TEXTURE REMOVAL IN COLOR IMAGES BY ANISOTROPIC
D
IFFUSION
Baptiste Magnier, Philippe Montesinos and Daniel Diep
Ecole des Mines d’ALES, LGI2P, Site EERIE, Parc Scientifique G. Besse, 30035 Nimes Cedex 1, France
Keywords:
Color image, Texture removal, Smoothing filter, Rotating filter, Vectorial anisotropic diffusion.
Abstract:
In this paper, we present a new method for removing texture in color images using a smoothing rotating filter.
From this filter, a bank of smoothed images provides pixel signals for each channel image able to classify a
pixel belonging to a texture region. We apply this classification in each channel image in order to compute
two directions for the anisotropic diffusion. Then, we introduce a new method for vector anisotropic diffusion
which controls accurately the diffusion near edge and corner points and diffuses isotropically inside textured
regions. Several results applied on real images and a comparison with vector anisotropic diffusion methods
show that our model is able to remove the texture and control the diffusion.
1 INTRODUCTION
Textural analysis has been a domain of active research
for almost forty years (Haralick, 2005) because tex-
ture renders image segmentation difficult (Arbelaez
et al., 2009). The texture is related to the spatial distri-
bution or statistical greyscale or color intensity (Karu
et al., 1996) and contains important information about
the structural arrangement of image surfaces and their
relationships with their direct environment. It is easy
to a human observer to recognize a texture (Julesz,
1981), however it remains difficult to precisely define
and analyze it automatically (Paragios and Deriche,
2002). This difficulty is reflected by the high number
of different definitions of the texture. In this paper, we
do not analyze the texture but simply try to identify it
and diffuse it anisotropically, so that it appears as an
homogenous region.
Edge detection in images with lots of textures mo-
tivated our work. Indeed, with classical edge detec-
tion methods (Deriche, 1993), if the standard devia-
tion σ of the Gaussian curve used is too small, tex-
tures will pollute the final result (see figure 1(b) and
figure 1(c)). On the contrary, a too large standard de-
viation loses precision on edges and especially cor-
ners (illustrated in figure 1(d)).
In image restoration, edge detection is often used
to detect image boundaries in order to control a dif-
fusion process. For example, in (Perona and Ma-
lik, 1990), image derivatives along four directions
are computed providing edge information. On ho-
(a) Original image
(b) σ = 1
(c) σ = 3 (d) σ = 5
F
igure 1: Standard deviation variation with different values
of σ.
mogenous regions, the diffusion is isotropic, on the
contrary, at edge points, diffusion in inhibited and
edges can be enhanced. Control is done with fi-
40
Magnier B., Montesinos P. and Diep D..
TEXTURE REMOVAL IN COLOR IMAGES BY ANISOTROPIC DIFFUSION.
DOI: 10.5220/0003363600400050
In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2011), pages 40-50
ISBN: 978-989-8425-47-8
Copyright
c
 2011 SCITEPRESS (Science and Technology Publications, Lda.)

nite differences so many contours of small objects
or small structures are preserved. In (Alvarez et al.,
1992), diffusion is isotropic on homogenous regions
but decreases and becomes anisotropic near bound-
aries. Gaussian filtering is used for gradient estima-
tion, so the control of the diffusion is more robust
to noise. Nevertheless, it remains difficult to distin-
guish between noise, texture and small objects that
need to be preserved by the diffusionprocess. In color
image restoration, several restoration models exist
(Sapiro and Ringach, 1996) (Blomgren and Chan,
1998) (Tschumperl´e and Deriche, 2001). These mod-
els make use of color gradient norms (Di Zenzo,
1986) in order to control the diffusionat corner points.
The three color channels should not be diffused inde-
pendently in order not to lose the coupled diffusion
(for example in(Blomgren and Chan, 1998)).
In this paper, we present a rotating filter (devel-
opped by (Montesinos and Magnier, 2010)) able to
detect textures in vector images. Then, we introduce
a new method which controls accurately the diffu-
sion near edges and corner points. In particular, our
detector provides two different directions on edges,
thus preserving corners. These informations allow an
anisotropic diffusion in these directions contrary to
(Alvarez et al., 1992) and (Tschumperl´e and Deriche,
2001) where only one direction was considered.
We first present in Section 2 our rotating smooth-
ing filter. A new pixel classification using a bank
of filtered images is introduced in Section 3. Our
anisotropic diffusion scheme is introduced in Section
4, we extend the anisotropic diffusion for color im-
ages in Section 5. We discuss our method in Section
6. Section 7 is devoted to experimental results and
Section 8 concludes this paper.
2 ROTATING FILTER
In our method, for each pixel of the original image,
we use rotating filters in order to build a signal s
which is a function of a rotation angle θ and the un-
derlying signal. Smoothing with rotating filters means
that the image is smoothed with a bank of rotated
anisotropic Gaussian kernels:
G
θ
(x,y) = C.H

