Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Journal of Mathematical Imaging and Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Gaussian Scale-Space Theory
Pseudo-Linear Scale-Space Theory
International Journal of Computer Vision
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
An Explanation for the Logarithmic Connection between Linear and Morphological System Theory
International Journal of 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
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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Morphological and linear scale spaces are well-established instruments in image analysis. They display interesting analogies which make a deeper insight into their mutual relation desirable. A contribution to the understanding of this relation is presented here. We embed morphological dilation and erosion scale spaces with paraboloid structure functions into families of scale spaces which are found to include linear Gaussian scale space as limit cases. The scale-space families are obtained by deforming the algebraic operations underlying the morphological scale spaces within a family of algebraic operations related to lp norms and generalised means. Alternatively, the deformation of the morphological scale spaces can be described in terms of grey-scale isomorphisms. We discuss aspects of the newly constructed scale space families such as continuity, invariance, and separability, and the limiting procedure leading to linear scale space. This limiting procedure requires a suitable renormalisation of the scaling parameter. In this sense, our approach turns out to be complementary to that proposed by L. Florack et al. in 1999 which comprises a continuous deformation of linear scale space including morphological scale spaces as limit cases provided an appropriate renormalisation.