Scale-space filtering: A new approach to multi-scale description

  title={Scale-space filtering: A new approach to multi-scale description},
  author={Andrew P. Witkin},
  • A. Witkin
  • Published in ICASSP 19 March 1984
  • 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… 

Figures from this paper

Scale space filtering by Fejer kernel
  • J. Y. Shi, H. Tsui
  • Computer Science
    Proceedings of ICSIPNN '94. International Conference on Speech, Image Processing and Neural Networks
  • 1994
A new filtering kernel called Fejer kernel is proposed to try to tackle the problem of multiscale description of raw signal data and compares favorably with Gaussian scale space filtering in that it brings out the main features of the signal under large scales.
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
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
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
  • H. Dehghan
  • Computer Science
    Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136)
  • 1997
This paper presents a fast and adaptive procedure for constructing the zero-crossing contours of a signal, and presents two algorithms for finding the optimum smoothing scales and relating the Zero Crossing of adjacent scales by the developed similarity measure.
A multi-channel-based approach for extracting significant scales on gray-level images
This paper presents the construction of a novel representation of gray-level shape called the scale-spectrum space, which makes both spatial frequency channels of specific importance as well as
An Extended Class of Scale-Invariant and Recursive Scale Space Filters
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.
Multiscale Methods for Image Processing: The Wavelet and the Scale-Space Approaches
  • L. Dorini, N. J. Leite
  • Computer Science
    2009 Tutorials of the XXII Brazilian Symposium on Computer Graphics and Image Processing
  • 2009
A brief survey of two broadly used multiscale formulations, namely, wavelets and scale-space filtering is presented and some possible applications of these approaches in image processing are presented.
A nonlinear scale-space filter by physical computation
  • Yiu-fai Wong
  • Computer Science
    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 that provides a mechanism for removing noise; preserving edges and improved smoothing of nonimpulsive noise.
Morphological scale-space with application to three-dimensional object recognition
The essential scale-space causality property for local extrema of a signal under this operation is proved and it is shown that structuring functions from the "elliptic poweroids" lead to favourable dimensionality and semi-group properties.
Adaptive smoothing: a general tool for early vision
  • Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition
  • 1989


Uniqueness of the Gaussian Kernel for Scale-Space Filtering
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.
A computational theory of human stereo vision
  • D. Marr, T. Poggio
  • Physics
    Proceedings of the Royal Society of London. Series B. Biological Sciences
  • 1979
An algorithm is proposed for solving the stereoscopic matching problem. The algorithm consists of five steps: (1) Each image is filtered at different orientations with bar masks of four sizes that
Edge and Curve Detection for Visual Scene Analysis
Simple sets of parallel operations are described which can be used to detect texture edges, "spots," and "streaks" in digitized pictures and it is shown that a composite output is constructed in which edges between differently textured regions are detected, and isolated objects are also detected, but the objects composing the textures are ignored.
Detecting Natural ``Plateaus'' in One-Dimensional Patterns
A method of detecting natural ``plateaus'' (equals maximal intervals of approximately constant value) in a one-dimensional pattern is described. The method is based on examining neighborhoods of each
Structural Pattern Recognition
  • Michael L. Baird
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 1981
The authors restrict their attention to the finite and push-down automata used to accept or reject input strings and to automata for tree recognition, since these are the models thus far proved to be most useful for syntactic pattern recognition tasks.
Representation of Random Waveforms by Relational Trees
In a number of applications of image processing, much information about objects or textures in the image can be obtained by sequential analysis of individual scan lines.
Kak Digital Picture Processing
  • Kak Digital Picture Processing
  • 1976