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
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Generic Neighborhood Operators
IEEE Transactions on Pattern Analysis and Machine Intelligence
On refinement equations determined by Po´lya frequency sequences
SIAM Journal on Mathematical Analysis
Scale and the differential structure of images
Image and Vision Computing - Special issue: information processing in medical imaging 1991
An introduction to wavelets
A friendly guide to wavelets
Scale-Space Derived From B-Splines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
An Extended Class of Scale-Invariant and Recursive Scale Space Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Journal of Mathematical Imaging and Vision
B-spline scale-space of spline curves and surfaces
Computer-Aided Design
On the asymptotic convergence of B-spline wavelets to Gabor functions
IEEE Transactions on Information Theory - Part 2
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The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderon type inversion formulas, in both integral and semi-discrete forms, are derived for functions in L^p spaces. In the case of the Gaussian scale-space, the semi-discrete inversion formula can further be expressed as a sum of wavelet transforms with the even order derivatives of the Gaussian as mother wavelets. Similar results are obtained for B-spline scale-space, in which the high frequency component of a function between two consecutive dyadic scales can be represented as a finite linear combination of wavelet transforms with the derivatives of the B-spline or the spline framelets of Ron and Shen as mother wavelets.