Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Scale-Space Properties of the Multiscale Morphological Dilation-Erosion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Gaussian Scale-Space Theory
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
Scale-Spaces, PDE's, and Scale-Invariance
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale Adaptive Filtering Derived from the Laplace Equation
Proceedings of the 23rd DAGM-Symposium on Pattern Recognition
Numerical Geometry of Images: Theory, Algorithms, and Applications
Numerical Geometry of Images: Theory, Algorithms, and Applications
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
Forward-and-backward diffusion processes for adaptive image enhancement and denoising
IEEE Transactions on Image Processing
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
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In this paper we extend the notion of Poisson scale-space. We propose a generalisation inspired by the linear parabolic pseudodifferential operator $\sqrt{-\Delta+m^2}-m$, 0≤m, connected with models of relativistic kinetic energy from quantum mechanics. This leads to a new family of operators $\{Q^m_t\,|\,0\leq m,t\}$ which we call relativistic scale-spaces. They provide us with a continuous transition from the Poisson scale-space {Pt | t≥0} (for m=0) to the identity operator I (for $m \longrightarrow +\infty$). For any fixed t00 the family $\{Q_{t_0}^m~|~ m\geq 0\}$ constitutes a scale-space connecting I and $P_{t_0}$. In contrast to the α-scale-spaces the integral kernels for $Q^m_t$ can be given in explicit form for any m,t≥0 enabling us to make precise statements about smoothness and boundary behaviour of the solutions. Numerical experiments on 1D and 2D data demonstrate the potential of the new scale-space setting.