Scale-Space for N-dimensional discrete signals
1992 (English)In: Shape inPicture: Mathematical Description of Shape in Grey-Level Images: Proc. of Workshop in Driebergen, Netherlands, Sep. 7--11, 1992, Springer, 1992, 571-590 p.Conference paper (Refereed)
This article shows how a (linear) scale-space representation can be defined for discrete signals of arbitrary dimension. The treatment is based upon the assumptions that (i) the scale-space representation should be defined by convolving the original signal with a one-parameter family of symmetric smoothing kernels possessing a semi-group property, and (ii) local extrema must not be enhanced when the scale parameter is increased continuously.
It is shown that given these requirements the scale-space representation must satisfy the differential equation \partial_t L = A L for some linear and shift invariant operator A satisfying locality, positivity, zero sum, and symmetry conditions. Examples in one, two, and three dimensions illustrate that this corresponds to natural semi-discretizations of the continuous (second-order) diffusion equation using different discrete approximations of the Laplacean operator. In a special case the multi-dimensional representation is given by convolution with the one-dimensional discrete analogue of the Gaussian kernel along each dimension.
Place, publisher, year, edition, pages
Springer, 1992. 571-590 p.
, NATO ASI Series F, 126
scale, scale-space, diffusion, Gaussian smoothing, multi-scale representation, wavelets, image structure, causality
Computer Science Computer Vision and Robotics (Autonomous Systems) Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-58895OAI: oai:DiVA.org:kth-58895DiVA: diva2:474296
Workshop in Driebergen, Netherlands, Sep. 7--11, 1992
QC 201304232012-01-092012-01-092013-04-23Bibliographically approved