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Laurent Perrinet - Team InViBe
Institut de Neurosciences de la Timone UMR 7289
Aix Marseille Université, CNRS, 13385 cedex 5, Marseille, France
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http://invibe.net/LaurentPerrinet

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Email

<Laurent DOT Perrinet AT univ-amu  DOT fr>

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Institut de Neurosciences de la Timone (UMR 7289)
Aix Marseille Université, CNRS
Faculté de Médecine - Bâtiment Neurosciences
27, Bd Jean Moulin
13385 Marseille Cedex 05
France

Phone

+33.491 324 044

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<Laurent DOT Perrinet AT gmail DOT com>

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+33 6 19 47 81 20

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GoldenPyramid.jpg

Figure 2: The Golden Laplacian Pyramid. To represent the edges of the image at different levels, we may use a simple recursive approach constructing progressively a set of images of decreasing sizes, from a base to the summit of a pyramid. Using simple down-scaling and up-scaling operators we may approximate well a Laplacian operator. This is represented here by stacking images on a Golden Rectangle, that is where the aspect ratio is the golden section $\phi \eqdef \frac{1+\sqrt{5}}{2}$. We present here the base image on the left and the successive levels of the pyramid in a clockwise fashion (for clarity, we stopped at level $8$). Note that here we also use $\phi^2$ (that is $\phi+1$) as the down-scaling factor so that the resolution of the pyramid images correspond across scales. Note at last that coefficient are very kurtotic: most are near zero, the distribution of coefficients has long tails.


"Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius -- and a lot of courage -- to move in the opposite direction" -- Albert Einstein

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