2. These numbers give a significant indication about the future needs for asphalt pavement materials such as aggregates. In
the same time, conformal to the green highways initiative is a mandatory objective 16
. One of the main solutions is the
use of recycled pavement materials in asphalt concrete mixture. Hence, a proper way for quality control, verification,
classification, and grading of asphalt concrete mixture becomes of an important task.
In this work, we propose a grading and a classification system to analyze and grade asphalt concrete components by
using texture classification algorithms. This paper is organized as follows: a description of proposed grading standard for
asphalt concrete mixtures based on their textural properties is illustrated in section 2. Also, a brief background on
wavelet transform and our previous work in RGB analysis is given in section 3. In Section 4, the proposed algorithm is
discussed. Section 5 discusses simulation results along with different simulation examples. Finally, a conclusion is
presented in Section 6.
2. GRADING OF ASPHALT CONCRETE TEXTURE PATTERNS
Manual grading of asphalt concrete mixtures is based on human visual perception. This approach is very subjective and
subject to intra and inter-observer variations. Also, it is a time consuming task and raises difficulties as far as spatial
resolution is considered especially in the subgroups of homogenous and semi-homogenous classes. To overcome these
issues, automatic classification of asphalt concrete classes is needed especially with the existence of advanced computing
power and effective image processing algorithms.
In this paper, we combine features from wavelet transform to provide a new features extraction approach in the
automatic classification of 150 images that belong to five textural grades of asphalt concrete images (figure 1). Up to our
knowledge, there is no existing standard grading system for asphalt concrete mixture. Hence, we propose these major
five grades based to represent the highly dominant textures in asphalt concrete mixtures based on our observations. Also,
there may exist other sub-grades that may fall in between any two major grades.
These grades are chosen based on their textural complexity of asphalt concrete components as follows:
Grade 1: this grade is illustrated in the previous figure of the AC image on the left side of the figure. It has the most
homogenous texture compared to other grades. Mastics are the dominant components of the AC mixture. The second
predominant components are represented by the aggregates which are hard to distinguish visually. Air voids represent
the least AC components in this grade.
Grade 2: this grade (second from the left) has a less homogenous, or a semi-homogenous AC mixture compared to the
previous grade. Air gaps patterns are spread more than the previous grade. Also, the presence of aggregates is more
dominant than the previous grade.
Figure 1 The proposed five grades of asphalt concrete texture images (Grade 1-Grade 5 from left to right)
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3. Grade 3: T
Aggregates r
larger textura
Grade 4: gra
become harde
Grade 5: the
start to take p
in this grade o
3.1 Wav
Wavelet Tran
( )
,
x
m n
ψ us
For the const
two-scale diff
( ) 2
x
k
φ = ∑
For wavelet d
be given as:
1,
j n
c + = ∑
For 2-D wave
and high pass
signal up to tw
Horizontal, V
This pattern (m
epresent the d
al space as the
ade4 texture (
er to be visual
main feature
place compare
of AC images
velet Transfo
nsform: In w
ing translation
truction of the
fference equati
( ) (2 )
h k x k
φ −
decomposition
, ( 2
j k
k
c h k −
∑
elet transform
s filters, h and
wo levels of d
Vertical, and D
middle image
dominant com
mastics.
( fourth from
lly observed. A
of this grade (
ed to previous
s.
orm
wavelet transf
n and dilation
, ( )
m n x
ψ =
e mother func
ion expressed
) (2) ; ψ
n to a Jth-leve
1,
) ; j n
n d +
m, the basis fu
d g, respective
decomposition
Diagonal subm
F
e) is more of
mponents of th
m left) has al
Also, more he
(last from left
s patterns. Sm
3.
form, the sig
n of the mother
/ 2
2 (2
m m
ψ
− −
=
ction ( )
x
ψ , the
as:
( ) 2
k
x
ψ = ∑
el, the relation
, (
j k
k
c g k
= ∑
unctions opera
ly. The follow
ns. The coeffic
matrices in the
Figure 2 1-D w
f a heterogen
he AC mixtur
lmost equal p
eterogeneity is
t) is the domin
mall aggregate
BACKGR
nal is transfo
r wavelet (x
ψ
)
x n
− (1)
e determinatio
( ) (2
k
g k x
φ
∑
n of the decom
2 )
n
− (5-
ate along the h
wing figure ill
cients at the H
e 2D transform
wavelet decompo
eous mixture
re. Also, air v
portions of ag
s observed due
nance of the a
s and air void
ROUND
ormed into a
)
x as follows:
for integers
on of a scalin
)
k
− (3)
mposed coeffi
-6) where 0
horizontal and
lustrates the w
HH, HG, GH, a
m space.