P
θ

x
y

e
−

x y

P
−1
θ




1
2 λ
2
1
0
0
1
2λ
2
2




P
θ
x
y
!
where C is a normalization coefficient, P
θ
a rotation
matrix of angle θ, x and y are pixel coordinates and λ
1
and λ
2
the standard-deviations of the Gaussian filter.
As we need only the causal part of the filter (illus-
trated on figure 2(a)), we simply “cut” the smoothing
kernel by the middle, this operation correspondsto the
Heaviside function H. By convolution with these ro-
tated kernels (see figure 2(b)), we obtain a collection
of directional smoothed images I
θ
= I ∗G
θ
.
For computational efficiency, we proceed in a first
step to rotate the image at some discretized orienta-
tions from 0 to 360 degrees (of ∆θ = 1, 2, 5, or 10
degrees, depending on the angular precision needed
and the smoothing parameters) before applying non
rotated smoothing filters with λ
1
and λ
2
the standard-
deviations of the Gaussian filter (illustrated on figure
2(a)). As the image is rotated instead of the filters,
the filtering implementation is quite straightforward
(Deriche, 1993) (Montesinos and Magnier, 2010). In
a second step, we apply an inverse rotation of the
smoothed image and obtain a bank of 360/∆θ images.
Y
X
1
2
_
λ
λ
1
2
(a) Smoothing filter
θ
(b) Rotating filters
Figure 2: A smoothing rotating filter.
3 PIXEL CLASSIFICATION
In the following the image will be represented as a
function defined as:
I(x
1
,x
2
) : IR
2
→ IR
d
The case where d = 1 corresponds to grey level
images, the case d = 3 corresponds to color images.
3.1 Pixel Signals
In this subsection we will consider the case d = 1.
Applying the rotating filter at one point of an image
and making a 360 scan provides to each pixel a char-
acterizing signal. The pixel signal is a single function
s(θ) of the orientation angle θ. Figure 4 is an exam-
ple of s-functions measured at 8 points located on the
image of figure 3. Each plot of figure 4 represents
in polar coordinates the function s(θ) of a particular
point. From these pixel signals, we now extract the
descriptors that will discriminate edges and regions.
In the case of a pixel in a homogeneous region,
s(θ) will be constant (see figure 4 point 2). On the
contrary, in a textured region, s(θ) will be stochastic
TEXTURE REMOVAL IN COLOR IMAGES BY ANISOTROPIC DIFFUSION
41

