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Transitions Involving Views of Geometric Features (FC)

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2165)

Abstract

In Chap. 8 we gave the classification of stable view projections of type (FC). In this chapter we further give the classification of generic transitions of type (FC). We summarize the classification for the five classes of transitions in Theorem 12.1 and in subsequent sections consider the individual cases.

Keywords

  • Normal Form
  • Generic Transition
  • Tangent Plane
  • Abstract Case
  • View Direction

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 12.1
Fig. 12.2
Fig. 12.3
Fig. 12.4
Fig. 12.5
Fig. 12.6
Fig. 12.7
Fig. 12.8
Fig. 12.9
Fig. 12.10
Fig. 12.11
Fig. 12.12
Fig. 12.13
Fig. 12.14
Fig. 12.15
Fig. 12.16
Fig. 12.17
Fig. 12.18
Fig. 12.19

References

  1. Additional material on corners and some other cases, pdf file available at https://www.liv.ac.uk/~pjgiblin/papers/corners2-3.pdf and http://www.math.unc.edu/Faculty/jndamon

  2. J. Damon, P. Giblin, G. Haslinger, Local image features resulting from 3-dimensional geometric features, illumination, and movement: I. Int. J. Comput. Vis. 82, 25–47 (2009)

    CrossRef  MATH  Google Scholar 

  3. F. Tari, Projections of piecewise-smooth surfaces. J. Lond. Math. Soc. (2) 44, 152–172 (1991)

    Google Scholar 

  4. F. Tari, Some applications of singularity theory to the geometry of curves and surfaces. Ph.D. thesis, University of Liverpool, 1990

    Google Scholar 

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© 2016 Springer International Publishing Switzerland

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Damon, J., Giblin, P., Haslinger, G. (2016). Transitions Involving Views of Geometric Features (FC). In: Local Features in Natural Images via Singularity Theory. Lecture Notes in Mathematics, vol 2165. Springer, Cham. https://doi.org/10.1007/978-3-319-41471-3_12

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