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Pre-symmetry Sets of 3D Shapes

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Deep Structure, Singularities, and Computer Vision (DSSCV 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3753))

Abstract

We show that the pre-symmetry set of a smooth surface in 3-space has the structure of the graph of a function from ℝ2 to ℝ2 in many cases of interest, generalising known results for the pre-symmetry set of a curve in the plane. We explain how this function is obtained, and illustrate with examples both on and off the diagonal. There are other cases where the pre-symmetry set is singular; we mention some of these cases but leave their investigation to another occasion.

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© 2005 Springer-Verlag Berlin Heidelberg

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Diatta, A., Giblin, P. (2005). Pre-symmetry Sets of 3D Shapes. In: Fogh Olsen, O., Florack, L., Kuijper, A. (eds) Deep Structure, Singularities, and Computer Vision. DSSCV 2005. Lecture Notes in Computer Science, vol 3753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11577812_4

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  • DOI: https://doi.org/10.1007/11577812_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29836-6

  • Online ISBN: 978-3-540-32097-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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