6
2
8
1
5
4
3
7
Figure 3: Points selection on an original image.
0.25
0.5
90270
180
0
Point 1
0.5
1
90270
180
0
Point 2
0.25
0.5
90270
180
0
Point 3
0.5
1
90270
180
0
Point 4
0.25
0.5
90270
180
0
Point 5
0.1
0.2
90270
180
0
Point 6
0.25
0.5
90270
180
0
Point 7
0.25
0.5
90270
180
0
Point 8
Figure 4: Polar representation of s(θ) for the points selected
in figure 3.
0 30 60 90 120 150 180 210 240 270 300 330 360
0.36
0.37
0.38
0.39
0.4
0.41
0.42
0.43
s(θ)
degrees
Figure 5: Flat cartesian representation of s(θ) at the point 8
which corresponds to a pixels inside texture region.
(as illustrated in figure 5). In the case where the pixel
lies between several different regions, s(θ) will con-
tain several flat areas (see point 1 on figure 3, s(θ) is
illustrated in figure 4 in polar coordinates and in fig-
ure 6 for a cartesian representation).
3.2 Flat Area Detection in Grey Scale
The main idea for analyzing a 360 scan signal is to
detect significant flat areas, which correspond to ho-
0 30 60 90 120 150 180 210 240 270 300 330 360
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
s(θ)
degrees
Figure 6: Original signal s(θ) at the point 1.
0 30 60 90 120 150 180 210 240 270 300 330 360
−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
s
θ
(θ)
η
.
degrees
α
1
Figure 7: First derivative of s(θ).
mogeneous regions of the image. Figure 6 shows the
pixel signal s(θ) extracted from point 1 of figure 3.
This particular point is located at the limit of two re-
gions. After smoothing, the derivative s
θ
(θ) is calcu-
lated and represented on figure 7, and so is the sec-
ond derivative s
θθ
(θ) represented on figure 8. From
the derivative s
θ
(θ) , flat areas are detected as inter-
vals (i.e. angular sectors) with a null derivative, i.e.
sets of values exceeding a given threshold s
th
in am-
plitude. This threshold is represented on figure 7 by
the two horizontal dot lines. Their median direction
noted η corresponds to the gradient direction. Let us
note these intervals α
i
with α
1
the largest angular sec-
tor, α
2
the second largest and so on. From the sec-
ond derivative s
θθ
(θ), we can extract the directions ξ
1
and ξ
2
which delimit the flat area detected. ξ
1
and ξ
2
are calculated as the directions of maximum (or min-
imum) curvature (see figure 8). As illustrated on fig-
ure 9, they are the directions of a smoothed edge curve
crossing the considered pixel (entering and leaving di-
rections). These directions will be used by the simple
anisotropic diffusion scheme that will be presented in
the next section.
The method to remove the texture consists to
diffuse isotropically inside homogenous (point 2)
and textured regions (points 6 and 8) and diffuse
anisotropically on directions ξ
1
and ξ
2
at edge (points
1, 4, 5 and 7) and corner points (point 3). Black points
in figure 10 shows where flat areas have been detected
VISAPP 2011 - International Conference on Computer Vision Theory and Applications
42

0 30 60 90 120 150 180 210 240 270 300 330 360
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
s
θθ
(θ)
.
ξ
ξ
η
1
2
degrees
Figure 8: Second derivative of s(θ).
η
ξ
ξ
1
2
η
texture
ξ
ξ
η
Figure 9: η, ξ
1
and ξ
2
directions.
Figure 10: Flat areas detection.
( λ
1
= 10, λ
2
= 1.5 and a discretization angle of 5 de-
grees) in the figure 3, so this image will be smoothed
anisotropically in black regions of figure 10.
3.3 Flat Areas Classification for
Diffusion in Color Images
In this subsection, we will now consider the case d =
3. We denote I
i
the i
th
component of I (1 6 i 6 d) i.e.:
I(x
1
,x
2
) =


R(x
1
,x
2
) = I
1
(x
1
,x
2
)
G(x
1
,x
2
) = I
2
(x
1
,x
2
)
B(x
1
,x
2
) = I
3
(x
1
,x
2
)


where R, G and B are the image channels (Red,
Green and Blue).
(a) I (b) I
1
(c) I
2
(d) I
3
Figure 11: Original image and its three color channels.
Our aim is to compute ξ
color
1
and ξ
color
2
from each
channel color I
i
in a first step (an example of each
channel is presented in figure 11). In a second step,
we want to smooth each I
i
using our diffusion scheme
presented in section 4.2 with ξ
1
= ξ
color
1
and ξ
2
=
ξ
color
2
.
Firstly, we apply our flat area detection presented
in section 3.2 for each I
i
and we compute the size of
the greatest flat areas, noted α
i
1
for the largest flat area
and α
i
2
for the second largest. Secondly, we attribute
a score υ
i
depending of α
i
1
and α
i
2
. Our classification
rules are presented in table 1.
Pixels located close to edges get a high score,
whereas pixels at a distance from edges receive a low
score. Moreover, obtuse angles α
i
1
get a higher score
than acute angles because acute angles may be em-
bedded in noise or textures.
We present also this classification of the figure 11
(b), (c) and (d) in figure 12 (a), (b) and (c) in grey
scale (0 = black and 5 = white).
Thirdly, from υ
i
are computed ξ
color
1
and ξ
color
2
with the following formula:
(
ξ
color
1
= argmax
ξ
1
1
,ξ
2
1
,ξ
3
1
(υ
1
,υ
2
,υ
3
)
ξ
color
2
= argmax
ξ
1
2
,ξ
2
2
,ξ
3
2
(υ
1
,υ
2
,υ
3
)
(1)
Figure 12 (d) shows in grey scale the result of
υ
color
= max(υ
1
,υ
2
,υ
3
).
TEXTURE REMOVAL IN COLOR IMAGES BY ANISOTROPIC DIFFUSION
43

