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A Novel Aggregate Classification Technique Using Moment Invariants andCascaded Multilayered Perceptron Network
Mohammad Subhi Al-Batah, Nor Ashidi Mat Isa, Kamal Zuhairi Zamli,Zamani Md Sani, Khairun Azizi Azizli
PII: S0301-7516(09)00042-8DOI: doi: 10.1016/j.minpro.2009.03.004Reference: MINPRO 2153
To appear in: International Journal of Mineral Processing
Received date: 11 June 2008Revised date: 13 February 2009Accepted date: 7 March 2009
Please cite this article as: Al-Batah, Mohammad Subhi, Mat Isa, Nor Ashidi, Zamli,Kamal Zuhairi, Sani, Zamani Md, Azizli, Khairun Azizi, A Novel Aggregate ClassificationTechnique Using Moment Invariants and Cascaded Multilayered Perceptron Network,International Journal of Mineral Processing (2009), doi: 10.1016/j.minpro.2009.03.004
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A Novel Aggregate Classification Technique Using Moment Invariants and Cascaded Multilayered Perceptron Network
Mohammad Subhi Al-Batah1, Nor Ashidi Mat Isa2, Kamal Zuhairi Zamli3,
Zamani Md Sani4, Khairun Azizi Azizli5
1,2,3,4 School of Electrical and Electronic Engineering, 5School of Materials and Mineral Resources Engineering,
1,2,3,4,5Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Penang, Malaysia E-mail: 1 [email protected], 2 [email protected] , 3 [email protected], 4 [email protected],
Abstract
Occupying more than 70% of the concrete’s volume, aggregates play a vital role as the raw feed for
construction materials; particularly in the production of concrete and concrete products. Often, the
characteristics such as shape, size and surface texture of aggregates significantly affect the quality of the
construction materials produced. This article discusses a novel method for automatic classification of
aggregate shapes using moment invariants and artificial neural networks. In the processing stage, Hu,
Zernike and Affine moments are used to extract features from binary boundary and area images. In the
features selection stage, discriminant analysis is employed to select the optimum features for the aggregate
shape classification. In the classification stage, a cascaded multilayered perceptron (c-MLP) network is
proposed to categorize the aggregate into six shapes. The c-MLP network consists of three MLPs which are
arranged in a serial combination and trained with the same learning algorithm. The proposed method has
been tested and compared with twelve machine learning algorithms namely Levenberg-Marquardt (LM),
Broyden-Fletcher-Goldfarb-Shanno quasi-newton (BFG), Resilient back propagation (RP), Scaled
conjugate gradient (SCG), Conjugate gradient with Powell-Beale restarts (CGB), Conjugate gradient with
Fletcher-Reeves updates (CGF), Conjugate gradient with Polak-Ribiere updates (CGP), One step secant
(OSS), Bayesian regularization (BR), Gradient descent (GD), Gradient descent with momentum and
adaptive learning rate (GDX) and Gradient descent with momentum (GDM) algorithms. Also, the
classification performance of the c-MLP network is compared with those of the hybrid multilayered
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perceptron (HMLP), the radial basis function (RBF) as well as discriminant analysis classifiers.
Concerning the cascaded MLP, 3 stage c-MLP gives the best accuracy compared to the 2 stage c-MLP and
the standard MLP. Compared to other learning algorithms, LM algorithm achieved the best result. As far as
the overall conclusion is concerned, c-MLP gives better classification performance than that of the HMLP,
RBF and discriminant analysis.
Index Terms - Aggregate classification; Pattern classification; Moment invariants; Image processing;
Discriminant analysis, Cascaded multilayered perceptron (c-MLP) network; Artificial neural network.
1. Introduction
Quarries provide earth materials such as sand, clay, gravel and crushed rocks that will be processed further
into raw material inputs for buildings and construction, agriculture and industrial processes. The demand for
these materials is derived by the demand for the goods and services that these materials provide, with each
user industry defining specifications fit for their final products (Rajeswari et al., 2004). The rapid growth
from construction sector automatically accelerates and gives rise for higher demand for aggregates which is
the major constituent of construction particularly for concrete.
At least three-quarters of the volume of concrete is occupied by aggregates and hence it is not surprising
to know that its quality is of considerable importance (Neville, 1995). Report from Rajeswari (2004),
showed that the nature and the degree of stratification of rock deposit, the type of crushing plant used and
the size reduction ratio as amongst the key factors that greatly influence the shape of aggregate particles and
the quality of fresh and hardened concrete. The ability to produce high strength concrete with good bonding
characteristics and at the same time maintaining the workability of fresh concrete and adequate strength for
the hardened concrete is an excellent contribution to the science of concrete technology which is known
racing for higher strength. Similarly, report from Hudson (1995, 1996) clearly showed that improvement in
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the shape of aggregates had been proven to be a major factor in the reduction of the water to cement ratio
needed to produce a concrete mixture. This high quality aggregate also has the ability to decrease the cost
of production and placement of concrete and hence increase the characteristics of the concrete such as
strength and its overall quality.
Rajeswari et al. (2003) also stated that the improvement in the shape of crushed rocks used as aggregates
as amongst the most important characteristics of high quality aggregates particularly for use in the concrete
or construction industry. Aggregates with beefed up characteristics such as more cubical and
equidimensional in shape with better surface texture and ideal grading are considerably gaining much more
attention particularly from the concrete industry as these aggregates greatly assist in increasing the strength
and enhancing the quality of concrete. This work also scientifically showed the optimum orientation and
packing of high quality shape aggregate particles (i.e. cubical and angular) in a concrete mix compared to
the poorly shaped particles (i.e. irregular, elongated, flaky and flaky&elongated). Hence, aggregates with
improvement in particle shape and texture acts as a catalyst for the development of good mechanical
bonding and interlocking between the surfaces of aggregate particles in a concrete mix.
