# Scale-Space Filtering

@inproceedings{Witkin1983ScaleSpaceF, title={Scale-Space Filtering}, author={Andrew P. Witkin}, booktitle={IJCAI}, year={1983} }

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…

## 2,920 Citations

Uniqueness of the Gaussian Kernel for Scale-Space Filtering

- Mathematics, Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 1986

It is shown that the Gaussian probability density function is the only kernel in a broad class for which first-order maxima and minima, respectively, increase and decrease when the bandwidth of the filter is increased.

Scaling Theorems for Zero Crossings of Bandlimited Signals

- Mathematics, Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1996

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).

Zero-crossing contour construction for scale-space filtering

- MathematicsConference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136)
- 1997

The description of a signal or an image is only meaningful over a limited range of resolutions. The interest in and perception of different features of a signal depends not only on the signal, but on…

Regularization, Scale-Space, and Edge Detection Filters

- Mathematics, Computer ScienceECCV
- 1996

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.

Logical Filtering in Scale

- 2002

Using a Gaussian scale space, one can use the extra dimension, viz. scale, for investigation of “built-in” properties of the image in scale space. We show that one of such induced properties is the…

Understanding image structure from a new multi-scale representation of higher order derivative filters

- Mathematics, Computer ScienceImage Vis. Comput.
- 2007

A biologically inspired multi-scale derivative filter in which the higher order derivatives are expressed as a linear combination of a smoothing function at various scales is proposed, which is very effective in extracting the features from a noisy picture.

Statistical analysis of scale-space

- Mathematics, Computer ScienceSignal Process.
- 1992

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

- Mathematics, Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1995

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

- Computer ScienceJ. Vis. Commun. Image Represent.
- 1991

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

- MathematicsNeural 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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