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International Conference on Advances in Experimental Structural Engineering

November 8-9, 2013, Taipei, Taiwan

An Image Analysis Method on Crack Observations of a Cylinder RC Pier

Yuan-Sen Yang1, Chung-Ming Yang

2, Chang-Wei Huang

3, Chiun-lin Wu

4

1 Associate Professor, National Taipei University of Technology, Taiwan. E-mail: [email protected]

2 Ph.D. Candidate, National Taipei University of Technology, Taiwan3 Associate Professor, Chung Yuan Christian University, Taiwan4 Research Associate, National Center for Research on Earthquake Engineering, Taiwan

ABSTRACT

This paper presents an image analysis method on crack observations of a cylinder reinforced concrete pier. The

paper depicts the methodology and mathematical models of the image analysis method, as well as the analysis

flowchart, the image analysis algorithms used in this work, the image analysis tools, and the implementation of

the analysis software named ImPro Stereo. Finally, an application of this image analysis tool to an in-situ

full-scale bridge test is presented to demonstrate the performance and limits of this method.

KEYWORDS:image analysis, RC piers, crack observationslank line 10 t

1. BACKGROUND

Crack observations plays an important role in concrete experiments. The directions, patterns, and density of

crack distributions reveal different failure modes and many other significant information to researchers.

Conventionally, cracks are observed by suspending a test, allowing researchers to approach the concrete surfaces,

and manually sketching lines on the cracks. This crack observation procedure is a reliable way to record the

development of the cracks, however, can only be used only at the suspension of a test, and only if it is perfectly

safe to send human to the experimental area.

As the digital imaging technology is rapidly improving, image analysis offers an alternative and cost-effective

way for structural experimental measurement. Displacements, strain fields, crack detection, or even dynamic

motions can be captured and measured by using image analysis. Most of the image analysis works that requires

high precision and accuracy are applied in well-controlled indoor environment. Outdoor in-situ experiments are

normally involved with uncontrolled environment conditions such as strong wind, inconsistent light source, or

limited space for camera setup.

This paper presents an image analysis method that is designed for thin crack observations. The cracks are

considered to be thinner than that a dark line can appear on the crack in the image. Edge detection based

approaches are not considered in this method. Movement analysis method that have been developed in the

computer vision discipline was employed to analyzed the small movement in this method. The formula and the

procedure of the method is briefly introduced, followed by an application of this method to an in-site bridge pier

test.

2. FORMULA AND PROCEDURE

The procedure of the proposed image analysis method for an RC pier includes the following major steps: (1)

stereo calibration; (2) control points positioning; (3) surface formula approximation; (4) image rectification; (5)

displacement and deformation analysis; (6) visualization. The procedure was implemented into a tool named

ImPro Stereo [1]. Most of the computer implementation of the ImPro Stereo was built upon the MATLAB with

mixing language for external calls to OpenCV library [2]. This section introduces the mathematical formula andthe computer implementation of each step.

Stereo calibration estimates the extrinsic and intrinsic parameters of the stereo camera system. The extrinsicparameters are the geometrical relationship between the left and right camera, i.e., translational and rotational

matrices between two camera coordinate systems). The intrinsic parameters of each camera describe how toconvert an image point to a homogeneous plane (the z=1 plane of the camera coordinate), mainly including focal

lengths, image size, principal point, and lens distortion. The mathematical formula can be found in many


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literatures (e.g., [2]) and is not presented in this paper. There are many computer tools available for stereo

calibration. This work employed a camera calibration toolbox named Bouguets Camera Calibration Toolbox(BCCT) [3]. As the stereo calibration information can be found in general computer vision textbook or

documentations aforementioned and is not presented here into details.