(a) υ
1
(b) υ
2
(c) υ
3
(d) υ
color
Figure 12: Flat areas detections with υ
i
,{i = 1,2,3}.
Table 1: Flat area α
i,{i=1,2,3}
j,{j=1,2}
classification.
Size of α
i
j
υ
i
type
4
3
π < α
i
1
<
3
2
π 2 obtuse angle
π < α
i
1
<
4
3
π 3 obtuse angle
2
3
π < α
i
1
< π 4 border line
2
3
π < α
i
1
and
2
3
π < α
i
2
5 edge
1
2
π < α
i
1
<
2
3
π 1 corner
other 0 other
4 ANISOTROPIC DIFFUSION
In this section, we consider only a scalar image I.
4.1 Principle of Anisotropic Diffusion
As stated in the introducing section, we want to de-
sign a a smoothing process able to remove texture,
preserve edges and smooth homogeneous regions.
Like many restoration schemes (for example (Alvarez
et al., 1992), (Perona and Malik, 1990) and (Korn-
probst et al., 1997)) which can be interpreted from
a geometrical point of view, we are going to define
a diffusion scheme which will take into account the
pixel classification established in the previous section.
Basically we want to smooth isotropically inside
textured and homogeneous regions whereas we want
to diffuse anisotropically (Weickert, 1998) on and
near boundaries. The first idea could be to use a heat
equation on textured and homogeneous regions and a
Mean Curvature Motion (MCM) (Catt´e et al., 1995)
scheme on edge points, leading to a diffusion scheme
described by equation 2.
∂I
t
∂t
= F(I
0
)∆I
t
+ (1−F(I
0
))
∂
2
I
t
∂ξ
2
(2)
where :
t is the diffusion time,
ξ is the direction of diffusion (contour tangent),
I
0
is the original image,
I
t
is the diffused image at time t,
F(I
0
) represents the control function or gradient.
4.2 Our Diffusion Scheme
Unlike (Alvarez et al., 1992), our classification func-
tion F(I
0
) does not provide us with a precise control
on image boundaries, for the MCM scheme here takes
an important part and moves corner points according
to the curvature of iso-intensity lines. As a conse-
quence, this scheme behaves as the MCM scheme,
for example a square is transformed into a circle after
some iterations. For minimizing this effect we are go-
ing to consider the two directions ξ
1
and ξ
2
provided
by our pixel classification process on image bound-
aries.
The new diffusion process can be now described
by the new following equation:
∂I
t
∂t
= F(I
0
)∆I
t
+ (1−F(I
0
))
∂
2
I
t
∂ξ
1
∂ξ
2
(3)
on which diffusion is driven by the two directions ξ
1
and ξ
2
. We present some results of our diffusion on
scale image in section 7. In the next section, we ex-
tend our diffusion scheme to color images.
5 PDE AND ANISOTROPIC
DIFFUSION IN VECTOR
IMAGES
5.1 Vectorial Geometry and Color
Gradient Norms
In previous works (Sapiro and Ringach, 1996) (Blom-
gren and Chan, 1998) (Tschumperl´e and Deriche,
2001), authors define a vector gradient norm N (I)
VISAPP 2011 - International Conference on Computer Vision Theory and Applications
44