osition filter ban
compared to
voids are easi
ggregates, mas
e to the smalle
ir voids. Larg
ds reserve alm
a family of o
s m and n
ng function (
φ
where ( )
g k
icients to direc
0 j J
≤ ≤
d vertical dire
wavelet decom
and GG corre
nk
o the previou
ily observed r
stics and air
er aggregates
ger gaps betwe
most the same
orthogonal ba
( )
x is needed
) ( 1) (1
k
h k
= − −
ct previous co
ctions as a pa
mposition filter
spond to the A
us two grades
representing a
gaps. Mastics
size.
een aggregates
textural space
ases functions
d to satisfy the
) (4)
k
oefficients can
air of low pass
r bank for 1-D
Approximated
s.
a
s
s
e
s
e
n
s
D
d,
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4. 3.2 Previous work in RGB morphological filtering
Color textural images need to be pre- processed in order to investigate the contribution of color components in textural
patterns. This step is mandatory to be incorporated into texture analysis and classification. Color distribution over a
textural space can be described by the relationship between chromatic and structural distribution 13
. Achromatic color
component is used for textural pattern information. However, luminance (Y), and chrominance ( U and V) components
are utilized for extracting color information 13,14,15
. Considering HIS color model, the pure color is described by the hue
(H) component, while the degree of the color dilution by white light is described by the saturation (S) component13
. In
RGB model, RGB color model consists of three independent color planes representing the three chromaticities
components: Red, Green, and Blue. In order to specify a pixel RGB value, each color component is specified
independently within the range 0 to 255. 7
In 7
, we presented an algorithm that focuses on extracting edge details that cannot be highlighted for detection using the
standard assigned HVS vector weight for RGB colors. Given a tri-chromatic RGB image, one might consider designing a
rational morphological filter that takes into consideration the assigned HVS weight for each component in tri-chromatic
space. Let Fn and Fm denote two different as follows:
1 2 1 3
2 1 2 3
2 1 2 3
: (0.2989R,0.5870G,0.1140B) ; (7)
: ( log (0.2989 ), log (0.5870 ), log (0.1140 ));
( log ( ), log ( ));
( log ( ), log ( ));
( log ( ), log ( )) (8)
Fn
R G B
Fm R R G G B B
R R
R w R w G R w R w B
G G
G w G w R G w G w B
B B
B w B w R B w B w G
α α α
β β β
α α
β β
α α
β β
α α
β β
− −
− −
− −
where β and α are constants assigned to each color channel, 1 2 3
, ,
w w w represent different assigned weight for R,G,B
color components respectively. The ratio of different morphological operations may take any of the following forms:
max( )
1
max( )
Fn
Fm
β
⎛ ⎞
⎜ ⎟
⎝ ⎠
;
min( )
2
max( )
Fn
Fm
β
⎛ ⎞
⎜ ⎟
⎝ ⎠
;
min( )
3
min( )
Fn
Fm
β
⎛ ⎞
⎜ ⎟
⎝ ⎠
;
max( )
4
min( )
Fn
Fm
β
⎛ ⎞
⎜ ⎟
⎝ ⎠
(9) ; where β is a normalization constant
The above expressions yield successful results in investigating the intensity of each RGB component at each pixel taking
into consideration the HVS perception characteristics. This algorithm is used as a preprocessing step for colored textural
images prior to features extraction and classification.
4. ALGORITHM
4.1 Haar wavelet energy feature
In our work, we consider Haar wavelet decomposition for feature vectors generation in wavelet domain. The Haar
wavelet transform is an orthogonal transform that provides a transform domain where differential energy is concentrated
in localized areas. Haar transform is considered to be one of the simplest and the fastest wavelet transform especially
when considering the fast-Haar transform 8
. The Haar transform basis function can be expressed as follows:
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5. (11)
Considering features extraction from wavelet domain, the major extracted features in wavelet analysis are wavelet
energy and entropy due to their popularity in features extraction and classification applications 9
. In this paper, we use
the wavelet energy feature “F1”, that can be expressed as follows:
2
ij
i j
x
energy
nxn
=
∑∑
(12)
4.2 Phase measure of wavelet coefficients
Wavelet coefficients of a one dimensional signal can be expressed as :
1 1 2 1 2
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) (13)
j
i j
i
x n A n D n A n D n D n
D n A n
= + = + +
= +
∑
where “D” represents the detailed coefficients, and “A” represents approximated coefficients.
