Journal of Mathematical Imaging and Vision
International Journal of Computer Vision - Joint special issue on image analysis
Global Convergence Rates of Nonlinear Diffusion for Time-Varying Images
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
A Geometric Model for Cortical Magnification
BMVC '00 Proceedings of the First IEEE International Workshop on Biologically Motivated Computer Vision
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
Using Catastrophe Theory to Derive Trees from Images
Journal of Mathematical Imaging and Vision
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
α scale spaces on a bounded domain
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
Detection and localization of random signals
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Morphological bilateral filtering and spatially-variant adaptive structuring functions
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Multiplicative Calculus in Biomedical Image Analysis
Journal of Mathematical Imaging and Vision
Fiber enhancement in diffusion-weighted MRI
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Regularization of positive definite matrix fields based on multiplicative calculus
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Morphological and Linear Scale Spaces for Fiber Enhancement in DW-MRI
Journal of Mathematical Imaging and Vision
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It has been observed that linear, Gaussian scale-space, and nonlinear, morphological erosion and dilationscale-spaces generated by a quadratic structuring functionhave a lot in common. Indeed, far-reaching analogies have been reported,which seems to suggest the existence of an underlying isomorphism. However, an actual mapping appears to be missing.In the present work a one-parameter isomorphism is constructed in closed-form, which encompasses linear and both types of morphological scale-spaces as (non-uniform) limiting cases. The unfolding of the one-parameter family provides ameans to transfer known results from one domain to the other. Moreover, for anyfixed and non-degenerate parameter value one obtains a novel type of“pseudo-linear” multiscale representation that is, in a precise way, “in-between” the familiar ones. This is of interest in its own right, as itenables one to balance pros and cons of linear versus morphological scale-space representations in any particular situation.