Scale-Space Theories for Scalar and Vector Images

Authors:
Luc Florack
Affiliations:
-
Venue:
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Year:
2001

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Abstract

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.