Overall, stronger aggregates with improvement in particle shape and textural characteristics tend to
produce stronger concrete as the weak planes and structures are being reduced. Substitution of
equidimensional particles derived as crushed product produce higher density and higher strength concrete
than those which are flat or elongated because they have less surface area per unit volume and therefore
pack tighter when consolidated. Aggregates which are flat or elongated decrease the workability by poor
packing, reducing the bulk mass and consequently decreasing the compressive strength of concrete with
much more requirements of sand, cement and water. Thus, it is of utmost importance to change the
traditional quarrying scenario towards optimization of the crusher performance to produce high quality
aggregates so that this will be in tandem with the current development and changes in the concrete industry.
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Furthermore, it is necessary to develop a more quantitative and systematic measurement system for
aggregate classification.
Traditionally, standard techniques and test procedures complying with British Standards, American
Society for Testing and Materials (ASTM) and New Zealand Standards have been widely used to analyze
and evaluate the shape, size grading and surface texture of aggregates. Generally, the grading profile of
aggregates is identified by sieving with standard sieves and sieve shakers. The flakiness and elongation
gauges are the aids used to determine the flakiness and elongation indices (FI’s and EI’s) of coarse
aggregates while the shape of fine aggregates is determined through the voids content percentage
(uncompacted and compacted) and flow cone method. However, the analysis for coarse aggregate particles
has limitations since it involves manual gauging of individual aggregate particles. It is also difficult for
engineers to analyze the concrete for improvement in real time due to lack of accuracy and systematic
database storage for the mass aggregate production.
Over the past 20 years, many works have been done to improve the methods for analyzing aggregate
images using digital image processing (DIP) technique particularly to shorten the time for classification thus
making it more cost effective and faster compared to the conventional processes. Much of the work tried to
explore the advantages of DIP to have a real time classification system and the data information storage for
the aggregates, making it more automated thereby simplifying the analysis in the future. Different methods
and algorithms were developed to tackle the issues encountered and to improve the process further. Kwan et
al. (1999) adopted DIP to analyze the shape of coarse aggregate particles. Application of DIP for the
measurement of coarse aggregate size and shape is presented in the works of Maerz (1998) and Maerz and
Lusher (2001). Mora and Kwan (2000) had developed a method of measuring the sphericity, shape factor
and convexity of coarse aggregate for concrete using DIP technique.
A number of methods using imaging systems and analytical procedures to measure aggregate
dimensions are already available. An imaging system consisting of a mechanism for capturing images of
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aggregates and methods for analyzing aggregate characteristics have been developed such as Multiple Ratio
Shape Analysis (MRA) by Jahn (2000), VDG-40 Videograder by Emaco Ltd Canada, Weingart and
Prowell (1999), Computer Particle Analyzer (CPA) by Tyler (2001), Micromeritics OptiSizer (PSDA) by
Strickland, Video Imaging System (VIS) by John B. Long Company, Buffalo Wire Works (PSSDA) by
Penumadu, Camsizer by Jenoptik Laser Optik System and Research Technology, WipShape by Maerz and
Zhou (2001), University of Illinois Aggregate Image Analyzer (UIAIA) by Tutumluer et al. (2000),
Aggregate Imaging System (AIMS) by Masad (2003) and Laser-Based Aggregate Analysis System (LASS)
by Kim et al. (2001). Description of the existing test methods can be found in Al-Rousan (2004).
To select a set of appropriate numerical attributes of features from the interested objects for the purpose
of classification is one of the fundamental problems in the design of an imagery pattern recognition system.
One of the solutions, the utilization of moments for object characterization has received considerable
attention in recent years. Moment is an important shape descriptor in computer vision and has been used
widely in pattern recognition applications (Munoz-Rodriguez et al., 2005; Realpe and Velazquez 2006;
Rizon et al., 2006). Moment can be applied as a method to describe characteristics of certain object such as
surface area, position, orientation and many other parameters (Awcock and Thomas, 1995). There are
numerous types of moment such as invariant moment, Affine, Legendre, Zernike, pseudo-Zernike, rotation
and complex moment that have been used in object or pattern recognition applications (Teh and Chin,
1988).
In the present study, 7 orders of Hu, 11 orders of Zernike and 6 orders of Affine moments are used. Two
sets of these moment are implemented, one from the aggregate area and the other from the boundary. So a
48 - features vector has been constructed from each aggregate sample.
In most of the features extraction cases, larger than necessary number of feature candidates are
generated. However, the irrelevant or uncorrelated features could actually cause a reduction in the
performance of the classifier (Melo et al., 2003). In order to solve this problem, features selection
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techniques such as discriminant analysis, principle component analysis and circle segments need to be
carried out to summarize the data and assist identifying the appropriate features for more focused analysis.
In this work, the discriminant analysis (DA) is used to determine the important and useful features for
aggregate classification. The DA is a very popular supervised learning technique (Hand, 1981). DA is fast,
easy to implement and readily available in statistical packages.
As far as the use of artificial neural network (ANN) is concerned, Kim et al. (2002) presented the use of
digital image analysis and ANN to detect variations in aggregate size distribution. Joret et al. (2007)
introduced Aggregate Shape Classification (ASHAC) system to classify the aggregate into well and poor
shaped. Mat-Isa et al. (2005) employed the hybrid multilayered perceptron (HMLP) network and the MLP
network for identifying the shape of aggregates.
