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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 46, 2015 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Peiyu Ren, Yancang Li, Huiping Song 
Copyright © 2015, AIDIC Servizi S.r.l., 
ISBN 978-88-95608-37-2; ISSN 2283-9216 

A Data Field Clustering Method for Classification of Concrete 
Dam Cracks 

Long Zhao*a, LinFeng Jiangb 
a 
State Key Laboratory of software Engineering, Wuhan University, Wuhan, China

 

b 
QiLu University of Technology, Shandong, China

 

zxcvbnm9515@163.com 

Crack detection based on digital image processing is more and more widely applied in the maintenance of 
concrete dam diseases. However, due to the complexity of the crack image, it is difficult to achieve high 
accuracy of the crack classification. To improve the shortcomings and deficiencies in cracks extraction and 
classification algorithm under crack detection system this article focuses on the application of general data 
field to effectively solve the problem of crack classification. We propose a new data field clustering method for 
classification of concrete dam cracks. Clustering is an important step when building a classifier for dam crack.  
Clustering is a process of discovering densely populated regions. In the data space, it groups a set of data in a 
way that maximizes the similarity within clusters and minimizes the similarity between two different clusters. 
The mutual information (MI) of two grids is a measure of the grid’s mutual dependence. This definition is 
useful in the field of clustering, because it gives a way to quantify the relevance between different grids. A data 
field clustering method for classification of dam cracks adopts the potential values within grid and potential 
values between different grids. Well-known crack classification methods are compared with our method. The 
experimental results show that the proposed method has an obvious increase on the precision and 
interpretability. 

1. Introduction 

Using digital image processing technology to identify and classify the cracks in the dam can help us to fully 
grasp the dam crack information, and provide a reference for dam maintenance management and disaster 
warning and forecast. Crack category is one of the most important information of the crack. After the 
recognition and differentiation of the concrete crack, some appropriate methods are needed to determine the 
type of crack. Different kinds of cracks are different to the dam body. Based on the characteristics of various 
types of cracks. This paper extracts the feature points that can effectively distinguish the cracks from the 
projection method based on the generalized data field, and obtains better classification results. In order to 
overcome the over-segmentation problem appeared after crack extracting, this paper proposes the concept of 
general data field, which is based on the characteristic that the ratio between grayscale change steep area 
and total area is statistically less in dam crack images, and serves the increase and decrease of gradient 
entropy after region merging as the criterion of judging region merging. Afterwards, combined with that 
criterion, this paper designs an adaptive algorithm which can calculate the threshold of watershed edge 
segmentation, and that algorithm can solve the over-segmentation problem in crack image extracting 
effectively. Clustering is one of the effective ways to solve the problem of crack classification. Clustering uses 
some evaluation criteria to choose a most significant grids and reduce the dimensions. This thesis has mainly 
studied the classification of crack images. The contribution of grid is shown by the sum of potential values in 
data field. In order to meet the crack parameters needs of maintenance, the length of transverse and 
longitudinal cracks and the minimum circumscribed rectangle area of block and reticular cracks have been 
selected and calculated. The rest of this paper is organized as follows. Section 2 discusses the related 
classification methods introduced for crack detection. Section 3 explains the data field and the steps of 
clustering. Our method is given in Section 4. The experiment of rival clustering methods are analyzed in 
Section 5. A conclusion is drawn in Section 6. 
 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1546115

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Zhao L., Jiang L.F., 2015, A data field clustering method for classification of concrete dam cracks, Chemical 
Engineering Transactions, 46, 685-690  DOI:10.3303/CET1546115  

