Differential and Integral Geometry of Linear Scale-Spaces

Linear scale-space theory provides a useful framework to quantify the differential and integral geometry of spatio-temporal input images. In this paper that geometry comes about by constructing connections on the basis of the similarity jets of the linear scale-spaces and by deriving related systems of Cartan structure equations. A linear scale-space is generated by convolving an input image with Green’s functions that are consistent with an appropriate Cauchy problem. The similarity jet consists of those geometric objects of the linear scale-space that are invariant under the similarity group. The constructed connection is assumed to be invariant under the group of Euclidean movements as well as under the similarity group. This connection subsequently determines a system of Cartan structure equations specifying a torsion two-form, a curvature two-form and Bianchi identities. The connection and the covariant derivatives of the curvature and torsion tensor then completely describe a p...

• Type: Journal
• Year: 1998
• Where: JMIV
• Authors: Alfons H. Salden, Bart M. ter Haar Romeny, Max A. Viergever
• Keywords: Input Images, JMIV 1998, Linear Scale-space, Similarity Jets