Chapter 4: Discrete scale-space theory in higher dimensions
In chapter 4 in Scale-Space Theory in Computer Vision,
the one-dimensional scale-space theory from
chapter 3
is generalized
to discrete signals of arbitrary dimension.
The treatment is based upon the assumptions that
-
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
-
local extrema must not be enhanced
when the scale parameter is increased continuously.
Given these requirements, the scale-space representation
must satisfy a
semi-discretized version of the
diffusion equation.
In a special case the
representation is given by convolution with the
one-dimensional discrete analogue of the Gaussian kernel
along each dimension.
Responsible for this page:
Tony Lindeberg