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heat

$ \bigcirc$Name


heat Heat Equation (finite differences scheme with 4 neighbors)




$ \bigcirc$Command Synopsis


heat [-n n] [-s s] in out



-n n : number of iterations (default: 10)

-s s : time step (default: 0.1), can be negative

in : input image

out : output image




$ \bigcirc$Function Summary


Fimage heat (in , n , s )

Fimage in ;

int *n ;

float *s ;




$ \bigcirc$Description


This module implements the heat equation with a finite differences scheme using a 4-neighbors estimation of the Laplacian. The transform u $ \mapsto$ T(u), defined by

T(u)(x, y) = s . $\displaystyle \left(\vphantom{ \frac{}{} u(x+1,y)+u(x-1,y)+u(x,y+1)+u(x,y-1) }\right.$$\displaystyle {\frac{{}}{{}}}$u(x + 1, y) + u(x - 1, y) + u(x, y + 1) + u(x, y - 1)$\displaystyle \left.\vphantom{ \frac{}{} u(x+1,y)+u(x-1,y)+u(x,y+1)+u(x,y-1) }\right)$   +  (1 - 4s)u(x, y),

is iterated n times on the image in, with the convention that u is periodic. Notice that the s parameter can be taken negative for deblurring purposes.




$ \bigcirc$Version 1.1


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


$ \bigcirc$Author


Lionel Moisan






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