(Di Zenzo, 1986) which is representative of I image
contours. Moreover, they calculate variation direc-
tions η and ξ corresponding to a local vector geom-
etry.
More details are available in the APPENDIX.
5.2 Some Vectorial Diffusion Methods
In the scalar case, the anisotropic diffusion is based
on the local variation of the gradient (see section 4.1).
For a color image, it is necessary to take into account
vectorial information, provided that the three color
channels should not be restored independently. Sev-
eral methods for color image restoration have been
developed. Among these methods, we find the three
following diffusion models.
In (Sapiro and Ringach, 1996), the authors pro-
pose a diffusion for each pixel of the image which is
always done in the direction ξ. Near edges, the dif-
fusion decreases and edges are not smoothed. More-
over, in the homogenous regions, the diffusion is not
isotropic but in the direction of ξ. So this model can-
not remove textures.
In (Blomgren and Chan, 1998), the gradient norm
is different and depends of each channel. So, the dif-
fusion model leads to the problem of decoupled dif-
fusion because it is unidirectional and the smoothing
direction is independent for each channel. Moreover,
in order to make this diffusion scheme stable, the time
step must be very small, and consequently, the num-
ber of iterations must be very high.
5.2.1 Diffusion of Tschumperl
´
e
Tschumperl´e’s vector diffusion (Tschumperl´e and
Deriche, 2001) is the diffusion closest to our scheme.
Indeed, the author presents a diffusion method which
smoothes isotropically in homogenous regions, and
applies a tangent smoothing along the vector edge ξ
elsewhere. The diffusion scheme is the following:
∂I
t
∂t
= g

p
λ
+

I
ηη
+ I
ξξ
(4)
where g is a positive decreasing function such that:
g(s) → 1 when s → 0
g(s) → 0 when s → ∞.
Near edges the diffusion is done mainly in the di-
rection ξ.
This diffusion anisotropic scheme which
smoothes in the ξ direction does not control the
diffusion at corners. We have proposed in section 4.2
a diffusion method which diffuse each image channel
in the two directions ξ
color
1
and ξ
color
2
.
(a) I
1
t
(b) I
2
t
(c) I
3
t
(d) I
t
Figure 13: Diffusion in each I
i
and the total diffusion I
t
after 100 iterations.
5.3 Our Diffusion Scheme in two
Different Directions in Color Images
Unlike diffusion methods presented in the previous
sections, we use neither a norm N (I), nor the multi-
spectral tensor (Di Zenzo, 1986) in our diffusion
scheme for vector images. Instead, we diffuse each
channel images I
i
using our diffusion scheme de-
scribed in section 4.2 with the following equation:
∂I
t
∂t
= F(I
0
)∆I
t
+ (1−F(I
0
))
∂
2
I
t
∂ξ
color
1
∂ξ
color
2
(5)
Finally, from each I
i
t
(see figure 13 (a), (b) and
(c)), we can synthesize the color image I
t
(figure 13
(d)).
6 DISCUSSION OF THE
PROPOSED METHOD
Theoretically, along an edge, if the center is locally
on an isophote line (Kimmel et al., 1997), with our
method, F(I
0
) = 0 and the diffusion scheme is the fol-
lowing:
∂I
t
∂t
=
∂
2
I
t
∂ξ
1
∂ξ
2
. (6)
TEXTURE REMOVAL IN COLOR IMAGES BY ANISOTROPIC DIFFUSION
45