In order to investigate phase difference information between approximated and detailed coefficients, we investigate the
following relation in a 2D representation:
1
tan (14)
ij
i j
ij
i j
A
D
θ −
⎛ ⎞
⎜ ⎟
= ⎜ ⎟
⎜ ⎟
⎠
⎝
∑∑
∑∑
This relation represents the second extracted feature “F2” in Haar wavelet domain. However, prior to utilizing phase
feature vector in the final classification procedure, it is normalized using the least-square regression normalization.
1 1
(2) (10)
1 1
H
+ +
⎛ ⎞
= ⎜ ⎟
+ −
⎝ ⎠
1
(2 ) ( 1 1)
[ ] (2 ) , 2,3, ,
1 1
2 2 (2 ) ( 1 1)
n
H
n
Haar H n
n n n
I
−
⎛ ⎞
⊗ + +
⎜ ⎟
= = =
⎜ ⎟
− − ⊗ + −
⎝ ⎠
K
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6. 4.3 Wavelet-based Fractal Dimension (FD)
The architectural and geometrical features of asphalt concrete images present a rich domain for fractal analysis through
the concept of fractal dimension (FD). The fractal dimension provides a geometrical description of an image by
measuring the degree of complexity and how much space a given set occupies around each of its points 10
. The
variations of different architectures and components of AC images associated with different grades shows distinct
features that can be recognized for classification using fractal dimension. In this part, the concept of deriving fractal
dimension from wavelet decomposed detailed coefficients is presented.
One might consider the detailed coefficients in a given wavelet decomposition as a domain for representing visual
textural characteristics in terms of horizontal, vertical and diagonal details. Wavelet coefficients are first mapped to the
spatial domain of graylevel scale in the bounded range of [0,255]. Then, a further threshold stage for binarization
purpose is introduced as an adaptive process to reflect local statistics by deploying standard deviation in local windows
11
. The proposed binarization threshold T is expressed as follows:
( , ) ( , ) . ( , ) (15)
T i j mean i j C i j
σ
= +
Where ( , )
mean i j is the local mean, C is a global constant, and ( , )
i j
σ is the local standard deviation.
The purpose of the previous processes is to have an image with edge details suitable for fractal analysis using fractal
dimension (FD) measure. Given a set S in Euclidean n-space, the self similarity of S is obtained if Nr distinct copies of S
exist by r ratio 12
. The following equation provides the fractal dimension measure “FD” as the slope measure expressed
as follows:
log( )
(16)
log(1/ )
N
r
FD
r
=
For the submatrices of the horizontal, vertical, and diagonal architectural details, the fractal dimension is found by
averaging all slopes/fractal dimensions from each detailed submatrix as follows:
, ,
( )
(17)
H V D
i
D n
i
FD
i n
= ∑
where FD (n) represents the average fractal dimension of all detailed submatrices (n) ,at decomposition level i. For
features normalization, the generated feature vector is normalized using the least-squared regression method. This
procedure of using wavelet-based fractal measure for generating the third feature vector “F3” will be combined with the
previous two feature vectors for the final classification presented in the next section. The following block diagram
illustrates the overall procedure of the developed algorithm.
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7. 5. SIMULATION RESULTS AND DISCUSSION
The data set used in simulation consists of 150 textural images of asphalt concrete mixture. These images are taken from
asphalt core using X-ray Computed Tomography (CT) scan. The data set is divided into 5 subgroups, with 30 images
each according to their textural complexities, as shown previously in figure 1. Images were prepared by the University of
Texas at El Paso 5
.
5.1 Wavelet energy
In order to investigate the performance of Haar wavelet energy feature, the Support Virtual Machine (SVM) classifier
with the general “Hold-Out” cross validation method is used. Haar wavelet decomposition is performed at two
decomposition levels on the normalized features of the five grades with 30 images in each grade. The classification
performance is presented in the following table.