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2. Related work 

The dam crack has some characteristics which can be used in the classification and damage degree of crack. 
The geometrical features such as length width ratio area and density are also proposed. K Ohno and M Ohtsu 
think the crack mode of cracking in concrete is normally changing from tensile mode to shear mode at 
impending failure. The classification of the cracks of the radial basis function neural network based on is 
designed. Li, H. proposed a method for blade crack classification based on the signals monitored by using a 
squared envelope spectrum. In the case of no intervention, accurate, automatic, real-time extraction of dam 
crack type and severity information. After extracting, crack images are always prone to cracked and 
incomplete. At the same time, traditional watershed algorithm has the advantage that it can maintain weak 
edge information good. Wen-Pei Sung et al proposed artificial neural networks to detect the damage of the 
dam in real time, and the better classification results are obtained, but the operation space and the speed of 
the algorithm are much slower. The new compound error function of BP neural network is designed, and the 
improvement of the training speed of neural network is improved. The distribution density is the percentage of 
the pixels in the image of dam crack. This definition can be understood as a one-way crack distribution density 
is small, and the distribution density of mesh cracks. But if there are two values of the noise points and the 
length of the crack length, the distribution density of the cracks is very close to the distribution density of the 
crack, which is more or less. So the distribution density of the characteristic value is simple and easy to use, 
but it can easily lead to the wrong type of some crack. Ioannis Valavanis and Dimitrios Kosmopoulos use the 
geometric and texture features to classify the damaged image. Noorsuhada Md No et al used the relationship 
between average frequency and RA value indicated clear trend with respect to crack classifications. Hence, 
this paper applies general data field to extracting of crack. 

3. Definition of generalized data field 

Data field sets each data in the dataset as an energy source which radiates its energy into the space and then 
generates a data field. The mutual effect among different data object is indicated by a field strength function, 
which might take various kinds of forms, such as nuclear form and gravitational form. The effect power at one 
place comes from different source could be overlaid, whose superposed result is named as potential value. 
Nuclear field strength on x of data field from y is calculated as follows. φ( ) = e (|| ||)                                                                                   (1) 
The first derivation of field strength on x of data field from y	is: 
F( ) = (y − x) ∗ m ∗ e | | 										                                                           (2) 
Impact factor is a parameter which controls the distance of mutual influence between two data objects. By 
defining an appropriate impact factor, data field model could describe the data distribution rather well. The 
clustering centers are the points which have local maximum potential values: 

φ(x) = | | ∑ m × K H (x − X )      (3) 
Where K(x) is a multivariate potential function, H is a positive-definitive 1×d matrix. n is the feature number of 
D. H is a non-singular constant matrix. Set hj is the jth data points of H.ℎ 	 = ∑ ( ( ) − ( )) .  
The data field measurement is calculated by a grid-based importance measure algorithm. The potential 
function accord the data points are estimated within the grid. The potential values of each data point are 
calculated in different grids, and then integrate all the potential values to calculate the weight of each grid. 

3.1 The steps of crack clustering 
The input and output of this method are as follows: Input:Multidimensional data items’ feature vectors, user-
specific grid number, user-specific impact factor parameter, noise thread function (optional).Output: clusters of 
cracks. This method is divided into the following steps: First, feature space is divided into grids, each data 
point is put into a grid to form a grid-based data space. Second, an adaptive generalized data field is built to 
calculate the potential value of each data point, and the distribution of the potential values is calculated based 
on the characteristics grid. Third, according to the distribution of characteristics space is calculated. The edge 
of cluster starts from the clustering center, the absolute value of first derivative potential value stops 
increasing. Partition feature space into grids and assign data items to grids, initialize impact factor, calculate 
the potential value and first derivative value. The last step is searching the clustering centers. Search points 
where first derivative potential value equals 0. Accord to the steps above, we can detect the edges of cracks. 
Search the neighborhood of clustering centers and mark all candidate grids. Filter candidate grids and detect 
full clusters with Flood-Fill algorithm. 

