Scale-Space Filtering

@inproceedings{Witkin1983ScaleSpaceF,
  title={Scale-Space Filtering},
  author={Andrew P. Witkin},
  booktitle={IJCAI},
  year={1983}
}
  • A. Witkin
  • Published in IJCAI 1983
  • Mathematics, Computer Science
The extrema in a signal and its first few derivatives provide a useful general-purpose qualitative description for many kinds of signals. A fundamental problem in computing such descriptions is scale: a derivative must be taken over some neighborhood, but there is seldom a principled basis for choosing its size. Scale-space filtering is a method that describes signals qualitatively, managing the ambiguity of scale in an organized and natural way. The signal is first expanded by convolution with… 
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Two scaling theorems for band-limited signals are proposed and it is shown that they are applicable to a broader class of signals and a bigger family of filtering kernels than in Babaud et al. (1986), Yuille et al (1986) and Wu-Xie (1990).
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It is shown that regularization boils down to Gaussian scale-space if the authors require scale invariance and a semi-group constraint to be satisfied, and implies the minimization of a functional containing terms up to infinite order of differentiation.
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Statistical analysis of scale-space
TLDR
Theorems which give the probabilities of zero-crossings in the output in the presence of noise are proved and theorems are then applied to the case of Gaussian smoothing.
An Extended Class of Scale-Invariant and Recursive Scale Space Filters
TLDR
The authors show that only a discrete subset of filters gives rise to an evolution which can be characterized by means of a partial differential equation.
On the computation of a scale-space primal sketch
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A theory for constructing such an explicit representation on the basis of formal scale-space theory is presented, which gives a description of the image structure that is rather coarse and is useful for studying representations based on intensity discontinuities.
A nonlinear scale-space filter by physical computation
  • Yiu-fai Wong
  • Mathematics
    Neural Networks for Signal Processing III - Proceedings of the 1993 IEEE-SP Workshop
  • 1993
Using the maximum entropy principle and statistical mechanics, the author derives and demonstrates a nonlinear scale-space filter. For each datum in a signal, a neighborhood of weighted data is used…
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