File:GoldenPyramid.jpg

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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.

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reproducible at https://github.com/bicv/LogGabor/blob/master/LogGabor.ipynb

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current21:53, 5 October 2017Thumbnail for version as of 21:53, 5 October 20175,850 × 3,615 (1.75 MB)LaurentPerrinet (talk | contribs)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-scal...
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