Anisotropic diffusion is a time-dependent process in image processing useful for denoising and related tasks. Applied at an input image, the latter is gradually simplified in such a way that edges tend to be preserved. Meaningful image structures can then be detected depending on the diffusion time and the spatial scale of a structure. One of the most important points in anisotropic diffusion filtering is introducing a stopping criterion for the time evolution as this defines the quality of output images. In this paper, we follow the approach of a recent method by Ilyevsky and Turkel for determining a useful stopping time. While following the same basic idea, we simplify the underlying algorithm and improve at the same time the quality of filtering results significantly. The superiority of our scheme is validated by several numerical experiments with standard test images in the field.

1.
P.
Perona
,
J.
Malik
,
Scale space and edge detection using anisotropic diffusion
,
IEEE Trans. Pattern Anal. Mach. Intell.
12
(
1990
)
629
639
.
2.
J.
Weickert
,
Applications of nonlinear diffusion in image processing and computer vision
,
Acta Mathematica Universitatis Comenianae
70
(
2001
),
33
50
.
3.
A.
Ilyevsky
,
E.
Turkel
,
Stopping criteria for anisotropic PDEs in image processing
,
J. Sci. Comput.
45
(
2010
)
337
347
.
4.
J.
Weickert
,
Anisotropic Diffusion in Image Processing
,
Teubner
,
Stuttgart
,
1998
.
5.
I.
Capuzzo Dolcetta
,
R.
Ferretti
,
Optimal stopping time formulation of adaptive image filtering
,
Appl. Math. Optim.
43
(
2001
)
245
258
.
6.
G.
Gilboa
,
N.
Sochen
,
Y.Y
Zeevi
,
Estimation of optimal PDE based denoising in the SNR sense
,
IEEE Trans. Image Proc.
15
(
2006
)
2269
2280
.
7.
M.
Khanian
,
A.
Davari
,
Application of Iterative Jacobi Method for an Anisotropic Diffusion in Image Processing
.
Mathematics Scientific Journal
,
8
,
2
(
2013
),
41
48
.
8.
M.
Khanian
,
A.
Feizi
,
A.
Davari
,
An Optimal Partial Differential Equations-based Stopping Criterion for Medical Image Denoising
,
Journal of Medical Signals and Sensors
,
4
,
1
(
2014
),
72
83
.
9.
P.
Mrazek
,
M.
Navara
,
Selection of optimal stopping time for nonlinear diffusion filtering
,
Int. J. Comput. Vision
25
(
2003
)
189
203
.
10.
C.
Tsiotsios
,
M.
Petrou
,
On the choice of the parameters for anisotropic diffusion in image processing
,
Pattern Recognition
46
(
2013
)
1369
1381
.
11.
O.
Scherzer
,
J.
Weickert
,
Relations between regularization and diffusion filtering
,
Journal of Mathematical Imaging and Vision
12
(
2000
),
43
63
.
12.
J.
Sporring
,
J.
Weickert
,
Information measures in scale-spaces
.
IEEE Transactions on Information Theory
45
(
1999
),
1051
1058
.
13.
V.
Solo
,
Automatic stopping criterion for anisotropic diffusion
, In:
Proc. ICASSP’01
,
Salt Lake City, Utah
(
2001
),
3441
3444
.
14.
Z.
Wang
,
A.C.
Bovick
,
H.R.
Sheikh
and
E.P.
Simoncelli
,
Image quality assessment: from error visibility to structural similarity
,
IEEE Transactions on Image Processing
13
(
2004
),
600
612
.
This content is only available via PDF.
You do not currently have access to this content.