ξ
ξ
2
1
.
.
.
.
. .
.
(a) Diffusion with 3×3
m
ask along edges
ξ
ξ
2
1
smoothing
filter
(b) Our diffusion.
along edges
Figure 14: Diffusion along ξ
1
and ξ
2
.
The grey level is constant along the isophote lines in
the directions ξ
1
and ξ
2
, so we obtain the following
equality:
∂I
t
∂ξ
1
=
∂I
t
∂ξ
2
= 0 (7)
and from this equality results the scheme diffusion:
∂I
t
∂t
= 0. (8)
If we use the diffusion scheme using a 3×3 mask, the
diffusion results in a linear interpolation in the direc-
tions ξ
1
and ξ
2
. In the example of the figure 14(a), we
will smooth pixels containing a dot and the diffusion
equation will be null. But, in our method, we diffuse
the image using our smoothing filter described in sec-
tion 2 in the directions ξ
1
and ξ
2
(see figure 14(b)).
This Gaussian filter smoothes the pixels farther than
one 3 ×3 mask (for example, if λ
1
= 5, the smooth-
ing distance will be approximatively15 pixels), so we
obtain:
∂I
t
∂ξ
1
6= 0 and
∂I
t
∂ξ
2
6= 0. (9)
However, in practice, we are rarely in the presence
of the case of the equation 7. Indeed, it would mean
that we are at a pixel where the isophotes are con-
stant in direction ξ
1
and ξ
2
. In this precise case, we
would be in an region totally noiseless (for example
a synthetic image). Nevertheless, in this situation,
this pixel would not be smoothed but it would not
change our diffusion method since we want to dif-
fuse homogenous regions and textures while preserv-
ing edges.
7 RESULTS
We present results obtained on real images using our
detector and compare them with other methods. The
edge detection method used to show the efficiency of
our diffusion scheme is described in (Deriche, 1993)
(using (Di Zenzo, 1986) for color) with a standard de-
viation of σ.
(a) Original image
(b) Result using (Alvarez et al., 1992) after 100 iterations
(c) Result of our diffusion after 50 iterations
Figure 15: Diffusion on a scalar image.
7.1 Results on Scalar Images
In the first image (figure 15), the aim is to smooth the
different textures present in the image (wall, bushes)
preserving all objects (windows, panel, sidewalk). We
used our detector with λ
1
= 10, λ
2
= 1.5, s
th
= 0.2 and
a discretization angle of 5 degrees. The result of the
anisotropic diffusion is presented in the figure 15(c)
after 50 iterations. Note that different objects are per-
VISAPP 2011 - International Conference on Computer Vision Theory and Applications
46

(a) Edge detection on the original image
(b) Edge detection on our diffused image
Figure 16: Edges detections comparison with σ = 2.
fectly visible whereas textures regions are smoothed
and some of them have been merged. We compare
our result with the method proposed in (Alvarez et al.,
1992) after 100 iterations (illustrated in figure 15(b)).
We can note that texture has not been completely re-
moved on the wall and that bushes boundaries are not
correctly preserved. If we change the K parameter or
the iteration number, we will never obtain the desired
result.
In order to show the efficiency of our method for
texture removal, we compare edge detection on the
original image and on the image obtained after the
diffusion. Figure 16 shows the difference between
an edge detection on the original image (figure 16(a))
and the diffused image (figure 16(b)) with the same
edge detection parameter (σ = 2). The hysteresis
lower threshold LT and the higher threshold HT are
equal respectively to 0.001 and 0.03 in the original
image, 0.001 and 0.02 in the diffused image. Edge
detection on the diffused image is less noisy than on
the original image. Moreover, edges of bushes, panel,
sidewalk and windows appear clearly, whereas edge
detection on the original image fails detecting some
bushes and wall contours.
7.2 Results on Vector Images
We present results on vector images with an identical
threshold s
th
for each channel of the image.
(a) Edge detection
(b) Edges projeted
on figure1(a)
Figure 17: Edge detection of figure 13 with σ = 3.
(a) MCM diffusion (b) Contours of (a)
Figure 18: MCM result.
The first result (figure 13(b)) in vectorial images
is obtained in section 5.3 after 100 iterations with
λ
1
= 10, λ
2
= 1.5, s
th
= 0.4 and a discretization an-
gle of 5 degrees. Superimposing the contours of this
image (figure 17(a)) on the original image in figure
1(a), we can compare the efficiency of our method for
texture removal (illustrated in figure 17(b)). Edge de-
tection threshold are LT = 0.001 and HT = 0.02 in
the diffused image. Our result smooths the stone and
keeps its edges. Bushes and tree leaves are smoothed
but the diffusion keeps the limit between illuminated
and dark leaves. Cars on the left are detected as a
single region. Finally, trees are not diffused in the
sky, our diffusion has kept trees boundaries and figure
17(a) and (b) shows that we diffuse neither the corners
nor edges.
We compare our method with the MCM (Catt´e
et al., 1995) in figure 18(a). Unlike our method, leaves
regions do not become homogenous regions after 100
iterations. This effect is apparent in edge detection
(see 18(b)) where edges are detected in the middle of
trees (LT = 0.001 and HT = 0.02).
TEXTURE REMOVAL IN COLOR IMAGES BY ANISOTROPIC DIFFUSION
47

