Abstract
It is known that the deformation of the apparent contours of a surface under perspective projection and viewer motion enable the recovery of the geometry of the surface, for example by utilising the epipolar parametrization. These methods break down with apparent contours that are singular i.e., with cusps . In this paper we study this situation and show how, nevertheless, the surface geometry (including the Gauss curvature and mean curvature of the surface) can be recovered by following the cusps. Indeed the formulae are much simpler in this case and require lower spatio-temporal derivatives than in the general case of nonsingular apparent contours. We also show that following cusps does not by itself provide us with information on viewer motion.
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Bruce, J. W. and Giblin, P. J. 1992. Curves and Singularities. 2nd edition, Cambridge University Press.
Cipolla, R. and Blake, A. 1992. Surface shape from deformation of apparent contours. Int. J. of Computer Vision, 9(2):83-112.
Cipolla, R., Åström, K. E., and Giblin, P. J. 1995. Motion from the frontier of curved surfaces. Proc. Fifth Int. Conf. on Computer Vision. Cambridge, Mass., pp. 269-275.
Cipolla, R., Fletcher, G. J., and Giblin, P. J. 1995. Surface geometry from cusps of apparent contours. Proc. Fifth Int. Conf. on Computer Vision, Cambridge, Mass., pp. 858-863.
Fletcher, G. J. and Giblin, P. J. 1996. Class based reconstruction of surfaces from singular apparent contours. Proc. Fourth European Conf. on Computer Vision, Cambridge, U. K., April 1996, pp. 107- 116.
Giblin, P. J. and Weiss, R. S. 1987. Reconstruction of surfaces from profiles. First Internat. Conf. on Computer Vision, London, pp. 136-144.
Giblin, P. J. and Soares, M. G. 1988. On the geometry of a surface and its singular profiles. Image and Vision Computing, 6:225-234.
Giblin, P. J., Pollick, F. E., and Rycroft, J. E. 1994. Recovery of an unknown axis of rotation from the profiles of a rotating surface. J. Opt. Soc. America, 11A:1976-1984.
Giblin, P. J. and Weiss, R. S. 1995. Epipolar curves on surfaces. Image and Vision Computing, 13:33-44. Epipolar fields on surfaces.
Koenderink, J. J. 1984. What does the occluding contour tell us about solid shape? Perception, 13:321-330.
Koenderink, J. J. 1990. Solid Shape. M. I. T. Press.
Koenderink, J. J. and Van Doorn, A. J. 1982. The shape of smooth objects and the way contours end. Perception, 11:129-137.
O'Neill, B. 1966. Elementary Differential Geometry. Academic Press.
Vaillant, R. and Faugeras, O. D. 1992. Using extremal boundaries for 3D object modelling. Patt. Recog. and Machine Intell., 14:157-173.
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Cipolla, R., Fletcher, G. & Giblin, P. Following Cusps. International Journal of Computer Vision 23, 115–129 (1997). https://doi.org/10.1023/A:1007920028712
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DOI: https://doi.org/10.1023/A:1007920028712