ANN learns the relationships that exist between the input and output variables from a set of training
data, builds a model to fit the data samples and uses the model to predict the outputs of new input data.
Different ANN architectures such as multilayer perceptron (MLP), radial basis function (RBF) and recurrent
neural networks (RNN) have all been proposed in the literature for pattern classification problems (Peh et
al., 2000). Among all these structures, the most commonly and widely-used is the MLP structure. The
popularity of the MLP is due in part to their computational simplicity, finite parameterization, stability and
smaller structure size for a particular problem as compared to other structures. The MLP is generally
straightforward to use and provide good approximation of any input-output mapping (Barletta and Grisario,
2006).
In this work, the aggregate data was extremely random owing to manual collection of aggregate
samples. Consequently, it was not possible for the standard MLP to recognize and categorize these highly
complex samples into six shapes with good accuracy. To overcome this difficulty, a cascaded MLP
network is introduced which is denoted as c-MLP in this literature. Here, the proposed c-MLP consists of
three MLPs which are arranged in a serial combination and trained sequentially, one after the other with the
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same learning algorithm. There are many types of powerful training algorithms and each of the algorithms
has its own limitation. Some of the algorithms may perform well in classification problems while some may
perform well in function approximation problems. The proposed method has been tested and compared with
twelve machine learning algorithms namely LM, BFG, RP, SCG, CGB, CGF, CGP, OSS, BR, GD, GDX
and GDM algorithm. More details of these algorithms are available in Aggarwal et al. (2005). Furthermore,
the effectiveness of the c-MLP trained with the twelve algorithms is compared against the HMLP trained
with the modified recursive prediction error (MRPE) algorithm and the RBF trained using k-means
clustering and given least square algorithm as well as discriminant analysis classifier.
2. Data collection and manual classification of aggregate shape
Data of aggregates are obtained from the School of Materials and Mineral Resources Engineering,
Universiti Sains Malaysia (USM). A total of the 4242 samples with different size and shapes are gathered
after crushing the stones using Metso Barmac Rock on Rock Vertical Shaft Impact (RoR VSI) crusher. A
new aggregate shape classification method based on the Euler’s Polyhedron formula developed by
Rajeswari (2004) as shown in Table 1 was used to classify the aggregate samples manually by the experts.
Out of the 4242 aggregates and based upon the various premises listed in Table 1, domain experts have
categorized 772 aggregates as angular shape, 769 as cubical, 675 as irregular, 692 as elongated, 978 as flaky
and 356 as flaky&elongated shape.
The feeds from a Malaysian Quarry have been crushed using Metso Barmac Rock on Rock Vertical
Shaft Impact (RoR VSI) crusher from New Zealand. A series of experiments was carried out to determine
the shape of the feed and crushed products of all the tests run using the parameters of Euler’s Polyhedron
formula, which states that the number of corners plus the number of faces was equal to the number of edges
plus two (Hartge et al., 1999). These three features were determined by counting the number of faces (f),
edges (e) and corners (c) of all the typical shaped particles existing in the feed and crushed products.
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Direct comparison of the number of faces, edges and corners were made with a perfect ‘cubic’; which
has six faces (f : 6), twelve edges (e : 12) and eight corners (c : 8) as shown in Figure 1. The feed and
crushed aggregate products could be classified manually into six groups of shapes (cubical, angular,
irregular, flaky, elongated and flaky&elongated). From these six shapes, the aggregates can be divided
further into two categories, the well-shaped aggregate (i.e. cubical and angular) and the poor-shaped
aggregate (i.e. irregular, flaky, elongated and flaky&elongated). The results for the shape classification
using the Euler’s Polyhedron formula are shown in Table 1 (Rajeswari, 2004).
The proportion of each type of particles in the feed and crushed products for any rotor speeds or cascade
test work could be better quantified and classified according to this six shape classification. It could be seen
that the number of faces for the flaky, elongated and flaky&elongated particles could be as low as two;
whereas the angular particles had greater number of faces (4 - 8). Also, the flaky, elongated and
flaky&elongated particles were more flat and less in crushed faces compared to angular and cubical type
particles. Similarly, the irregular particles apart from being blocky, could be seen as having less number of
faces, edges and corners compared to the other better shaped particles (cubical and angular) (Rajeswari,
2004).
3. Image acquisitions and feature extraction
The proposed methodology for image acquisition and feature extraction which uses a camera-object setup is
discussed in this section. CCD camera is used to gather images and information from a scene of interest.
The maximum resolution of the input image is fixed to 640 × 480. The camera-aggregate setup is shown in
Figure 2. Each aggregate to be recognized is placed in its stable condition at different places on the flat
surface with a contrast background. Illumination using controlled lighting condition is provided to have an
aggregate image without shadow and reflection. Typically, the height of the video camera is adjusted to
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within about 1000 mm from the aggregate to obtain a sufficiently large measurement area on the sample
tray. However, the camera can be placed at different position from the aggregate without effecting the
image’s features extraction, due to using the moments which are invariant to object rotation, translation and
size scaling in the image. The lens is adjusted accordingly to obtain a clear and sharp image for analysis.
For each aggregate, only one image is captured as the system is developed to recognize the shape of a
single aggregate’s image. The aggregate images are captured and digitized by frame grabber and stored in a
lossless digital format, bitmap (.bmp), inside the desktop computer memory. Total of 4242 aggregate
images (i.e. the same aggregate samples mentioned in Section 2) have been captured; 772 aggregate images
as angular shape, 769 as cubical, 675 as irregular, 692 as elongated, 978 as flaky and 356 as
flaky&elongated shape. After capturing process, the images are sent to the pre-processing and feature
extraction stage.
