Chapter 4: Discrete scalespace theory in higher dimensions
In chapter 4 in ScaleSpace Theory in Computer Vision,
the onedimensional scalespace theory from
chapter 3
is generalized
to discrete signals of arbitrary dimension.
The treatment is based upon the assumptions that

the scalespace representation should be defined
by convolving the original signal with a oneparameter
family of symmetric smoothing kernels possessing a
semigroup property, and

local extrema must not be enhanced
when the scale parameter is increased continuously.
Given these requirements, the scalespace representation
must satisfy a
semidiscretized version of the
diffusion equation.
In a special case the
representation is given by convolution with the
onedimensional discrete analogue of the Gaussian kernel
along each dimension.
Responsible for this page:
Tony Lindeberg