Control points positioning calculates the 3D coordinates of the control points of the observed surface by using

the stereo triangulation technique. The number of control points should be sufficient to determine the locationand shape of the observed surface. For example, three points are required to determine a plane; four points arerequired to determine a cylinder surface. The selection of the control points depends on the mathematical

formula of the assumed observed surface. In this method, the control points in the first pair of photos (initial

photos taken by left and right cameras) are selected manually by the user (e.g., using the mouse). The control

points in later pairs of photos (those of the deformed specimen) are positioned by image tracing, such as the

template matching [2] or digital image correlation (DIC) [4]. After the control points are positioned on the

photos (i.e., in the image coordinates), their 3D coordinates can be estimated by stereo triangulation. In this work,

the observed region is on a cylinder surface that is defined by four control points, as shown in Figure 2.1(a). The

user is supposed to pick the control points P1 to P4 on the photos so that the P1, P2 and P3 are on the same

height of the cylinder, while the P4 and P1 are on the same vertical longitudinal line of the cylinder. The 3D

coordinates of the control points are then calculated by stereo triangulation.

P1 P2 P3

P4

X

YZ

(a) Control points defining the observed region (b) Surface formula (c) image rectification

Figure 2.1 Control Points of a Cylinder Surface

Control points positioning in this work was implemented by using MATLAB graphical user interface (GUI)with mouse operations, the BCCT [3] stereo triangulation and the OpenCV template match subroutine [2]. The

GUI allows the user to position the control points on the first pair of photos with facilitate of image panning and

zooming. If a control point is represented by a tiny corner pattern stuck on the specimen (as described in [5]), a

corner finding algorithm in the BCCT is used to precisely position the control point. OpenCV template match

subroutine is employed to position the control points image coordinates in the later pairs of photos. The 3D

coordinates of the control points during the time each pair of photos were taken can be estimated by casting their

image coordinates with intrinsic/extrinsic parameters of the stereo camera system into BCCTs stereo

triangulation.

Surface formula approximation estimates the assumed formula of the surface of the observed region, as shown in

Fig. 2.1(b). Actually the formula is predefined in advance and are written in a computer language form, and thesurface formula approximation only estimates a few parameters (or coefficients) of the formula. In this method,

it is assumed that the initial and deformed surface of the observed region can be described by the formula with

variable parameters. Images of the observed region will be projected onto the formulated surface in the following

image rectification step. If the observed region surface departs from the formulated surface, a certain amount of

spurious deformation of the surface will be induced. In this work, the formula is a cylinder surface. It is assumedthat the observed region surface of the pier is approximately a cylinder, and the spurious deformation is ignored

as this work focuses on crack observation rather than strain field measurement. The formula of the cylinder is

(2.1)

where the is a point on the central axis of the cylinder and is at the same height of P4, R is the radius of the

cylinder, , , and are three orthonormal unit vector of the cylinder coordinate system, while is thecentral axis. The is roughly the direction from P1 to P3, and slightly adjusted to ensure it is perpendicular to


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. The observed region is the in which his from 0 (height of P4) to H(close to height of P1) and is

from 0 (angle of P1) to (close to angle of P3).

It should be noted that the accuracy of the formula may be sensitive to the accuracy of the control points 3D

coordinates. For example, as the three orthonormal unit vector , , and are determined by the directions

of lines among P1-P2-P3 and P1-P4, the calculated vectors is sensitive to the error of P1-P4 direction. Errors

may be induced if the P1-P4 is not parallel to the central line of the pier.

Image rectification in this method is a process to generate an image that represents the surface of the observed

region. In this work, this process is similar to unfold the curved surface of the observed region to a rectangular

image, as shown in Fig. 2.1 (c). The first step is to generate a set of 3D re-sampling points by equation (2.1)

substituting uniformly distributed parameters hand . These re-sampling points are actually the points of a 2D

structured mesh uniformly distributed over the observed region. Each point is then projected to the photo of oneof the cameras, and the image coordinate of the projected point can be calculated (see Fig. 2.2(a)). The light

intensity (i.e., light intensity of grey level or red/green/blue levels) of the point can be interpolated from its

neighboring pixels of the photo (see Figs. 2.2(b) and (c)). The internal of hand (i.e., the density of the mesh)

depends on the image size of the rectified image. For example, if the increment of h(h) isH/1000, the rectified

image height will be 1000 pixels. To keep the aspect ratio of width and height, the handR are the same. To

preserve the image information of the original photo, the h should be no greater than the physical lengthequivalent to one pixel in the photo. In this work, the hand are set according to equations (2.2) and (2.3):

(2.2)

(2.3)

