Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Properties of multiscale morphological smoothing by poweroids
Pattern Recognition Letters
Lattice calculus of the morphological slope transform
Signal Processing
Fundamenta Informaticae - Special issue on mathematical morphology
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Extended Class of Scale-Invariant and Recursive Scale Space Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algebraic framework for linear and morphological scale-spaces
Algebraic framework for linear and morphological scale-spaces
Gradient watersheds in morphological scale-space
IEEE Transactions on Image Processing
An Explanation for the Logarithmic Connection between Linear and Morphological System Theory
International Journal of Computer Vision
An explanation for the logarithmic connection between linear and morphological systems
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
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
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In the literature an image scale-space is usually defined as the solution of an initial value problem described by a PDE, such as a linear or nonlinear diffusion equation. Alternatively, scale-spaces can be defined in an axiomatic way starting from a fixed-scale image operator (e.g. a linear convolution or a morphological erosion) and a group of scalings. The goal of this paper is to explain the relation between these two, seemingly very different, approaches.