Uniqueness of the Gaussian Kernel for Scale-Space Filtering
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Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
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Linear Scale-Space has First been Proposed in Japan
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An Extended Class of Scale-Invariant and Recursive Scale Space Filters
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Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
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Proceedings of the 23rd DAGM-Symposium on Pattern Recognition
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On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Forward-and-backward diffusion processes for adaptive image enhancement and denoising
IEEE Transactions on Image Processing
On the role of exponential splines in image interpolation
IEEE Transactions on Image Processing
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
Automation of hessian-based tubularity measure response function in 3D biomedical images
Journal of Biomedical Imaging - Special issue on modern mathematics in biomedical imaging
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In this paper we propose a novel type of scales-spaces which is emerging from the family of inhomogeneous pseudodifferential equations $(I - \tau\Delta)^{\frac{t}{2}}u$ with τ ≥ 0 and scale parameter t ≥ 0. Since they are connected to the convolution semi-group of Bessel potentials we call the associated operators {R$^{n}_{t,{ \tau}}$ | 0≤ τ,t} either Bessel scale-space (τ=1), R$^{n}_{t}$ for short, or scaled Bessel scale-space (τ≠1). This is the first concrete example of a family of scale-spaces that is not originating from a PDE of parabolic type and where the Fourier transforms $\mathcal{F}(R^n_{t,\tau})$ do not have exponential form. These properties make them different from other scale-spaces considered so far in the literature in this field. In contrast to the α-scale-spaces the integral kernels for R$^{n}_{t,{\tau}}$ can be given in explicit form for any t, τ ≥ 0 involving the modified Bessel functions of third kind Kν. In theoretical investigations and numerical experiments on 1D and 2D data we compare this new scale-space with the classical Gaussian one.