The pre-processing stage consists of thresholding the image automatically using iterative thresholding
method, followed by growing and shrinking the image to provide a clear and better separation between
object and background (Low and Ibrahim, 1997; Umbaugh, 2005). In feature extraction stage, a lengthy
experiment was carried out to construct moment features from aggregate’s area and boundary. The features
include seven Hu, eleven Zernike and six Affine moments.
3.1 Hu moment invariants
One of the real challenges in this study is using the geometrical moments for feature extraction in aggregate
shape classification. The invariance property of Hu, Zernike and Affine moments against geometrical
transformations like scaling, translation and rotation makes it a good candidate feature extractor to be used
for aggregate recognition. Also, the simplicity of 2D moment calculation will reduce the processing time,
hence increases the system efficiency and suitability for real time computer vision system.
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In order to understand how to utilize moment invariant method, let bf be a binary digital image with
size YX × (i.e. whereX and Y are the image width and height, respectively) and ),( yxfb is the grey level
value for the pixel at row x and column y . The two-dimensional moments of order )( qp + of ),( yxfb
which is variant to the scale, translation and rotation is defined as
∑∑= =
=X
x
Y
yb
qppq yxfyxm
1 1
),( (1)
The central moments of order )( qp + of ),( yxfb is defined as
∑∑= =
−−=X
x
Y
yb
qc
pcpq yxfyyxx
1 1
),()()(µ (2)
where cx and cy are the centre of mass of the object defined as
00
01
00
10
m
myand
m
mx cc == (3)
The moment invariant under scale is defined as
γµµ
η)( '
00
'pq
pq = (4)
where 12
++= qpγ (5)
and )2(
'++=
qp
pqpq α
µµ (6)
Normalized un-scaled central moment is then given by
γµµ
ϑ)( 00
pqpq = (7)
From the second and third order moments, a set of seven invariant moments which is invariants to
translation, rotation and scale derived by Hu (1962) are:
02201 ϑϑϕ += (8)
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211
202202 4)( ϑϑϑϕ +−= (9)
20321
212303 )3()3( ϑϑϑϑϕ −+−= (10)
20321
212304 )()( ϑϑϑϑϕ +++= (11)
))(3( 123012305 ϑϑϑϑϕ +−= ])(3)[( 20321
21230 ϑϑϑϑ +−+
2123003210321 )(3)[)(3( ϑϑϑϑϑϑ ++−+ ])( 2
0321 ϑϑ +− (12)
])())[(( 20321
2123002206 ϑϑϑϑϑϑϕ +−+−= ))((4 0321123011 ϑϑϑϑϑ +++ (13)
21230123003217 ))[()(3( ϑϑϑϑϑϑϕ ++−= ))(3(])(3 03211230
20321 ϑϑϑϑϑϑ +−−+−
])()(3[ 20321
21230 ϑϑϑϑ +−+ (14)
Where pqϑ obtained from Equation (7).
The algorithm of Hu moment invariants is implemented as:
1. Calculating the value of cx and cy based on Equation (3).
2. Computing each value of ,00µ ,11µ ,02µ ,20µ ,21µ ,12µ 03µ and 30µ using Equation (2).
3. Computing each value of ,11ϑ ,02ϑ ,20ϑ ,21ϑ ,12ϑ 03ϑ and 30ϑ using Equation (7).
4. Calculating the value of Hu moments 1ϕ - 7ϕ according to Equation (8) until (14).
In order to take advantage of the information content of both the area and the boundary of the aggregate
image, two sets of seven Hu moment invariant functions are computed; one set derived from the area
)( 71 ϕϕ − and the other from the boundary )( 71 PP ϕϕ − . So, with this technique a 14 feature vectors are
generated.
3.2 Zernike moments
Zernike moments are defined over a set of complex polynomials which a complete orthogonal set over the
unit disk 122 ≤+ yx and can be denoted as (Belkasim, 2004).
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[ ] dxdyyxVyxfm
A
yx
mnmn ∫∫≤+
+=122
*),(),(1
π (15)
where ∞= ,...2,1,0m . ),( yxf represents the pixel value of the image at x and y coordinate, ),( yxVmn is
Zernike polynomial, complex conjugate is represented by ∗ symbol and n is requiring two conditions:
1. nm− = even, and 2. mn ≤
Zernike polynomial ),( yxVmn can be expression in polar coordinate using the relation
)exp()(),( θθ jnrRrV mnmn = (16)
where ),( θr denoting as disk unit and )(rRmn is orthogonal radial polynomial given by
∑
−
=
−=2
0
),,,()1()(
nm
s
smn rsnmFrR (17)
where smr
snm
snm
s
smrsnmF 2
)!2
()!2
(!
