Pseudo-Linear Scale-Space Theory
International Journal of Computer 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
Content based image retrieval using multiscale top points a feasibility study
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
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
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
The Monogenic Scale Space on a Rectangular Domain and its Features
International Journal of Computer Vision
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties
Journal of Mathematical Imaging and Vision
Linear Image Reconstruction by Sobolev Norms on the Bounded Domain
International Journal of Computer Vision
Computing the Local Continuity Order of Optical Flow Using Fractional Variational Method
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform
IEEE Transactions on Image Processing
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
Linear image reconstruction by Sobolev norms on the bounded domain
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
Continuity order of local displacement in volumetric image sequence
WBIR'10 Proceedings of the 4th international conference on Biomedical image registration
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Journal of Mathematical Imaging and Vision
Anisotropic $\alpha$-Kernels and Associated Flows
SIAM Journal on Imaging Sciences
A comparison of the deep structure of α-scale spaces
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and 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
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We consider α scale spaces, a parameterized class (α ∈ (0, 1)) of scale space representations beyond the well-established Gaussian scale space, which are generated by the α-th power of the minus Laplace operator on a bounded domain using the Neumann boundary condition. The Neumann boundary condition ensures that there is no grey-value flux through the boundary. Thereby no artificial grey-values from outside the image affect the evolution proces, which is the case for the α scale spaces on an unbounded domain. Moreover, the connection between the α scale spaces which is not trivial in the unbounded domain case, becomes straightforward: The generator of the Gaussian semigroup extends to a compact, self-adjoint operator on the Hilbert space L2(Ω) and therefore it has a complete countable set of eigen functions. Taking the α-th power of the Gaussian generator simply boils down to taking the α-th power of the corresponding eigenvalues. Consequently, all α scale spaces have exactly the same eigen-modes and can be implemented simultaneously as scale dependent Fourier series. The only difference between them is the (relative) contribution of each eigen-mode to the evolution process. By introducing the notion of (non-dimensional) relative scale in each α scale space, we are able to compare the various α scale spaces. The case α = 0.5, where the generator equals the square root of the minus Laplace operator leads to Poisson scale space, which is at least as interesting as Gaussian scale space and can be extended to a (Clifford) analytic scale space.