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prolate

$ \bigcirc$Name


prolate Create a prolate kernel




$ \bigcirc$Command Synopsis


prolate [-n n] s d out



-n n : image size (power of 2, default 256)

s : size of kernel in spatial domain (odd, e.g. 3)

d : relative diameter of kernel in Fourier domain (0 <  d <  =1)

out : resulting kernel (sxs Fimage)




$ \bigcirc$Function Summary


Fimage prolate (s , d , m , out )

int s ;

float d ;

Fimage out ;

int *m ;




$ \bigcirc$Description


This module produces a prolate convolution kernel for optimal image reduction [LP62]. Among all n×n images u such that u(x) = 0 outside a s×s window and $ \int$u2 = 1, the energy $ \int_{{\vert\xi\vert\leq dn/2}}^{}$|$ \hat{u}$($ \xi$)|2 is maximized ($ \hat{u}$ is the Fourier Transform of u), yielding an optimal image $ \bar{u}$. The result is then normalized to produce a unit mass kernel out = $ \bar{u}$/$ \int$$ \bar{u}$.




$ \bigcirc$See Also


fft2d.




$ \bigcirc$Version 1.1


Last Modification date : Thu Nov 29 20:23:56 2001


$ \bigcirc$Author


Lionel Moisan






next up previous contents index
Next: resthline Up: Reference Previous: osamss   Contents   Index
mw 2004-05-05