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This ebook constitutes the refereed court cases of the fifth foreign convention on Scale area and Variational equipment in computing device imaginative and prescient, SSVM 2015, held in Lège-Cap Ferret, France, in may perhaps 2015. The fifty six revised complete papers offered have been rigorously reviewed and chosen from eighty three submissions. The papers are equipped within the following topical sections: scale house and partial differential equation tools; denoising, recovery and reconstruction, segmentation and partitioning; circulation, movement and registration; images, texture and colour processing; form, floor and 3D difficulties; and optimization concept and strategies in imaging.
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Additional info for Scale Space and Variational Methods in Computer Vision: 5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31 - June 4, 2015, Proceedings
In Japanese) 12. : The structure of images. Biological Cybernetics 50, 363–370 (1984) 13. : Scale-Space Theory in Computer Vision. Kluwer, Boston (1994) 14. : Understanding Digital Signal Processing. Prentice Hall, Englewood Cliﬀs (2004) 15. : Morphological systems: Slope transforms and max-min diﬀerence and diﬀerential equations. Signal Processing 38(1), 57–77 (1994) 16. : Convex Analysis. Princeton University Press, Princeton (1970) 17. : The morphological equivalent of the Gauss convolution.
The inverse scale space ﬂow. By following , we obtain 0 if s|(V f )i | < 1, , else. −sign((V f )i ) zIS (s) = (29) such that for t = 1/s we obtain zIS (t) = zV M (t) = zGF (t) and all three deﬁnitions of wavelength and frequency representations coincide. Figure 3 shows an example of the above setup using the discrete cosine transform (DCT) for V . As we can see, the low pass reconstructions are obtained as hard thresholdings of the coeﬃcients, which is what we refer to as an ideal low pass ﬁlter.
For m → 0 sm,t converges to a ﬂat disc of radius t. This is expected from the results from the last section since the relativistic scale-spaces converge to the Poisson scale-space for m → 0 and we identiﬁed the ﬂat disc of radius t as the structuring function corresponding to the morphological Poisson scale-space. Table 2 summarises the results of this section. Table 2. Equations for linear scale-spaces and their morphological equivalents scale-space linear (pseudo-)PDE morphological PDE Gaussian ∂t u = Δu √ ∂t u = − −Δ u ∂t u = |∇u|2 Poisson α α relativistic (a) ∂t u = −(−Δ) u √ ∂t u = − −Δ + m2 − m u α-scale-space (b) ∂t u = |∇u| ∂t u = |∇u|2α ∂t u = |∇u|2 + m2 − m relativistic scale-space (c) comparison of Gaussian and relativistic space-space Fig.