)!(),,,( −
−−
−+
−= (18)
For a digital image ),( yxfb , Expression (15) can be denote with
∑∑+=
x ymnbmn yxVyxf
mA *)],()[,(
1
π, where 122 ≤+ yx (19)
Pejnovic et al. (1992) derived Zernike moments in terms of central moments (Equation 2). Up to the 4-
th order ( 4<+ qp ), the Zernike moments are given by:
πµµ )1)(2(3 0220
201
−+== AS (20)
2
211
202202
222
))(4)((9
πµµµ +−
== AS (21)
2
21230
221032
333
))3()3((16
πµµµµ −+−
== AS (22)
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2
21230
221032
314
))()((144
πµµµµ +++
== AS (23)
33133
331335 )( ∗∗ += AAAAS 2
2103210321034))()(3((
13824 µµµµµµπ
++−=
))(3()(3 123012302
1230 µµµµµµ +−−+− ))(3)( 22103
21230 µµµµ +−++ (24)
222
31222316 )( AAAAS ∗∗ += 2
12302
210320023)())(((
864 µµµµµµπ
++−=
)))((4 1230210311 µµµµµ +++ (25)
2
447 AS = 20422402
)6((25 µµµπ
+−= ))(16 21331 µµ −+ (26)
2
428 AS = 2022040042
)(3)(4(25 µµµµπ
−+−= ))3)(4(4 2111331 µµµ −++ (27)
409 AS = )1)(6)2(6(5
0220042240 ++−++= µµµµµπ
(28)
24244
2424410 )( ∗∗ += AAAAS )((4)(6((
25040040422403
µµµµµπ
−+−=
))3)(4(4))(3 2111331
20220 µµµµµ −+−−+ ))(3)(4(16 02204004 µµµµ −+−−
))(3)(4( 1331111331 µµµµµ −−+ (29)
2242224211 AAAAS ∗∗ += ))((3)(4(30
2002022040042µµµµµµ
π−−+−=
))3)(4(4 11133111 µµµµ −++ (30)
The following conditions are obeyed for calculating the Zernike moments:
1. Calculating the value of cx and cy based on Equation (3).
2. Computing each value of ,00µ ,11µ ,02µ ,20µ ,21µ ,12µ ,22µ ,03µ ,30µ ,31µ ,13µ 40µ and 04µ
using Equation (2).
3. Calculating the value of Zernike moments 1S - 11S according to Equation (20) until (30).
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In this study, two sets of eleven Zernike moment functions are computed; one set derived from the area
)( 111 SS − and the other from the boundary )( 111 PP SS − . Hence, with this technique we constructed 22
feature vectors.
3.3 Affine moments
The Affine moment invariants are derived to be invariants to translation, rotation, scaling of shapes and
under general 2D affine transformation. The six Affine moment invariants (Kadyrov & Petrou, 2001) used
are defined as follows:
)(1 2
110220400
1 µµµµ
−=I (31)
3123003122130
203
23010
002 46(
1 µµµµµµµµµ
+−=I )34 212
221
32103 µµµµ −+ (32)
)()((1
12210330112120321207
003 µµµµµµµµµ
µ−−−=I ))( 2
21123002 µµµµ −+ (33)
031211220
203
32011
004 6(
1 µµµµµµµ
−=I 210321120
21202
220030221
220 1296 µµµµµµµµµµµ ++−
12210211200330021120 186 µµµµµµµµµµ −+ 221
202201230
202203003
311 968 µµµµµµµµµµ +−−
)612 230
3022130
202
211123002
211 µµµµµµµµµµ +−+ (34)
)34(1 2
2213310440600
5 µµµµµµ
+−=I (35)
132231220440900
6 2(1 µµµµµµ
µ+=I )3
2223104
21340 µµµµµ −−− (36)
The algorithm of Affine moments is implemented as:
1. Calculating the value of cx and cy based on Equation (3).
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2. Computing each value of ,00µ ,11µ ,02µ ,20µ ,21µ ,12µ ,22µ ,03µ ,30µ ,31µ ,13µ 40µ and 04µ
using Equation (2).
3. Calculating the value of Affine moments 1I - 6I according to Equation (31) until (36).
Two sets of six Affine moment functions, one set derived from the area )( 61 II − and the other from the
boundary )( 61 PP II − , are computed in this research. Therefore, 12 feature vectors are generated using this
method.
In summary, a total of 4242 samples of aggregate were used in this study. Each input sample has 48
attributes extracted based on object’s mass and boundary, which are 14 Hu moments (1ϕ - 7ϕ , P1ϕ - P7ϕ ), 22
Zernike moments (1S - 11S , PS1 - PS11 ) and 12 Affine moments (1I - 6I , PI 1 - PI 6 ). Having extracted the 48
features, the next step is undertaken, which is to determine the useful and important features using features
selection techniques.
4. Features selection
After completing the features extraction process, all the 48 features for 4242 aggregates with its 6 groups
are tabulated in the Microsoft excel spreadsheet. Then, the discriminant analysis using SPSS software
version 14 is put into action to analyze, determine the optimum features (i.e. to eliminate the noisy and
unwanted features), quantify the performance of each group and calculate the overall accuracy of the
classification.
The 48 features are denoted as X1( 1ϕ ), X2( P1ϕ ), X3( 2ϕ ), X4( P2ϕ ), X5( 3ϕ ), X6( P3ϕ ), X7( 4ϕ ), X8( P4ϕ ),
X9( 5ϕ ), X10( P5ϕ ), X11( 6ϕ ), X12( P6ϕ ), X13( 7ϕ ), X14( P7ϕ ), X15( 1S ), X16( PS1 ), X17( 2S ), X18( PS2 ), X19( 3S ),
X20( PS3 ), X21( 4S ), X22( PS4 ), X23( 5S ), X24( PS5 ), X25( 6S ), X26( PS6 ), X27( 7S ), X28( PS7 ), X29( 8S ),
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X30( PS8 ), X31( 9S ), X32( PS9 ), X33( 10S ), X34( PS10 ), X35( 11S ), X36( PS11 ), X37( 1I ), X38( PI 1 ), X39( 2I ),
X40( PI 2 ), X41( 3I ), X42( PI 3 ), X43( 4I ), X44( PI 4 ), X45( 5I ), X46( PI 5 ), X47( 6I ) and X48( PI 6 )
Ward’s Linkage method with univariate and multivariate tests was applied to the analysis results. This
type of analysis was needed in order to identify clusters of analysis methods. Table 2 shows results of
univariate test for the original 48 features. Based on the results, the features X10, X29 and X33 have low
impact to identifying process with p-value distribution more than 5%. The other features showed high
impact to identifying process with p-value distribution less than 5%. Hence, null hypothesis is rejected for
X10, X29 and X33, while null hypothesis is accepted for the other 45 features.
