Name
cfdiffuse Onestep Diffusion of a Color Float Image using Total Variation minimization
Command Synopsis
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)
Function Summary
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 ;
Description
This module applies the Total Variation Minimization algorithm described
below to a color image in
, during the time t given by
deltat
.
The result is a diffused (smoothed) color image put in out
which
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 cfmdiffuse
.
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 C^{1} function:
and consider the problem where u H^{1}() = W^{1, 2}().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:
where u H^{1}() and v L^{2}(), v 1/.Start from any u^{1} and v^{1} (for instance v^{1} 1) and let:

(8) 
We have the following result.
PROPOSITION. The sequence (u_{n}) converges (strongly in L^{2}() and weakly in H^{1}()) to the minimizer of (5).
Now, to solve the PDE
See Also
Version 1.0
Last Modification date : Fri Feb 1 15:36:23 2002
Author
Antonin Chambolle, Jacques Froment