Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Optimal Local Weighted Averaging Methods in Contour Smoothing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Scale-Space Theory from Physical Principles
Journal of Mathematical Imaging and Vision
Feature Detection with Automatic Scale Selection
International Journal of Computer Vision
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
Scale-Spaces, PDE's, and Scale-Invariance
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Affine Invariant Flows in the Beltrami Framework
Journal of Mathematical Imaging and Vision
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
The Monogenic Scale Space on a Rectangular Domain and its Features
International Journal of Computer Vision
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
The monogenic scale space on a bounded domain and its applications
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
α scale spaces on a bounded domain
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Anisotropic α-kernels and associated flows
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
Journal of Mathematical Imaging and Vision
Anisotropic $\alpha$-Kernels and Associated Flows
SIAM Journal on Imaging Sciences
A study of the yosemite sequence used as a test sequence for estimation of optical flow
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Regularity and scale-space properties of fractional high order linear filtering
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
On α kernels, Lévy processes, and natural image statistics
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Uniqueness Results for Image Reconstruction from Features on Curves in α-Scale Spaces
Journal of Mathematical Imaging and Vision
Full length article: Singular integrals, scale-space and wavelet transforms
Journal of Approximation Theory
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In this paper we explore how the functional form of scale space filters is determined by a number of a priori conditions. In particular, if we assume scale space filters to be linear, isotropic convolution filters, then two conditions (viz. recursivity and scale-invariance) suffice to narrow down the collection of possible filters to a family that essentially depends on one parameter which determines the qualitative shape of the filter. Gaussian filters correspond to one particular value of this shape-parameter. For other values the filters exhibit a more complicated pattern of excitatory and inhibitory regions. This might well be relevant to the study of the neurophysiology of biological visual systems, for recent research shows the existence of extensive disinhibitory regions outside the periphery of the classical center-surround receptive field of LGN and retinal ganglion cells (in cats). Such regions cannot be accounted for by models based on the second order derivative of the Gaussian. Finally, we investigate how this work ties in with another axiomatic approach of scale space operators (propounded by Lindeberg and Alvarez et al.) which focuses on the semigroup properties of the operator family. We show that only a discrete subset of filters gives rise to an evolution which can be characterized by means of a partial differential equation.