Here, the 45 features which give high impact have been processed using multivariate test. Table 3
tabulates the p-value distribution of each feature using multivariate test. From the 45 features, only 23
optimum features have been chosen using the multivariate test as suitable features for aggregate’s shape
recognition. The 23 dominant features which have p-value distribution less than 0.05 are highlighted in
Table 3. The 23 optimum features are X1( 1ϕ ), X4( P2ϕ ), X5( 3ϕ ), X7( 4ϕ ), X9( 5ϕ ), X12( P6ϕ ), X13( 7ϕ ),
X15( 1S ), X16( PS1 ), X18( PS2 ), X25( 6S ), X26( PS6 ), X31( 9S ), X32( PS9 ), X36( PS11 ), X38( PI 1 ), X40( PI 2 ),
X42( PI 3 ), X43( 4I ), X44( PI 4 ), X45( 5I ), X46( PI 5 ) and X48( PI 6 ). From the results obtained, null hypothesis is
accepted at stated 23 features because it can afford to form relationship between the 6 groups and cause high
impact to identifying process with p-value distribution less than 5%. Null hypothesis is rejected for the other
22 features because it cannot form relationship between the 6 groups and have low impact to identifying
process with p-value distribution more than 5%.
Based on discriminant analysis, it is found that only 23 dominant features have the ability to classify the
aggregates into 6 groups (shapes) properly. Table 4 presents the dominant features (independent variables)
which give significant impact together with its discriminant coefficients given during the formation of
discriminant function.
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From Table 4, the discriminant function is derived as follows:
1297541 007.0320.1992.1200.1583.37230.6 XXXXXXZ p −−++−=
262518161513 046.33628.31866.46081.1696.4669.2 XXXXXX −++++−
424038363231 905.0185.1347.1878.0279.0449.2 XXXXXX −+−−−−
891.5385.1982.2351.2608.0326.0 4846454443 −−+−+− XXXXX (37)
The discriminant function pZ value is obtained by adding the sum of multiplication between
discriminant coefficient and dominant features values. Based on the pZ value, the group mean called the
centroid is determined. Table 5 shows the centroid (mid-point) for each aggregate group. Then, the type and
range of each group could be determined by examining the range between the separation points.
The separation point must be ascertained because the value can be used to identify the range for each
group of the aggregate. With ascending order, it is found that:
elongatedflakyelongatedirregularangularcubicalflaky &<<<<< .
Then, the separation points between the groups are defined as follows:
For the flaky and cubical group, the separation point is:
1155.22
)378.0()853.3(| −=
−+−=cubicalflaky
The separation point for the cubical and angular group is:
0535.02
485.0)378.0(| =
+−=angularcubical
The angular and irregular groups are separated at point:
6075.02
730.0485.0| =
+=irregularangular
The separation point between irregular and elongated group is:
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6865.12
643.2730.0| =
+=elongatedirregular
Finally, the separation point between elongated and flaky&elongated group is:
2345.32
826.3643.2&| =
+=elongatedflakyelongated
From separation points obtained, the range for each group is determined. The flaky group is located at
separation point which is less than -2.1155. Next, the cubical group is located between -2.1155 and 0.0535.
Then, the angular group is located between 0.0535 and 0.6075. After that, the range between 0.6075 and
1.6865 represents irregular group while the range between 1.6865 and 3.2345 represents elongated group.
Finally, the flaky&elongated group is located at separation point which is greater than 3.2345.
Apart from determining the dominant features which cause high impact, the discriminant analysis is also
able to classify the data into groups identified (i.e. determine the number of correctly classified data, the
number of misclassified data and the accuracy for each group). In this study, the discriminant analysis
conducted into 6 groups of aggregate gives results as shown in Table 6.
Table 6 shows the classification accuracy for the 6 aggregate groups using discriminant analysis. The
overall data are 4242; each data has 23 optimum features. The classification accuracy is 80.1% for angular
(618 angular data correctly classified out of 772 overall), 83.6% for cubical (643 out of 769), 75.3% for
irregular (508 out of 675), 86.1% for elongated (596 out of 692), 89.5% for flaky (875 out of 978) and
74.4% for flaky&elongated group (265 out of 356). To obtain the overall accuracy, it is calculated by taking
the average classification for the 6 groups as follows:
Accuracy =
data ofnumber Total
data classifiedcorrectly ofNumber *100 (38)
=
+++++4242
265875596508643618 *100
= 82.63 %.
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5. Classification using cascaded-MLP network
In recent years, the MLP network has been increasingly popular for applications in pattern classification,
learning and function approximation. The MLP network consists of three main layers namely input layer,
hidden layer and output layer. Each layer contains neurons which are linked to neurons of other layers
through the weight and bias values. The network learns the relationship between pairs of inputs (factors)
and output (responses) vectors by altering the weight and bias values.
