Development of Stereo Image Analysis for Measuring Small Deformation

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 171 (2017) 1256 – 1262

Sustainable Civil Engineering Structures and Construction Materials, SCESCM 2016

Development of stereo image analysis for measuring small deformation Tomohiro Yokoyamaa, *, Takashi Matsumotob a

Graduate School of Engineering, Hokkaido University, Kita 13 Nishi 8 Kita-ku Sapporo, 060-8628, Japan b Faculty of Engineering, Hokkaido University, Kita 13 Nishi 8 Kita-ku Sapporo, 060-8628, Japan

Abstract Carbon Fiber Reinforced Polymer, CFRP, is a promising material for the application to bridge girders. Since it is anisotropic and brittle, it is not easy to grasp its damage and fracture processes experimentally. In such a case, image analysis is able to capture characteristic strain distributions before fracture. In previous studies, CFRP box beams were tested under 4-point bending loading, and image analysis was conducted. However, because the image analysis was limited to 2D in-plane deformations, it was not able to capture 3D deformations. This study aims at developing stereo image analysis for measuring small deformation such as out-of-plane deformation. © 2017 2017Published The Authors. Published by Elsevier © by Elsevier Ltd. This is an openLtd. access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of SCESCM 2016. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of SCESCM 2016. Keywords: CFRP; anisotropic; brittle; stereo image analysis; small deformation; out-of-plane deformation

1. Introduction Recently, maintenance and repair of infrastructure is attracting more attention than before because of the aging of infrastructure. Carbon Fiber Reinforced Polymer, CFRP, is a composite material which is light weight, high strength and high corrosion resistant. It is used widely in the field like aerospace industry, car industry and sports products. In civil engineering, it is employed as a repair and strengthening material of bridge piers and beams. Furthermore, with the objectives of high durability and low maintenance cost, it is going to be employed as a main member like a

* Corresponding author. Tel.: +81-011-706-6172; fax: +81-011-706-6172. E-mail address: [email protected]

1877-7058 © 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of SCESCM 2016.

doi:10.1016/j.proeng.2017.01.419

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bridge girder. In order to design a CFRP member based on its ultimate state mechanisms, it is necessary to understand the effects of laminate structure and anisotropy. However, due to the brittle nature of ultimate state of CFRP, it is difficult to grasp the damage and fracture processes of CFRP [1, 2]. In such a case, image analysis is able to capture characteristic strain distributions before fracture. In previous studies, CFRP box beams were tested under 4-point bending loading, and image analysis was conducted. However, because the image analysis was limited to 2D in-plane deformations, it was not able to capture 3D deformations in the reality [3]. This study aims at developing stereo image analysis for measuring small deformation by taking and analyzing stereo images. The computer program of image analysis consists of lens distortion removal, threshold determination, image binarization, disparity measurement by digital image correlation and 3D coordinate mapping. With the stereo image analysis, small deformation such as out-of-plane deformation in CFRP beams under bending can be captured. 2. Procedures of stereo image analysis 2.1. 3D coordinate In photogrammetry, it is known that 3D coordinate can be obtained from stereo images. 3D coordinate (X, Y, Z) is given by X

Y

Z

x1 B x1  x2

y1 x1  x 2 C x1  x2

(1)

B

(2)

B

(3)

where B is inter-lens distance, and C is focal length. B and C are constant. (x1, y1) is 2D coordinate of left image and (x2, y2) is 2D coordinate of right image. The origin of (X, Y, Z) is O. The origin of (x1, y1) is O1, and the origin of (x2, y2) is O2 (Fig. 1). In this study, the left image is taken as a reference for two stereo images. Based on the measurement points set on the left image, disparity (x1 - x2) is measured by digital image correlation, and 3D coordinate is computed.

Fig. 1. Principles of photogrammetry.

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2.2. Image capture and processing Image capture was conducted with a commercially available digital stereo camera, FUJIFILM FINEPIX REAL 3D W3, which has two image sensors of 3648 × 2432 pixels (Fig. 2 and Fig. 3). The target area of image analysis is the web surface of flexural span and partly of shear span. A random pattern was made by using a spray so that digital image correlation method could be used for CFRP specimens. Image is changed to a grayscale image of 256 levels, and furthermore to a binary image. Image binarization uses a threshold value, and it is processed by discriminant analysis method. The threshold makes separation of two classes the highest (Fig. 4) [4].

a

b Fig. 2. Test setup (a) digital stereo camera; (b) image capture condition.

a

b Fig. 3. Stereo images (a) left image; (b) right image.

a

b

c

Fig. 4. Image binarization (a) original; (b) gray scale; (c) binary (threshold is 184).

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2.3. Disparity measurement Measurement points for image correlation and 3D coordinate computation is set as follows. Measurement points of 52 points in the horizontal direction and 20 points in the vertical direction are placed at the interval of 25 pixels (Fig. 5). Mask image (150 × 150 pixels) is cut around a measurement point of the left image, and region image (700 × 300 pixels) is similarly cut from the right image. The maximum cross-correlation coefficient between the mask image and the region image indicates the corresponding area in the region image (Fig. 6). In this manner, disparity measurement is conducted at all measurement points. The result of cross-correlation coefficient at a measurement point of picture (Fig. 5) is shown Fig. 6, and its disparity is measured as 457 pixels.

Fig. 5. Measurement points (52 × 20).

a

b Fig. 6. Disparity measurement (a) mask image; (b) region image.

