Computers & Geosciences 57 (2013) 77–80

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Computers & Geosciences

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Automatic quantification of crack patterns by image processing$

Chun Liu n, Chao-Sheng Tang, Bin Shi, Wen-Bin SuoSchool of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, PR China

a r t i c l e i n f o

Article history:Received 4 January 2013Received in revised form25 March 2013Accepted 9 April 2013Available online 20 April 2013

Keywords:CrackQuantificationGeometric parameterImage processingCIAS

04/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.cageo.2013.04.008

and software for the image processing de online: http://acei.cn/program/CIAS.esponding author. Tel.: +86 25 85386640.ail addresses: oxtown@gmail.com,@nju.edu.cn (C. Liu).

a b s t r a c t

Image processing technologies are proposed to quantify crack patterns. On the basis of the technologies,a software “Crack Image Analysis System” (CIAS) has been developed. An image of soil crack network isused as an example to illustrate the image processing technologies and the operations of the CIAS.The quantification of the crack image involves the following three steps: image segmentation, crackidentification and measurement. First, the image is converted to a binary image using a cluster analysismethod; noise in the binary image is removed; and crack spaces are fused. Then, the medial axis of thecrack network is extracted from the binary image, with which nodes and crack segments can beidentified. Finally, various geometric parameters of the crack network can be calculated automatically,such as node number, crack number, clod area, clod perimeter, crack area, width, length, and direction.The thresholds used in the operations are specified by cluster analysis and other innovative methods.As a result, the objects (nodes, cracks and clods) in the crack network can be quantified automatically.The software may be used to study the generation and development of soil crack patterns and rock fractures.

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1. Introduction

Quantitative analysis of crack pattern is an important aspect ofthe study of cracking behavior of soils and rocks. The shape, size,ruggedness, connectivity and branching of the crack patterns arenot only associated with their historical stresses and strains, butalso have implications for their future stability and functionality(Preston et al., 1997; Tang et al., 2008). Traditional manualcharacterization of the crack pattern is associated with low-accuracy, low-efficiency and artificial errors. In certain cases, theoriginal crack pattern can be disturbed by human activities andequipment, which usually results in large measurement errors(Lima and Grismer, 1992; Dasog and Shashidhara, 1993).

Advancement in the computer hardware and software capabil-ities has made image analysis a new and efficient tool that can beapplied to process crack images (Yan et al., 2002). So far, with theaim to investigate the dynamics of crack formation, certain imageprocessing technologies have been introduced to analyze thegeometry of cracks. However, crack networks are complexsystems, which involve crack segments, nodes, and the clodssurrounded by the cracks. Current tools are only limited to thequantification of basic geometric parameters of cracks, such ascrack direction (Lakshmikantha et al., 2009), crack shape (Liu et al.,2008), fractal dimension (Baer et al., 2009), etc. The advance in the

ll rights reserved.

eveloped in this paper are

research of cracking behaviors of materials requires a new tool toquantify crack networks and the geometry of all the objects incrack networks.

In order to quantify the geometry of crack networks, a software“Crack Image Analysis System” (CIAS) has been developed. By usingthis software, various geometric parameters can also be calculatedautomatically, such as node- and crack-numbers, clod area, clodperimeter, crack area, width, length, and direction.

2. Image processing of crack image

2.1. Preparation of crack image

In order to illustrate the image processing technologies and theoperations of the CIAS, an image of a laboratory soil crack wasused as an example. A plate of soil slurry was placed in a dry-ovenwith constant temperature 40 1C, and the final soil crack pattern isshown in Fig. 1a. Note that the figure represents the central part ofthe sample, an area which is 120�120 mm2 (1008�1008 pixels)in size. The cracks and the background are distinguished accordingto their different gray levels. Therefore, the brightness of cracksand background should be quite different. The photos were takenin moderate light condition, and the direction of camera wasperpendicular to the crack plane.

2.2. Image segmentation

As shown in Fig. 1b, the two crests in the gray-level histogramof the image represent the cracks and the clods. The global

Fig. 1. (a) Original crack image and (b) gray-level histogram and cluster analysis are used to distinguish the cracks and clods. (c) Binary image with white and black spots,bottom right side shows a discontinuous crack, which can be repaired by crack restoration (Fig. 2), and (d) the bridge between spots and real clods are eliminated usingClosing, and spots are removed.

Fig. 2. Schematic diagram of clod division and crack restoration (a) two clodsconnect with each other via a crack space (see Fig. 1c). (b) The cracks A are dilatedby a structuring element B, (c) Seed Filling is used to identify the two isolatedregions, S1 and S2. (d–e) The white pixels are integrated to nearby seed clods usingthe Merging algorithm. (f) The crack is repaired along the interface between clods.

C. Liu et al. / Computers & Geosciences 57 (2013) 77–8078

threshold to segment the image can be determined using a clusteranalysis method: (a) by using a given threshold T, the image can bedivided into two pixel sets: the white pixels (W), of which thegray-level is greater than T, and the black pixels (K), whichincludes the remaining pixels. (b) Let GW and GK represent theaverage gray level of the pixel sets W and K, respectively. The newthreshold is defined as the average of GW and GK.

The average gray level of the image is used as the initialthreshold. Then, repeat steps (a) and (b) until the thresholdconverges to a constant value, which is the optimal threshold.As shown in Fig. 1b, the optimal threshold is between the two crestsin the gray-level histogram, and as a result, the crack network isdiscriminated from the background automatically (Fig. 1c).