Figure 3 shows an example of a standard MLP network with inputs, 1x , 2x … 0nix and predicted outputs,
1y … my . The predicted output of the k-th node in the output layer of the MLP network denoted as ky can
be expressed as:
∑ ∑= =
+=
h in
j
n
ijiijjkk btxwFwty
1 1
1012 )()(ˆ ; for hnj ≤≤1 and mk ≤≤1 (39)
where 1ijw , 2
jkw denote the weights between input and hidden layer, weights between hidden and output
layer, respectively. 1jb and 0ix denote the thresholds in hidden nodes and inputs that are supplied to the input
layer, respectively. in , hn , and m are the number of input nodes, hidden nodes and output nodes,
respectively. )(•F is the activation function, the most commonly used one in the MLP is of the sigmoid
type, defined as:
xexF −+
=1
1)( ; (40)
where )(xF is always in the range [-1,1], ℜ∈∀x (the set of real numbers).
The weights 1ijw , 2
jkw , and thresholds 1jb are unknown and should be selected to minimize the prediction
error, defined as:
)(ˆ)()( tytyt kkk −=ε (41)
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where )(tyk and )(ˆ tyk are the actual outputs and network predicted outputs, respectively.
As this study proposes the MLP network to classify the aggregate into six shapes, thus the number of
output nodes for the MLP network is set to 6, which each node will represent one shape of aggregate. For
determining each shape, the actual output )(tyk of the MLP network should be as tabulated in Table 7.
Also, the predicted output )(ˆ tyk of the MLP network should be similar to that as tabulated in Table 7, else
error is occurred and calculated based on Equation (41). Based on this error and the input features of
aggregates, the MLP network will employ the learning algorithm to minimize the error and ensure that the
predicted output is obtained the similar as tabulated in Table 7.
In order to increase the performance of the standard MLP network, this study introduces the cascaded
MLP (c-MLP) network. Figure 4 shows the proposed c-MLP network form, which consists of 3 MLPs.
Based on Figure 4, the output layer of the first MLP is linked with the input layer of the second MLP and
the output layer of the second MLP is linked with the input layer of the third MLP.
For the classification purpose, the number of the inputs for the first MLP was assumed to depend on the
number of moment features, which were 23 input features while the numbers of outputs depend on the
number of aggregate shapes to be recognized, which were 6 in type. Since the third MLP takes input data
from the second and the second MLP takes input data from the first one sequentially, the number of inputs
and outputs of second and third must be equivalent to the number of outputs of the first MLP which is equal
to 6 (i.e. 23 input and 6 output nodes for the first MLP, but 6 input and 6 output nodes for the second and
third MLP).
For simplicity, we suggested that all the three MLP’s adopt the same initial setting. For example, if the
first MLP has 50 hidden nodes or being trained for 10,000 iterations (epochs), then the second and third will
hold the same value of hidden nodes and iterations, and so on. The three classifiers in the c-MLP network
function together to refine the weights of the input samples and improve the performance.
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After the input object is recognized using the first MLP, if any feature of an input object is not
recognized correctly, the second MLP will take up the task and the same is repeated in the third MLP, thus
increasing the classification capability of the system. In other words, each MLP has new input data with
different normalization, the second MLP re-trains the predicted outputs from the first and enhances the
probability of having a correct detection and directly minimizes the classification errors caused by the first
thus refining the weights of the faulty samples and this leads to increase the classification performance. The
predicted outputs from the second MLP automatically feeds to the third in which the same scenario is
repeated. In short, each succeeding MLP is employed to review and analyze the predicted outputs from the
preceding MLP and give high priority for the misclassified samples.
6. Classification performance analysis
A total of 4242 sample of aggregates (i.e. the same samples used in Section 2 and 3) with different size and
shapes were used to be classified into six classes; 772 angular, 769 cubical, 675 irregular, 692 elongated,
978 flaky and 356 flaky&elongated. 50% of the training examples were selected at random from the entire
data set (i.e. 386 angular, 385 cubical, 337 irregular, 346 elongated, 489 flaky and 178 flaky&elongated)
and the remaining 50% of the data (i.e. 386 angular, 384 cubical, 338 irregular, 346 elongated, 489 flaky
and 178 flaky&elongated) were used as testing set to determine the performance of the network.
The performance analysis of the neural networks is based on two important characteristics, which are
accuracy and mean square error (MSE). The measure of the ability of the classifier to produce accurate
classification is determined by accuracy, as mentioned in Equation (38). The MSE is an iterative method of
model validation where the model is tested by calculating the mean squared errors after each epoch. The
MSE test will indicate how fast a prediction error converges with the number of training data (Mashor,
2000). The MSE is defined as the average squared error between the actual output and the predicted output.
The MSE at the t-th epoch is given by:
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( )∑=
Θ−=Θdn
id
tiyiyn
ttMSE1
2))(,(ˆ)(1
))(,( (42)
where ))(,( ttMSE Θ , )(iy , and ))(,(ˆ tiy Θ are the MSE, actual output, and the predicted output for a given
set of estimated parameter )(tΘ after t epochs respectively, and dn is the number of data that were used to
calculate the MSE.
In applying neural network as pattern recognition or classification, one of the important criteria in
learning process is the determination of optimum architectures of neural network (i.e. number of hidden
nodes and epochs) (Negnevitsky, 2005). Generally, neural network can be considered as black box which
has a function to map and determine relationship between input and output. Hidden nodes are important as a
mapping platform between input and output relationship. Appropriate numbers of hidden nodes that are
connected to input and output nodes are important in securing the optimum performance of the neural
network. Also in learning process, neural network needs to be trained by the same training data for certain
number of iterations (epochs). This is important to ensure that the neural network is provided with sufficient
learning process in order to produce optimum performance. As these two parameters are important, this
paper will implement the analysis to determine the optimum number for both parameters.
