Scale-Space Theories for Scalar and Vector Images
We define mutually consistent scale-space theories for scalar and vector images. Consistency pertains to the connection between the already established scalar theory and that for a suitably defined scalar field induced by the proposed vector scale-space. We show that one is compelled to reject the Gaussian scale-space paradigm in certain cases when scalar and vector fields are mutually dependent.
Subsequently we investigate the behaviour of critical points of a vector-valued scale-space image—i.e. points at which the vector field vanishes— as well as their singularities and unfoldings in linear scale-space.
KeywordsCritical Path Scalar Image Vector Image Cofactor Matrix Creation Event
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- L.C. Evans. Partial Differential Equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, Rhode Island, 1998.Google Scholar
- L.M.J. Florack. Non-linear scale-spaces isomorphic to the linear case. In B.K. Ersb∅ll and P. Johansen, editors, Proceedings of the 11th Scandinavian Conference on Image Analysis (Kangerlussuaq, Greenland, June 7-11 1999), volume 1, pages 229–234, Lyngby, Denmark, 1999.Google Scholar
- M. Nielsen and O.F. Olsen. The structure of the optic flow field. In H. Burkhardt and B. Neumann, editors, Proceedings of the Fifth European Conference on Computer Vision (Freiburg, Germany, June 1998), volume 1407 of Lecture Notes in Computer Science, pages 281–287. Springer-Verlag, Berlin, 1998.Google Scholar
- M. Spivak. Differential Geometry, volume 1. Publish or Perish, Berkeley, 1975.Google Scholar