Scale-Space for N-Dimensional Discrete Signals
نویسنده
چکیده
This article shows how a (linear) scale-space representation can be de ned for discrete signals of arbitrary dimension. The treatment is based upon the assumptions that (i) the scale-space representation should be de ned 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 di erential equation @tL = AScSpL for some linear and shift invariant operator AScSp 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) di usion equation using di erent discrete approximations of the Laplacean operator. In a special case the multi-dimensional representation is given by convolution with the onedimensional discrete analogue of the Gaussian kernel along each dimension.
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