Abstract
We assume the presence of mirror symmetry in the viewed scene. In this scene we consider planar point sets and their mirror reflections. We observe the existence of a homology that maps the image of such a planar point set to the image of its mirror reflection. We show how to compute the vertex and the axis of this homology. Finally, the homology is used to reduce image noise by “symmetrization”.
This project was partially supported by a BOF-funds of the University of Antwerp.
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References
Mertens, L., Penne, R., Kubica, M., Senft, D.: Metric 3d reconstruction from monocular vision by way of one plane mirror. Technical Report IWT2005-06, Karel de Grote-Hogeschool (2005)
Ma, Y., Soatto, S., Košecká, J.: An Invitation to 3-D Vision. In: Interdisciplinary Applied Mathematics. Springer, New York (2004)
Mitsumoto, H., Tamura, S., Okazaki, K., Kajimi, N., Fukui, Y.: 3-D reconstruction using mirror images based on a plane symmetry recovering method. IEEE Trans. on Pattern Analysis and Machine Intelligence 14, 941–946 (1992)
Huynh, D.: Affine reconstruction from monocular vision in the presence of a symmetry plane. In: Int. Conf. on Comp. Vision., vol. 1, pp. 476–482 (1999)
Zabrodsky, H., Weinshall, D.: Utilizing symmetry in the reconstruction of 3-dimensional shape from noisy images. In: Eklundh, J.-O. (ed.) ECCV 1994. LNCS, vol. 801, pp. 403–410. Springer, Heidelberg (1994)
Faugeras, O.: Three-Dimensional Computer Vision. A Geometric Viewpoint. MIT Press, Cambridge (1993)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000)
Semple, J., Kneebone, G.: Algebraic Projective Theory. Oxford University Press, Oxford (1952)
Devernay, F., Faugeras, O.: Straight lines have to be straight. Machine Vision and Applications 13, 14–24 (2001)
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© 2005 Springer-Verlag Berlin Heidelberg
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Penne, R. (2005). Mirror Symmetry in Perspective. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2005. Lecture Notes in Computer Science, vol 3708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558484_80
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DOI: https://doi.org/10.1007/11558484_80
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29032-2
Online ISBN: 978-3-540-32046-3
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