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 vectorvalued scale-space image—i.e. points at which the vector field vanishes— as well as their singularities and unfoldings in linear scale-space.

• Type: Conference
• Year: 2001
• Where: SCALESPACE
• Authors: Luc Florack
• Keywords: Computer Vision, Consistent Scale-space Theories, Scale-space, SCALESPACE 2001, Vector Scale-space