Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Regularization, Scale-Space, and Edge Detection Filters
Journal of Mathematical Imaging and Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Gaussian Scale-Space Theory
The Perception of Visual Information
The Perception of Visual Information
The Structure of Locally Orderless Images
International Journal of Computer Vision
Pseudo-Linear Scale-Space Theory
International Journal of Computer Vision
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
From High Energy Physics to Low Level Vision
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Generalized Spatio-Chromatic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Families of generalised morphological scale spaces
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
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A basic requirement of scale-space representations in general is that of scale causality, which states that local extrema in the image should not be enhanced when resolution is diminished. We consider a special class of nonlinear scale-spaces consistent with this constraint, which can be linearised by a suitable isomorphism in the grey-scale domain so as to reproduce the familiar Gaussian scale-space. We consider instances in which nonlinear representations may be the preferred choice, as well as instances in which they enter by necessity. We also establish their relation to morphological scale-space representations based on a quadratic structuring function.