Compared to edge detection on the original im-
age (see figure 1(b),(c) and (d)), our diffusion allows
to apply an edge detection with a standard deviation
not too large (σ = 2) without deviating from corners
and boundaries and eliminating edges in the middle of
textures (leaves for example). Edge detection thresh-
old for the figure 1 are LT = 0.001 and HT = 0.02
(σ = 1), LT = 0.001 and HT = 0.03 (σ = 3) and LT =
0.001 and HT = 0.02 (σ = 5).
(a) Original image
(b) Our diffusion after 500 iterations
(c) Diffusion on (a) using (Tschumperl´e and Deriche, 2001)
after 100 iterations
Figure 19: Result of trail and plants diffusion.
The objective in figure 19(a) is to detect the trail
while smoothing all other regions. After 500 itera-
tions with λ
1
= 5, λ
2
= 1.5, s
th
= 0.2 and a discretiza-
tion angle of 5 degrees, our method has diffused trees
and grass (see figure 19(b)). We compare our diffu-
sion with the diffusion proposed in (Tschumperl´e and
(a) Edge detection on (a) with σ = 4
(b) Edge detection on (b) with σ = 4
Figure 20: Result of trail and plants diffusion.
(a) Regions detection on the original image
(b) Regions detection on our diffusion in figure 19(b).
Figure 21: Regions detection using (Monga, 1987) after 300
iterations.
Deriche, 2001) in figure 19(c). We have fixed τ = 0.3
and the number of iterations is equal to 100. This
VISAPP 2011 - International Conference on Computer Vision Theory and Applications
48

(a) Original image
(b) Our diffusion
(c) Edge detection on (a) with σ = 2
(d) Edge detection on (b) with σ = 2
Figure 22: Result of color textile patches diffusion.
diffusion scheme is not adapted to our problem of re-
moval texture because the diffusion is too local so we
need to increase the τ parameter then it creates a blur
effect.
Edge detections on the diffused image (figure
19(d)) allows to recognize the trail unlike edges de-
tection on the original image with the same parameter
σ = 4 (illustrated in figure 20(a)). LT = 0.001 and
HT = 0.02 on the original image, LT = 0.001 and
HT = 0.05 on the diffused image (see figure 20(b)).
Region segmentation is also better after our diffusion
(division fusion algorithm (Monga, 1987)). Indeed,
in figure 21 is illustrated the difference of region seg-
mentation after 300 iterations in the original image
and our diffusion result. Let us note that our diffusion
allows to keep trees and grass regions whereas region
segmentation on the original image does not differen-
tiate between these different regions.
In figure 22(a), the aim is to separate the differ-
ent colors of the textile. Our result is illustrated in
figure 22(b) after 50 iterations with λ
1
= 5, λ
2
= 1.5,
s
th
= 0.4 and a discretization angle of 5 degrees. Our
diffusion has smoothed tissue (illustrated in figure
22(b)) preserving boundaries between tissues regions
(see figure 22(d)). LT = 0.001 and HT = 0.08 on the
original image, LT = 0.001 and HT = 0.02 on the dif-
fused image.
An image data base with results is available on-
line (Magnier and Montesinos, 2010).
8 CONCLUSIONS
We have proposed in this paper a new removal texture
method in color images by pixel classification using
a rotating smoothing filter. The comparison of our
results with existing algorithms allows us to validate
our method. Our classification method seems very
promising as we have been able to classify correctly
texture region, homogenous region and edge regions
in many types of images. Edges or regions computed
on our results are not corrupted by noise or texels.
Next on our agenda is to extend and enhance this ap-
proach to color image restoration.
REFERENCES
Alvarez, L., Lions, P.-L., and Morel, J.-M. (1992). Im-
age selective smoothing and edge detection by non-
linear diffusion. SIAM Journal of Numerical Analysis,
29(3):845–866.
Arbelaez, P., Maire, M., Fowlkes, C., and Malik, J. (2009).
From contours to regions: An empirical evaluation.
Computer Society Conference on Computer Vision
and Pattern Recognition, 0:2294–2301.
Blomgren, P. and Chan, T. (1998). Total variation methods
for restoration of vector-valued images. Transactions
on Image Processing, 7(3):304–309.
Catt´e, F., Dibos, F., and Koepfler, G. (1995). A morpholog-
ical scheme for mean curvature motion and applica-
tions to anisotropic diffusion and motion of level sets.
SIAM J. Numer. Anal., 32:1895–1909.
Deriche, R. (1993). Recursively Implementing the Gaussian
and its Derivatives. Technical Report 1993, INRIA.
TEXTURE REMOVAL IN COLOR IMAGES BY ANISOTROPIC DIFFUSION
49