2.3. Spot removal

There are a large number of small spots in the binary image,such as white dots within the cracks and black spots over the clods(Fig. 1c). Isolated white regions (includes clods and spots) wereidentified using the Seed Filling algorithm (Yu et al., 2010). Thesedots and spots were then removed according to their differentsizes (Liu et al., 2011). Since the black and white spots are muchsmaller than the cracks and the real clods, the spot threshold canalso be specified using the cluster analysis method. The CIAS alsoprovides the traditional Closing operation (Gonzalez and Woods,2002) to reduce the noise (Fig. 1d).

3. Crack network identification

3.1. Clod identification and crack restoration

In the crack image, the soil block is divided into many smallclods, which can be identified using the Seed Filling algorithm(Yu et al., 2010). However, due to undesired image noise, some originalcontinuous fine cracks may become discontinuous in the binary image(bottom-right side of Fig. 1c). As a result, two neighboring clods mayconnect with each other via the bridge between them.

A clod division method is proposed to divide the clods and torepair the cracks. (1) First, a dilation operation (Gonzalez andWoods, 2002) is applied to the binary image to eliminate thenarrow bridge between clods. In this way, the crack space is fused(Fig. 2a–b), since the diameter of the space is smaller than thediameter of the dilation structuring element B. (2) As the space(i.e. bridge) has been eliminated, the two isolated clods (S1 and S2in Fig. 2c) can be identified using the Seed Filling algorithm

(Yu et al., 2010). (3) In Fig. 2d–e, the pixels of the dilated partsare integrated into the seed regions using the Merging algorithm(Liu et al., 2011), and the whole region is then divided into twoclods. (4) Finally, the crack is bridged along the interface betweenclods (Fig. 2f).

3.2. Crack identification

The cracks and nodes can be identified by the following steps:

(1)

The one-pixel-width medial axis of the crack network can beextracted by the Skeleton algorithm (Lakshmikantha et al., 2009).However, this procedure tends to leave parasitic branches, whichcan be cleaned up by Pruning (Fig. 3b; Gonzalez and Woods,2002). Generally, the length of the parasitic branch is less than thecrack width, and therefore the maximum crack width can be usedas the default Pruning threshold.

(2)

For each medial axis pixel, track its 8-neighbors in clockwisedirection. Let N represent the time that pixel color changes

Fig.netw

C. Liu et al. / Computers & Geosciences 57 (2013) 77–80 79

from black to white. As shown in Fig. 3b, if N¼2, it is a normalmedial axis pixel (P1); if N¼3, it is recognized as an intersec-tion (I2); and If N¼1, the current pixel is an end node.

(3)

Track the pixel from a node along the medial axis untilmeeting another node; then, a crack medial axis is recorded.The remaining crack pixels can be integrated to a crack axisusing the Merging algorithm (Liu et al., 2011).

4. Geometric parameters

4.1. Area and perimeter

The area and perimeter measurements are basically pixelcounting and distance summation of boundary pixels, respectively.Since lines or curves are serrate at the micro scale, application oftraditional methods (distance summation) incorrectly predicts agreater perimeter. Therefore, an optimized method (Liu et al.,2011) is used to calculate the perimeter, based on the principle ofremoving redundant boundary pixels. According to Liu et al.(2011), the deviation percentages of the traditional perimetersare greater than 5%, while the values using the improved newmethod are within 0.2%.

4.2. Clod length, width and direction

Feret diameter (Sezer et al., 2008) was used to calculate thewidth, length and direction of the clod. The Feret diameter isdefined as the orthogonal distance between a pair of the paralleltangents to the feature at a specified angle to the unit. The clodlength and width are the maximum- and minimum Feretdiameters whereas the clod direction is defined as the directionof maximum Feret diameter.

Fig. 4. Flow chart of the image processing operations and result images.

4.3. Crack length, width and direction

Crack length is defined as the cumulative length of the crackmedial axis pixels between two nodes, such as I1I2 of Fig. 3b.As shown in Fig. 3c, the crack width around a medial axis pixel (O)is defined as the summation of distance to two boundary pixelsA and B, which are the closest pixels to the pixel O. The classic leastsquare method is used to calculate the slope of the cracksaccording to the coordinates of the medial axis pixels. The crackslope can then be easily converted to the crack direction.

3. Schematic diagram of crack identification. (a) There is a parasitic branch in the sork is used to identify nodes (I1 and I2) and (c) Crack pixels are merged to the cra

5. The CIAS and results

A program “Crack Image Analysis System” (CIAS) has beendeveloped according to the methods (see article footnote). Allthe methods were coded from scratch using VC# programminglanguage in the Windows operating system. The program isautomatic, and the user's operation involves two steps: (1) importthe crack image into the program and segment it; and (2) set theelement radius for crack restoration, and click “Auto analysis”.The program then processes the image as shown in Fig. 4 andpresents the results. The crack image includes 47 clods and 112crack segments. Fig. 5 shows the distributions of number of cracksat different length and width. The crack lengths and widthsdistributions range from 29.7 to 261.4 and from 1.4 to 29.1 pixels,respectively (1 pixel represents 0.119 mm).

Up to date, the CIAS have been used to study the fundamentalsof soil cracks (Tang et al., 2008, 2011). Further, the software canalso be used to quantify rock fractures.

Acknowledgments

The authors would like to give special thanks for Mr. ShangDeng and anonymous reviewers to correct this paper in Englishwriting and expression. Financial support from key project of

keletons of the crack, which can be cleaned up by Pruning, (b) medial axis of crackck axes to identify crack segments.

Fig. 5. Distributions of crack length and width.

C. Liu et al. / Computers & Geosciences 57 (2013) 77–8080

Natural Science Foundation of China (NSFC, no. 41230636) andNational Basic Research Program of China (973 Program, no.2011CB710605) is gratefully acknowledged.

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