Table 1 Classification performance of Haar wavelet energy feature
Grades
Energy feature vector “F1”
Correct Classification %
Decomposition
Level 1
Decomposition
Level2
Grade 1 86.6 86.6
Grade 2 80.0 80.0
Grade 3 80.0 96.0
Grade 4 94.6 93.3
Grade 5 80 80.0
Average 84.2 87.1
Based on the observation of classification performance from the previous table, it is noted that a better classification
performance is achieved using the energy feature at the second decomposition level. Also, there is a superior
classification performance of grade 3 textures compared to the remaining grades. This increases the average
Texture
Image
F1=Energy
F2=Phase
F3=FD
A D1
“H”
D2
“V”
D3
“D”
Feature
vectors fitting
and
Normalization
SVM
Classifier
Figure 3 Block diagram of the proposed algorithm
Haar wavelet
Decomposition
RGB pre-
processing
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8. classification performance using the second decomposition level. Hence, decomposition level 2 is chosen for generating
the “Haar” energy feature vector, denoted as “F1”, prior to the final SVM classification for all feature vectors.
5.2 Wavelet Phase Measure
In this part, a feature vector is generated using the phase of wavelet approximated coefficients ratio to the sum of all
detailed coefficients as expressed previously. The generated feature vector “F2” is normalized before the SVM classifier
is utilized to measure the classification performance. The following table illustrates simulation results using this feature.
Table 2 Classification performance using wavelet phase measure
Grades
Phase feature
vector “F2”
Correct
Classification %
Grade 1 80.0
Grade 2 80.0
Grade 3 80.0
Grade 4 81.3
Grade 5 89.3
Average 82.3
The phase information-based classification resulted in a higher performance in grade 5 textures compared to the previous
wavelet energy feature. Although a lower average is achieved, the final combination of features is expected to result in a
higher classification performance due to the effect of the increase classification performance for grade 5 texture images.
5.3 Wavelet-based Fractal Dimension (FD)
In this part, the generated feature vector “F3” represents the average fractal dimension measure for all the detailed
coefficients. The purpose of utilizing such feature vector is to highlight the similarities of textural architectures observed
visually at the submatrices of the detailed coefficients. The results of the normalized feature vector classification using
SVM are indicated in the below table.
Table 3 Classification performance using wavelet-based fractal measure
Grades
FD feature
vector “F3”
Correct
Classification %
Grade 1 80.0
Grade 2 78.8
Grade 3 80.0
Grade 4 97.3
Grade 5 81.2
Average 83.46
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9. As can be observed from this table above, the major advantage of utilizing wavelet-based fractal dimension is to have a
higher discrimination of grade 4 texture images. The next step is to fuse all features for classification which is
highlighted in the next section using different cross validation methods.
5.4 Features Combination
The generated feature vectors F1, F2 and F3 are combined for classification using SVM classifier with the following
different cross validation procedures: Hold-out all samples, Leave-one-out, K-fold cross validation with k=5 and 10. In
K-fold cross validation, feature selection is performed K times, where each time it is performed on a different training
set. From the table below, the highest correct classification rate of 91.4% is achieved using 5-fold cross validation
method. The lowest classification rate achieved is 80% using the “leave-one-out” technique.
Table 4 Overall classification performance
Texture
Class
F1+F2+F3
Hold-out
F1+F2+F3
Leave-One-Out
F1+F2+F3
5-fold
F1+F2+F3
10-fold
Grade 1 94.6
Average
88.8%
100.0
Average
80.0%
97.3
Average
91.4%
98.0
Average
91.2%
Grade 2 84.0 50.0 79.3 78.6
Grade 3 82.6 100.0 88.0 86.6
Grade 4 96.0 100.0 96.6 96.6
Grade 5 86.6 50. 96.0 96.0
6. CONCLUSION
In this Paper, we introduce a new method for evaluation, quality control, and verification of asphalt concrete mixtures
using automatic grading of their texture images. Also, we presented a new novel asphalt concrete texture grading system
based on textural patterns. The introduced algorithms combine features from wavelet transform and wavelet-based
fractal analysis. The small number of extracted features proved to be effective and superior to other classification
algorithms utilizing larger sets of feature vectors where a dimensionality problem occurs. Moreover, the proposed
classification system has a fast performance due to the selection of Haar wavelet transform for features extraction, and
SVM classifier for feature vectors classification. The proposed algorithm reached 91.4% of correct classification rate,
which indicates its effectiveness in textural classification problems.
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