Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-space primal sketch: construction and experiments
Image and Vision Computing
Scale and the differential structure of images
Image and Vision Computing - Special issue: information processing in medical imaging 1991
International Journal of Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The Intrinsic Structure of Optic Flow Incorporating Measurement Duality
International Journal of Computer Vision
Greyscale photograph geometry informed by dodging and burning
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
Tensor scale: An analytic approach with efficient computation and applications
Computer Vision and Image Understanding
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A manner in which a notion of effective scale can be introduced in a formal way is developed. For continuous signals, a scaling argument directly gives a natural unit for measuring scale-space lifetime in terms of the logarithm of the ordinary scale parameter. That approach is, however, not appropriate for discrete signals since an infinite lifetime would be assigned to structures existing in the original signal. It is shown how such an effective scale parameter can be defined to give consistent results for both discrete and continuous signals. The treatment is based on the assumption that the probability that a local extremum disappears during a short-scale interval should not vary with scale. As a tool for the analysis, estimates are given of how the density of local extrema can be expected to vary with scale in the scale-space representation of different random noise signals both in the continuous and discrete cases.