Di Zenzo, S. (1986). A note on the gradient of a multi-
image. Computer Vision, Graphics, and Image Pro-
cessing, 33(1):116–125.
Haralick, R. (2005). Statistical and structural approaches to
texture. Proceedings of the IEEE, 67(5):786–804.
Julesz, B. (1981). Textons, the elements of texture percep-
tion, and their interactions. Nature, 290(5802):91–97.
Karu, K., Jain, A., and Bolle, R. (1996). Is there any texture
in the image? Pattern Recognition, 29(9):1437–1446.
Kimmel, R., Malladi, R., and Sochen, N. (1997). Images
as embedding maps and minimal surfaces: movies,
color, and volumetric medical images. IEEE Com-
puter Society Conference on Computer Vision and
Pattern Recognition, 0:350.
Kornprobst, P., Deriche, R., and Aubert, G. (1997). Nonlin-
ear operators in image restoration. In Proceedings of
the International Conference on Computer Vision and
Pattern Recognition, pages 325–331. IEEE.
Magnier, B. and Montesinos, P. (2010). Tex-
ture removal results. http://www.lgi2p.mines-
ales.fr/∼magnier/Research/Texture
Removal/Demos
Monga, O. (1987). An optimal region growing algorithm
for image segmentation. International Journal on Pat-
tern Recognition and Artificial Intelligence, 1(3):351–
376.
Montesinos, P. and Magnier, B. (2010). A New Perceptual
Edge Detector. In Advanced Concepts for Intelligent
Vision Systems.
Paragios, N. and Deriche, R. (2002). Geodesic active con-
tours for supervised texture segmentation. In IEEE
Computer Society Conference on Computer Vision
and Pattern Recognition, volume 2. IEEE.
Perona, P. and Malik, J. (1990). Scale-space and edge detec-
tion using anisotropic diffusion. In IEEE Transactions
on Pattern Recognition and Machine Intelligence, vol-
ume 12, pages 629–639. IEEE.
Sapiro, G. and Ringach, D. (1996). Anisotropic diffu-
sion of multivalued images with applications to color
filtering. Transactions on Image Processing, IEEE,
5(11):1582–1586.
Tschumperl´e, D. and Deriche, R. (2001). Constrained and
unconstrained PDEs for vector image restoration. In
Proceeding of the Scandinavian Conference on Image
Analysis, pages 153–160.
Weickert, J. (1998). Anisotropic diffusion in image process-
ing. Citeseer.
APPENDIX
In (Di Zenzo, 1986), the author propose a study of the
image based on the geometry of surfaces and looks
for the local variations of kdIk
2
at the point (x
1
,x
2
):
kdIk
2
=

dx
1
dx
2

T

g
11
g
12
g
12
g
22

dx
1
dx
2

(10)
where g
i j
is known as the multi-spectral tensor:
g
i j
=
∂I
∂x
i
·
∂I
∂x
j
. (11)
The two eigenvalues of g
i j
are the extremum of
kdIk
2
and the orthogonal eigenvectors η and ξ are the
corresponding variation directions:





λ
±
=
g
11
+g
22
±
√
(g
11
−g
22
)
2
+4g
12
2
2
η =
1
2
arctan
2g
12
g
11
−g
22
ξ = η+
π
2
Then several gradient norms N (I) have been de-
fined.
In (Sapiro and Ringach, 1996), N (I) =
p
λ
+
−λ
−
, this decreasing function is used to
weight the diffusion PDE. But this norm fails for
corner detection when λ
+
= λ
−
.
In (Blomgren and Chan, 1998), for a global min-
imisation process, N (I) =
p
λ
+
+ λ
−
corresponds to
the square root of the trace of the multi-spectral ten-
sor. This norm can not be compared with others
norms because it does not represent a local variation
in an image.
In (Tschumperl´e and Deriche, 2001), the norm
N (I) =
p
λ
+
corresponds to the value of the maxi-
mum variation. As opposite to the previous norm, this
one does not give more importance to certain corners.
VISAPP 2011 - International Conference on Computer Vision Theory and Applications
50