To determine the network parameters, the experiments were carried out by varying the number of
hidden neurons from 1 to 50. For each number of hidden neuron, the network was trained by varying the
number of epochs from 1 to 10,000. The purpose was to find the number of epoch that produced the best
generalization for each number of hidden neuron. The optimum epoch and hidden neuron, which produced
the minimum value of mean squared error for the testing set, was noted and its classification accuracy was
determined.
To find the best learning algorithm, the proposed method has been tested and compared with twelve
machine learning algorithms namely LM, BFG, RP, SCG, CGB, CGF, CGP, OSS, BR, GD, GDX and
GDM algorithms. For each learning algorithm, the performance for the c-MLP with three MLPs (i.e. 3c-
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MLP) was compared with the c-MLP with two MLPs (i.e. 2c-MLP) and standard MLP network. Moreover,
the performance comparison with other classifiers namely HMLP, RBF and discriminant analysis are
studied.
7. Results and discussions
Table 8 shows the testing performance for the c-MLP with three MLPs (i.e. 3c-MLP), c-MLP with two
MLPs (i.e. 2c-MLP) and standard MLP network, using twelve different learning algorithms based on 23
features selection using the DA technique. The performance for the training data is not included in this
paper as the data only used for training and teaching the neural network.
As seen in Table 8, the performance achieved by using the 3c-MLP is significantly better compared to
those from the 2c-MLP and the standard MLP. In addition, the best performance obtained using LM
algorithm and the worst performance obtained using GD algorithm as compared to other learning
algorithms. The best accuracy rates achieved using LM algorithm are 93.5%, 94.9% and 97.1% in case of
the MLP, 2c-MLP and 3c-MLP, respectively and the MSE are 0.0148, 0.0126 and 0.0079 for the MLP, 2c-
MLP and 3c-MLP, respectively. Moreover, the worst accuracy rates achieved using GD algorithm are
74.8%, 77.3% and 80.5% using the MLP, 2c-MLP and 3c-MLP, respectively and the MSE are 0.0458,
0.0431 and 0.0396 for the MLP, 2c-MLP and 3c-MLP, respectively.
The result in Table 8 shows that the classification performance for the 3c-MLP is better than that of the
2c-MLP and the standard MLP, implying the performance increases with the increase in number of
classifiers. The result also shows that the aforementioned c-MLP network can successfully be adopted for
weak learning algorithms in order to improve the classification performance significantly as in GD and
GDM algorithm. Again, the empirical results strongly demonstrate that the performance of the strong
classifiers as LM, BFG, RP, SCG, CGB, CGF, CGP, OSS, BR and GDX can be advanced using the
cascaded MLP.
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On the other hand, the performance of the proposed 3c-MLP trained with LM algorithm (as it’s the best
classifier) is compared with the HMLP, RBF and Discriminant Analysis as presented in Table 9. Over the
whole classifiers, the best testing accuracy achieved 97.1% with 0.0079 MSE using the 3c-MLP which is
better as compared with those from the HMLP (93.44%, 0.015 MSE), the RBF (90.28%, 0.0215 MSE) and
the Discriminant Analysis (82.63%, 0.0371 MSE).
From Table 9, it is shown that the proposed 3c-MLP trained with LM algorithm is able to achieve better
classification performance than that of the HMLP, RBF and Discriminant Analysis. From the results, the 3c-
MLP outperformed the HMLP in terms of the percentage of accuracy by more than 3.60%. In addition, the
3c-MLP outperformed the RBF and Discriminant Analysis with difference of accuracy percentage equal to
6.82% and 14.47%, respectively.
The result also shows that the 3c-MLP is the best classifier to further classify the aggregates into six
shapes with high performance for each shape. Over the whole networks comparison, the 3c-MLP performed
better than other classifiers with recorded testing accuracy 94.04%, 98.46%, 94.13%, 98.52%, 99.79% and
95.55% for angular, cubical, irregular, elongated, flaky and flaky&elongated, respectively.
8. Conclusion
In this paper, an efficient aggregate shape classification system using moment invariants and cascaded MLP
network is introduced. Here, Hu, Zernike and Affine moments are calculated per boundary and area for
4242 images, where each image represents one of the six shapes in type. Using discriminant analysis, 23
optimum features have been chosen as suitable features for aggregates classification. The c-MLP is tested
and compared with twelve different learning algorithms as well as comparing with other classifiers namely
the HMLP, RBF and Discriminant Analysis. The comparison results show that the c-MLP network trained
with LM algorithm can successfully be adopted for automatic aggregate shape classification with
significantly high testing accuracy up to 97.1%. As seen in the experiments, the c-MLP is able to further
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classify the aggregate shapes into angular, cubical, irregular, elongated, flaky and flaky&elongated with
high performance for each shape which is better than other classifiers. Our work concludes that the
proposed c-MLP network is a powerful technique not only for accurate aggregates classification but also for
improving the performance of learning algorithms. This technique is proved to be effective when three
possible problems coexist, first, lack of sufficient input data to achieve low error rates; second, the poor
features of the data; and third, a weak learning algorithm. As extension of this study, we plan to investigate
the performance of the c-MLP in combination with other kinds of networks such as the RBF network, RNN,
ART, ANFIS, etc., especially when dealing with multiple-input-multiple-output (MIMO) data.
Acknowledgement
This work is supported by the Ministry of Science, Technology and Innovation (MOSTI) Malaysia, under
Science Fund grants entitled ‘Development of an Automatic Real-Time Intelligent Aggregate Classification
System Based on Image Processing and Neural Networks’ and ‘Development of a New Architecture and
Learning Algorithm of Artificial Neural Network for Determination of Potential Drug in Herbal Medicine’.
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