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
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
Using Catastrophe Theory to Derive Trees from Images
Journal of Mathematical Imaging and Vision
Multiscale Methods for Image Processing: The Wavelet and the Scale-Space Approaches
SIBGRAPI-TUTORIALS '09 Proceedings of the 2009 Tutorials of the XXII Brazilian Symposium on Computer Graphics and Image Processing
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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.