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Calculate impact factor σ. σ = max s × ifp                                                                                 (4) 
Where si represents the length traverse of each grid and it marks all these grids which contains local maximum 
potential value as candidate grids. Calculate potential value and first derivative potential value according to 
equator. > 0&& < 0,	1 ≤ < − 1																																																								 	 		 	(5)	
where  is the first derivative potential value of grid  on dimension i. A candidate grid could be a grid 
which contains clustering center (center grid in short) only if it existed to be candidate grid on all dimensions. 
For each center gridCenter = (v ,v ,…,v ), search its neighborhood and mark grids M  which satisfies: ≥ 																																																																														 	 	 	(6)	
Where	 ,1 ≤ ≤ ,	1 ≤ ≤  is the location of Grid  on the dimension i of feature space, and  
satisfies the same condition as well. Calculate noise thread t using the noise thread function [ ( )], where 

 is the quantity of data objects inside grid inside edges. Filter all grids whose 	 <t. Using flood-fill 
algorithm to finds out all connected area in grids. Each connected area corresponds to a cluster in the original 
feature space 
After preprocessing and segmentation of the image, the pixels of the crack region are 1, and the pixels of the 
background region are 0, and we use this feature to analyze all kinds of crack images. The specific method is 
as follows: (1) the digital image can be expressed in matrix. Target recognition systems usually extract 
features that have the following characteristics: the characteristic values of different samples from the same 
category should be very close, and the characteristics of samples from different classes should be different, so 
it is not relevant to extract information from the original data, so it is easy to distinguish between the various 
components of the original data. Feature selection and extraction of the basic tasks: first, to find the most 
discriminative description of the model, the two is to reduce the dimension of the description data. Practice 
has proved that the feature extraction is essential when the dimension of the data space is large. When the 
number of samples is small, too many features can also reduce the performance of classification and the 
complexity of computer. So it is very important to choose the most representative features. 
We were on the potential function of the image features are as follows: the image pixel statistics distribution 
histogram and Fourier descriptors as the basic feature. Aiming at the characteristics of the crack image, we 
have to carry out the vector processing of the crack profile in the training set, thus separating the single crack 
area. To get the crack area, we put all the cracks in the data field. So the data field changing trends of 
different kinds of cracks are obtained. In the data field, the point of the distance between the smaller class and 
the larger class is obtained. 

3.2 The classification standard of cracks 
Dam cracks can be divided into vertical and horizontal cracks according to the distribution. The longitudinal 
cracks along the dam axis, located in the central crest appears in a few, on the downstream side near the 
crest. Another common crack of the dam is the transverse crack, that is, the crack is perpendicular to the dam 
axial. 
Fine cracks occur on the surface, in a regular or irregular network. It is caused by shrinkage of concrete (or 
other cement). Although the fine cracks do not affect the structural integrity of the concrete, does not affect its 
durability and wear resistance, but it is very conspicuous, the impact is beautiful. 
Both vertical and horizontal cracks will damage the integrity of the dam and reduce the bearing capacity of the 
dam. Transverse joints will be cut or crack seepage dam body, when the depth is larger will cause leakage of 
the dam, thereby endangering the safety of the dam. Therefore, we should pay special attention to it. Special 
attention should be paid to the cracks in the downstream side of the dam. If there is a large gap in the seam, 
and there is a wrong sign on the upper and lower seam, it is also the initial stage of the landslide. The dam is 
in high temperature and low water level operation state, it is recommended to study the operating conditions, 
to grasp the temperature and water level changes in the production of panel defects and impact. Strengthen 
the dam safety monitoring, strengthen the monitoring of the seam change and seepage flow, analyze the data, 
and control the working state of the dam. According to the number of pixels and the nearest neighbor rule, the 
matrix is used to make the grid block, determine the direction of the crack and the direction of the connection, 
use the horizontal and vertical direction as the projection direction, and the two value matrix is projected on 
the X axis and the Y axis. Contains longitudinal binary image, the projection uniform distribution on the Y axis, 
the concentration distribution in the X axis; and transverse images contain, projection uniform distribution on 
the x-axis, concentrated on the Y axis; for the cracking and crack point projection uniformity on the X axis and 
the Y axis. The aggregation degree of the two valued image pixels is usually used to describe the image 
pixels, the noise is less, but the number of connected domains of the unidirectional crack is more likely to be 

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the same. So we adopt general data field to calculate the domains of cracks. The method of calculating the 
number connected domains in data space is able to distinguish the type of crack. 

