Abstract
This paper addresses the problem of reconstructing texture-less objects of quadric like shape. It is known that a quadric can be uniquely recovered from its apparent contours in three views. But, in the case of only two views the reconstruction is a one parameter family of quadrics. Polarization imaging provides additional geometric information compared to simple intensity based imaging. The polarization image encodes the projection of the surface normals onto the image and therefore provides constraints on the surface geometry. In this paper it is proven that two polarization views of a quadric contain sufficient information for a complete determination of its shape. The proof itself is constructive leading to a closed-form solution for the quadric. Additionally, an indirect algorithm is presented which uses both polarization and apparent contours. By experiments it is shown that the presented algorithm produces accurate reconstruction results.
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References
Canterakis, N.: 3d zernike moments and zernike affine invariants for 3d image analysis and recognition. In: Scandinavian Conf. on Image Analysis, SCIA (1999)
Cross, G., Zisserman, A.: Quadric surface reconstruction from dualspace geometry. In: Proc. of Intl. Conf. on Computer Vision (ICCV), pp. 25–34 (1998)
Drbohlav, O., Sara, R.: Unambiguous determination of shape from photometric stereo with unknown light sources. In: Proc. of Intl. Conf. on Computer Vision (ICCV), vol. 1, pp. 581–586 (2001)
Drbohlav, O., Sara, R.: Specularities reduce ambiguity of uncalibrated photometric stereo. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 46–62. Springer, Heidelberg (2002)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000)
Karl, W.C., Verghese, G.C., Willsky, A.S.: Reconstructing ellipsoids from projections. Computer Vision, Graphics and Image Processing 56(2), 124–139 (1994)
Ma, S.D., Li, L.: Ellipsoid reconstruction from three perspective views. In: Proc. of Intl. Conf. on Pattern Recognition (ICPR), pp. 344–348 (1996)
Rahmann, S.: Polarization images: a geometric interpretation for shape analysis. In: Proc. of Intl. Conf. on Pattern Recognition (ICPR), vol. 3, pp. 542–546 (2000)
Rahmann, S., Canterakis, N.: Reconstruction of specular surfaces using polarization imaging. In: Proc. of IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), vol. 1, pp. 149–155 (2001)
Schur, I.: Vorlesungen über Invariantentheorie. Springer, Heidelberg (1968)
Wolff, L.B.: Surface orientation from two camera stereo with polarizers. In: Optics, Illumination, Image Sensing for Machine Vision IV. SPIE Proceedings, vol. 1194, pp. 287–297 (1989)
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Rahmann, S. (2003). Reconstruction of Quadrics from Two Polarization Views. In: Perales, F.J., Campilho, A.J.C., de la Blanca, N.P., Sanfeliu, A. (eds) Pattern Recognition and Image Analysis. IbPRIA 2003. Lecture Notes in Computer Science, vol 2652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44871-6_94
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DOI: https://doi.org/10.1007/978-3-540-44871-6_94
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