cfdiffuse One-step Diffusion of a Color Float Image using Total Variation minimization
cfdiffuse [-t deltat] [-l epsilon] in out
-t deltat : Time for the diffusion (default 10.)
-l epsilon : Lower bound for the RGB norm (default 1.)
in : original image (input cfimage)
out : diffused image (output cfimage)
void cfdiffuse (deltat , epsilon , in , out , MDiag0 , MDiag1 , U0 , Yimage , Vimage , L2h , L2v )
float *deltat , *epsilon ;
Cfimage in , out ;
Fsignal MDiag0 , MDiag1 , U0 ;
Cfimage Yimage , Vimage ;
Fimage L2h , L2v ;
This module applies the Total Variation Minimization algorithm described
below to a color image
in, during the time t given by
The result is a diffused (smoothed) color image put in
keeps the sharpness of the edges.
Such algorithm may be used to restore a noisy image.
To get a sequence of diffused images, see the module
The following is a short description of the used scheme, the Total Variation Minimization via a Relaxation Algorithm. For more information please see [CL97].
Let be the following C1 function:
As goes to zero it may be shown that the minimizer of (5) goes to the minimizer of the following energy:
Now, set for simplicity's sake = 1 and choose a small, fixed (for instance, 1). In the sequel we will denote simply by . Consider the following functional:
Start from any u1 and v1 (for instance v1 1) and let:
We have the following result.
PROPOSITION. The sequence (un) converges (strongly in L2() and weakly in H1()) to the minimizer of (5).
Now, to solve the PDE
Last Modification date : Fri Feb 1 15:36:23 2002
Antonin Chambolle, Jacques Froment