The factor 0.5 in equation (2.2) can be adjusted by the user. A small factor results in larger rectified images and

longer computing time in the following steps, while a small factor results in risk of losing image details in thephotos. Image rectification is quite time consuming in this version of ImPro Stereo, probably because this part is

implemented in Matlab scripts rather than a pre-compiled binary library. Generating a rectified image with a sizeof 1700 by 2400 pixels or so on an Intel Mobile 2.66-GHz T9550 CPU powered laptop costs more than 20

seconds.

h

a re-sampling point in 3D coordinate

a pixel of the re-sampling point

(a) re-sampling in 3D coord. (b) projecting to photo (c) generating rectified image

Figure 2.2 Process of Image Rectification

Displacement and deformation analysis estimates the displacement and deformation of the rectified images of

deformed pairs of photos with respect to the initial one. This process can be done by using DIC [4] or opticalflow analysis [6]. This work employed an optical flow analysis method implemented in OpenCV [2,6] mainly

because of its good performance in computing time and sub-pixel accuracy. Analyzing a rectified image with a

size of 1700 by 2400 pixels or so on aforementioned laptop costs less than only 0.2 seconds.

The final step is visualization. ImPro Stereo provides two visualization ways: presenting in plane plots (Fig.

2.3(a)) and projection on photos (Fig. 2.3(b)). Plane plots present displacement or deformation fields of the

observed region with color bars indicating field values of different colors. The perspective effect is removed so

that the size scale is consistent over the region. The projecting on a photo projects the field on the photo,representing where the observed region in an intuitive way.Blank line 10 t


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Blank line 10 t

(a) a plane plot (b) projection on a photo

Figure 2.3 Visualization Methods

3. IN-SITU TESTBlank line 10 p

This section presents the application of the proposed image analysis method for concrete crack observation in an

in-situ experiment of a bridge named Niu-dou located in I-Lan County, Taiwan. The in-situ test includes twocyclic tests on piers coded P3 and P4, respectively, and a pseudo-dynamic test on a pier coded P2. This paper

presents a partial ImPro Stereo application on P4. The images and data amount of the entire Niu-dou bridge

experiment is huge, and many of the follow-up image analysis, data correction and validation, numerical

simulation, and other related research works are still underway. This paper presents only a small part of research

work. Figure 3.1 (a) shows the experiment setup of a pier. Figure 3.1 (b) indicates the locations of the stereo

camera system and the observed region.

Observed region

Cameras

(a) Niu-dou bridge being tested (b)P4-pier setupFigure 3.1 The Niu-dou Bridge In-site Test

Blank line 10 tThe lower part of the bridge pier, including the observed region in this work, was painted white with regular

black grid lines, but there is no speckle painting. Speckle painting was normally used in the past experiments to

provide sufficient image features facilitating following image analysis [6]. However, speckle painting is not

generally acceptable for regions which cracks to appear are to be observed by the naked eyes. The black grid

lines painted in this test have interval of 0.1 meters along both horizontal and vertical directions. Besides theblack lines, grids between lines do not contain any artificial image features. Fortunately, the concrete surface

observed region is very rough, resulting in irregular light intensity and shadows, providing some features for the

image analysis (see Fig. 2.2(b)).

Figure 3.2 shows the rectified images after running the aforementioned stereo calibration, control pointspositioning; cylinder surface formula approximation; and the image rectification. For better image recognition,

the control points are selected on the intersections of grid lines. The observed region is a 40cm by 70cm curved

rectangle near the bottom of the pier. This region is selected only because the rectified images of this region

preserve good rectangle shape that are consistent with the black grid lines. In many other trials of observed


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regions, the rectified images are distorted improperly, probably due to the inaccuracy of the sketched grid lines.

As mentioned above, the parameters of the cylinder surface formula are sensitive to the accuracy of the controlpoints, which in this case are at the intersection of grid lines. Significant spurious deformation may be induced if

the control points P1-P4 are not parallel to the central axis or the P1-P2-P3 curve are not on the same horizon.