4. Experiment 

Matlab is a high performance and powerful computing and simulation software. In the experiment, 180 kinds of 
crack images are used in the experiment, including 180 kinds of crack images, 100 images are used for 
training samples and 80 images are used for testing samples. 

 

Figure 1: Tree crack  

GA method which is proposed by E. Salari and X. Yu and SOM method which is proposed by Mathavan et al 
were used to compare with our classification method. Genetic algorithm using is simple and easy to operate. 
The chromosome length was 20, the population size was 17, and the maximum evolutionary algebra was set 
to 30, and the fitness function was set as the absolute value of the difference between predicted data and 
actual data.  

	
Figure 2: Horizontal crack 

 

Figure 3: Vertical crack 

 

 

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Figure 4: Mesh crack 

Table 1 shows the important factor of experiment environments. 

Table 1:  Experiment Environment 

Computers HP xw6600 Workstation 

Operation System Windows 7 Ultimate 

Software Platform Matlab R2014b 

Toolbox LIBSVM-3.18 

 
Different crack types occupy crack object as primes have relatively large differences, the transverse cracking 
and longitudinal cracking and other linear cracks often account for the whole dam image for a very small 
proportion. The unit area of crack object pixel number is less. Since the dam crack image has become the two 
value image matrix containing cracks, in each grid, a two value matrix is formed in general data field. The 
basic idea of the algorithm is to calculate crack geometry data center coordinates, and to coordinate geometry 
data field center as the center, then calculate external rectangular cracks in the number of pixels and the ratio 
of the rectangular area is rectangular crack pixels distribution density. If calculated density is smaller than 
given threshold, to expand outside the rectangle side length, then calculate the distribution of crack density, 
until the calculated value is larger than the threshold. 

4.2 The results of cluster 
Traverse all data objects and assign them into grids, record the quantity and average feature value of image in 
each grid. Represent the original feature space with these grids, each grid could be viewed as a data object 
with mass m and feature vector loc. 

Table 2: The right number of three methods 

Type  Test number SOM GA our method 

Horizontal 20 17 18 19 

Vertical crack 20 19 19 20 

Mesh crack 20 18 20 20 

Tree crack 20 17 18 19 

 
The effectiveness of our algorithm has been proved through the experiment. Our theoretical analysis and 
experimental observations reveal that our approach is the method of choice by offering a simple yet effective 
method and give a better understanding of crack classification problem for dam images. Through 
extraterritorial rectangle two pixels between the longest distances, short axis is to point to the joint normal to 
the long axis of the rectangle with the largest connected domain of secant line length. The ratio R reflect crack 
of linear features: in addition, inter pixel connectivity plays the important role of the moving target in the image 
boundary and region pixel is determined. 

5. Conclusion 

Inspired by field theory in physics, Deren Li et al proposed data field model to describe the interaction among 
data objects. Similar to physics, each data object is viewed as a particle with certain mass and radiates its 
data energy to the whole data field in order to demonstrate its existence and action in the tasks of spatial data 
mining. This paper adopts the method of crack classification based on the generalized data field. By the 
experiment, the characteristic value of the modified potential function can be used as the basis for 

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distinguishing between the cracks and the cracks. Our theoretical analysis and experimental observations 
reveal that our approach is an effective clustering method and give a better understanding of the clustering on 
crack images. Our method is efficient and detect clusters of arbitrary shape and insensitive to the outliers. 
Considering the fact that the distance of mutual effect between data objects in data field ,this method could be 
optimized by merge each if grids to be a large grid when calculating the potential and first derivative potential 
value. The data field mutual information is calculated in the grid. The effectiveness of this algorithm has been 
proved through a series of experiments. It is insensitive to the order of input images. The overall performance 
of this method is better than the other algorithms. 

Acknowledgement 

This work was supported by the funds of Shandong provincial water conservancy scientific research and 
technology promotion project. The project number is SDSLKY201320 (Research on hidden danger intelligent 
warning system of water conservancy security based on big data). 

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