Abstract
Surface curvature along extremal boundaries is potentially useful information for navigation, grasping and object identification tasks. Previous theories have shown that qualitative information about curvature can be obtained from a static view. Furthermore it is known that, for orthographic projection, under planar viewer-motion, quantitative curvature information is available from spatio-temporal derivatives of flow. This theory is extended here to arbitrary curvilinear viewer-motion and perspective projection.
We show that curvatures can actually be computed this way in practice, but that they are highly sensitive to errors in viewer-motion estimates. Intuitively, relative or differential measurements of curvature might be far more robust. Rather than measuring the absolute deformation of an apparent contour, differential quantities depend on the rate at which surface features are swept over an extremal boundary as the viewer moves. It is shown that, theoretically, such differential quantities are indeed far less sensitive to uncertainty in viewer-motion. Ratios of differential measurements are less sensitive still. In practice sensitivity is reduced by about two orders of magnitude. We believe this represents a significant step in the development of practical techniques for robust, qualitative 3D vision.
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References
H.G. Barrow and J.M. Tenenbaum. Recovering Intrinsic Scene Characteristics from Images. A.I Center Technical Report 157, SRI International, 1978.
A. Blake and G. Brelstaff. Geometry from specularities. In Proc. 2nd Int. Conf. on Computer Vision, pages 394–403, 1988.
A. Blake and R. Cipolla. Robust Estimation of Surface Curvature from Deformation of Apparent Contours. Technical Report OUEL 1787/89, University of Oxford, 1989.
R.C. Bolles, H.H. Baker, and D.H. Marimont. Epipolar-plane image analysis: an approach to determining structure. International Journal of Computer Vision, vol.1:7–55, 1987.
M. Brady, J. Ponce, A. Yuille, and H. Asada. Describing surfaces. Computer Graphics Image Processing, 32:1–28, 1985.
P. Giblin and R. Weiss. Reconstruction of surfaces from profiles. In Proc. 1st Int. Conf. on Computer Vision, pages 136–144, London, 1987.
C.G. Harris. Determination of ego — motion from matched points. In 3rd Alvey Vision Conference, pages 189–192, 1987.
J.J. Koenderink and A.J. Van Doorn. The shape of smooth objects and the way contours end. Perception, 11:129–137, 1982.
J.J. Koenderink. What does the occluding contour tell us about solid shape? Perception, 13:321–330, 1984.
H.C. Longuet-Higgins and K. Pradzny. The interpretation of a moving retinal image. Proc.R.Soc.Lond., B208:385–397, 1980.
S.J. Maybank. The angular velocity associated with the optical flow field arising from motion through a rigid environment. Proc. Royal Society, London, A401:317–326, 1985.
R.Y. Tsai and T.S. Huang. Uniqueness and estimation of three-dimensional motion parameters of a rigid objects with curved surfaces. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6(1):13–26, 1984.
R.Y. Tsai. A versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses. IEEE Journal of Robotics and Automation, RA-3(4):323–344, 1987.
D. Weinshall. Direct computation of 3D shape and motion invariants. AI Memo 1131, MIT, 1989.
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© 1990 Springer-Verlag Berlin Heidelberg
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Blake, A., Cipolla, R. (1990). Robust estimation of surface curvature from deformation of apparent contours. In: Faugeras, O. (eds) Computer Vision — ECCV 90. ECCV 1990. Lecture Notes in Computer Science, vol 427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014896
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DOI: https://doi.org/10.1007/BFb0014896
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