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Initial DR: +0.375% DR: +0.75% DR: -1.0% DR: -1.5% DR: +3% DR: 5%

ImPro Stereo

Figure 3.2 Rectified Images after Running Cylinder Rectification (DR: drift ratio of the pier)

In this work, the estimated strain yy fields were used to observe the concrete cracks. As the pier contains

sufficient ties for concrete confinement, the flexural failure mode occurred as was expected. Cracks appearedgenerally along horizontal lines. Horizontal cracks appear in the strain yy fields. It should be mentioned that the

estimated strain yy fields in this work contain more or less spurious deformation, and is only good for crack

observation, not for accurate strain measurement.

Figure 3.3 presents the observed strain yy concentration lines when the pier was deformed to drift ratio of 0.25%

(a2), -0.25% (b2), and -0.375% (c2). The (a1), (a2), and (a3) indicates the crack lines that sketched on the

specimen surface by researchers. In the figures, the manual crack sketched lines are additionally indicated by the

red dots for the ease of reading because the manual crack sketched lines on the specimen surface cannot appear

clearly in the figures. It can be seen that two horizontal crack lines appeared in the estimated strain yy field (a2)

when the drift ratio was only +0.25%. These cracks were not observed until the drift ratio achieved +/- 0.375%.

(a1) manual (a2) image analysis (b1) manual (b2) image analysis (c1) manual (c2) image analysis

(a) Test Point 1 (DR: +0.25%) (b) Test Point 2 (DR: -0.25%) (c) Test Point 4 (DR: -0.375%)

Figure 3.3 Comparison of Manual Crack Sketches and Image Analysis

However, not all of the image analysis of the P4 pier test is successful. In addition to the spurious deformation

that might be induced by the inaccuracy of control points on the grid lines intersection, image interference


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induced by the sunlight changes (see Fig. 3.4) and manual crack sketched lines, and unexpected slight camera

movement during hours of test duration, are some of the challenges of the image analysis work of this test.Further studies and new solutions are underway to conquer these challenges.

t

(a) 12:25PM (b) 12:51PM (c) 1:17PM (d) 1:57PM

Figure 3.4 Different shadow patterns on observed region at different time through the test

4. SUMMARY

This paper presents the formula and procedure of an image analysis method for crack observations in a concrete

pier test. By using cylinder formula approximation and image rectification, the surface of the observed regions

can be unfolded and be presented in a plane image for following displacement and deformation analysis. An

experiment study of an in-situ bridge cyclic test shows that the proposed method presents concrete cracks even

before they were observed by naked eyes. The computer implementation of this method, ImPro Stereo, can be

downloaded on the Internet [1].

More studies are required to solve the following challenges: (1) spurious deformation induced by the inaccuracy

of control point positions; (2) long computing time on image rectification; (3) image interferences induced by

sunlight changes and manual crack sketched lines; and (4) slight camera movement during long testing time.

AKCNOWLEDGEMENTThe research work reported in this paper was partially supported by the National Center for Research on

Earthquake Engineering and National Science Council (projects number: NSC 99-2221-E-027-042-MY3 and

NSC 101-2211-E-126-MY3).

REFERENCES

Blank line 10 pt1. Yang, Y. S., Chen, H. M., Lee, C. S., Jien, Y. H., Hu, Z. H., Lai, W. Z. (2013). ImPro Stereo. Official site of

the ImPro Stereo. Software available at web address: https://sites.google.com/site/improstereoen/2. Bradski, G., and Kaehler, A. (2008).Learning OpenCV Computer Vision with the OpenCV Library, O'Reilly

Media.

3. Bouguet, J. Y. (2013). Camera Calibration Toolbox for Matlab. Software available at web address:http://www.vision.caltech.edu/bouguetj/calib_doc/

4. Tung, S. H., Shih, M. H., and Sung, W. P. (2008). Development of Digital Image Correlation Method toAnalyse Crack Variations of Masonry Wall. Sadhana, 33: 6, 767-779.5. Yang, Y. S., Huang, C. W., and Wu, C. L. (2012). A Simple Image-based Strain Measurement Method forMeasuring the Strain Fields in an RC-Wall Experiment,Earthquake Engineering & Structural Dynamics, 41:

1,1-17.

6. Bouguet, J. Y. (2000). Pyramidal Implementation of the Lucas Kanade Feature Tracker Description of theAlgorithm, Technical report, Microprocessor Research Labs, Intel Corporation. Available athttp://robots.stanford.edu/cs223b04/algo_tracking.pdf

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