smooth curved 3D shapes. Image and Vision Computing, pages 479–498, July 1997.
J. J. Koenderink. What does the occluding contour tell us about solid shape? Perception, 13, 1984.
D. Kriegman and J. Ponce. On recognizing and positioning curved 3D objects from image contours. IEEE Trans. Pattern Anal. Mach. Intelligence, 12(12):1127–1137, 1990.
D. J. Kriegman and J. Ponce. Computing exact aspect graphs of curved objects: Solids of revolution. Int. J. Computer Vision, 5(2):119–135, 1990.
J. Liu, J. Mundy, D. Forsyth, A. Zisserman, and C. Rothwell. Efficient recognition of rotationally symmetric surfaces and straight homogeneous generalized cylinders. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 123–128, 1993.
D. G. Lowe. The viewpoint consistency constraint. Int. J. Computer Vision, 1(1):57–72, 1987.
A. Mackworth and F. Mokhtarian. The renormalized curvature scale space and the evolution properties of planar curves. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 318–326, 1988.
H. Murase and S. Nayar. Visual learning and recognition of 3-D objects from appearence. Int. J. Computer Vision, 14(1):5–24, 1995.
S. Petitjean, J. Ponce, and D. Kriegman. Computing exact aspect graphs of curved objects: Algebraic surfaces. Int. J. Computer Vision, 9(3):231–255, 1992.
J. Ponce and D. Chelberg. Finding the limbs and cusps of generalized cylinders. Int. J. Computer Vision, 1(3), October 1987.
J. Ponce, A. Hoogs, and D. Kriegman. On using CAD models to compute the pose of curved 3D objects. CVGIP: Image Understanding, 55(2):184–197, Mar. 1992.
M. Richetin, M. Dhome, J. Lapresté, and G. Rives. Inverse perspective transform from zero-curvature curve points: Application to the localization of some generalized cylinders from a single view. IEEE Trans. Pattern Anal. Mach. Intelligence, 13(2):185–191, February 1991.
J. Rieger. Global bifurcations sets and stable projections of non-singular algebraic surfaces. Int. J. Computer Vision, 7(3):171–194, 1992.
R. Vaillant and O. Faugeras. Using extremal boundaries for 3D object modeling. IEEE Trans. Pattern Anal. Mach. Intelligence, 14(2):157–173, February 1992.
B. Vijayakumar, D. Kriegman, and J. Ponce. Invariant-based recognition of complex curved 3-D objects from image contours. Computer Vision and Image Understanding, pages 287–303, Dec. 1998.
M. Zeroug and G. Medioni. The challenge of generic object recognition. In M. Hebert, J. Ponce, T. Boult, and A. Gross, editors, Object Representation for Computer Vision, pages 271–232. Springer-Verlag, 1995.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Renaudie, D., Kriegman, D., Ponce, J. (2000). Duals, Invariants, and the Recognition of Smooth Objects from Their Occluding Contour. In: Computer Vision - ECCV 2000. ECCV 2000. Lecture Notes in Computer Science, vol 1842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45054-8_51
Download citation
DOI: https://doi.org/10.1007/3-540-45054-8_51
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67685-0
Online ISBN: 978-3-540-45054-2
eBook Packages: Springer Book Archive