Cross correlation function between two images is given by

 f g k , l

p p

¦ ¦ f i, j g i  k , j  l

(4)

i 1j 1

where g (i, j) is the left image, f (i, j) is the right image, p is the number of vertical and horizontal pixels, and f i, j is the conjugate of f (i, j). By searching for the coordinate (k, l) to give the maximum correlation, it is possible to obtain the disparity of a measurement point. As a result, disparity is measured, and 3D coordinate is computed. 2.4. Lens distortion removal Lens distortion is caused by the optical design of a lens, and is included in all images. In order to conduct photogrammetry, it is necessary to remove lens distortion. If photogrammetry is conducted with lens distortion, good performance cannot be obtained. In this study, lens distortion removal is operated by correction functions. They are determined by the comparison between distorted and undistorted values of 3D coordinate. Graph paper with 10 mm grid is captured with the stereo

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camera from the distance of 500 mm. Distorted 3D coordinate of each grid point is measured by the procedures of 2.1. to 2.3., and it is compared to undistorted 3D coordinate. For example, Fig. 7 shows lens distortion of upper right of image. The correction functions are made from center of image.

a

b Fig. 7. Lens distortion (a) whole area of image; (b) upper right of image.

The correction functions are given by f X ( x1 , y1 )

f Y ( x1 , y1)

f Z ( x1, y1)

Xu X

Yu Y Zu Z

(5)

(6)

(7)

where f (x1, y1) is a correction function of (x1, y1), (x1, y1) is 2D coordinate of the left image, (Xu, Yu, Zu) is undistorted 3D coordinate and (X, Y, Z) is distorted 3D coordinate of each grid point that is measured by the procedures of 2.1. to 2.3.. Then, undistorted 3D coordinate of CFRP specimens is computed with correction functions. By multiplying distorted 3D coordinate by the correction functions, undistorted 3D coordinate is computed. The correction function is successfully removed lens distortion. 3. Results of stereo image analysis Stereo image analysis is conducted for three types of CFRP box beams which were tested under 4-point bending loading to fracture. They are named as QI (Quasi-Isotropic), HB (Hybrid) and CP (Cross-Ply), based on the difference in laminate structure, and their laminate structures are shown in Table 1. For example, in [0/90]5/[90/0]5, each number means the fiber orientation angle of the corresponding layer. The subscript, 5, indicates that five [0/90] sets are continuously stacked. The fiber used is carbon, except for high-strength polyethylene in diagonal layers of HB [3]. The results of stereo image analysis are shown Fig. 8, Fig. 9 and Fig. 10. Unit of 3D coordinate is mm. Measurement points are grid points of horizontal and vertical lines, and the optical axis of the camera is perpendicular to two thick red lines. The 3D coordinate can be seen from all direction so it shows many knowledge. About a crack of QI, hand measurement shows that the skewed and wide crack has its height of 2.5 mm. Stereo image analysis shows that the height is 2.2 mm (Fig. 8). About a vertical and thin crack of HB, hand measurement shows the height of 1.0 mm, while stereo image analysis 1.0 mm (Fig. 9). And, about a vertical and thin crack of CP, hand measurement shows 3.0 mm, while stereo image analysis 2.0 mm (Fig. 10). Therefore, 3D coordinate of

Tomohiro Yokoyama and Takashi Matsumoto / Procedia Engineering 171 (2017) 1256 – 1262

stereo image analysis agrees well with that of hand measurement. The hand measurement is a trial. So it is less accurate. In future, microscope measurement will be conducted. Table 1. Laminate structures of specimens for bending tests. Name

Laminate structure

QI

[0/45/-45/90]5/[90/-45/45/0]5

HB

[0/45/-45/90]4/[90/-45/45/0]4

CP

[0/90]5/[90/0]5

Table 2. Height of clacks.

a

Name

Hand measurement

Stereo image analysis

QI

2.5 mm

2.2 mm

HB

1.0 mm

1.0 mm

CP

3.0 mm

2.0 mm

b

c

d Fig. 8. QI (a) left image; (b) left image with grid line; (c) crack; (d) 3D coordinate.

a

b

c

d Fig. 9. HB (a) left image; (b) left image with grid line; (c) crack; (d) 3D coordinate.

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a

c

b

d Fig. 10. CP (a) left image; (b) left image with grid line; (c) crack; (d) 3D coordinate.

4. Conclusion Stereo image analysis is successfully developed for the measurement of small deformation in CFRP specimens. It allows to compute 3D coordinate and to measure small deformation such as out-of-plane deformation. If the stereo images are captured during 4-point bending loading, damage and fracture processes can be analyzed with this stereo image analysis. Acknowledgements This work was supported by JSPS Grant-in-Aid for Scientific Research (B) Grant Number 15H04028. References [1] H. Sakuraba, T. Matsumoto, and T Hayashikawa, A study on the flexural behavior of CFRP box beams with different laminate structures, Keynote Lectures and Extended Abstracts of the Twelfth East Asia-Pacific Conferences on Structural Engineering and Construction (EASEC-12), 539-540, 2011 (in Japanese). [2] H. Sakuraba, T. Matsumoto, and T. Hayashikawa, Flexural strength of CFRP box beams with different laminate structures, ASEAN Engineering Journal Part C, 2(1), 65-75, 2013 (in Japanese). [3] H. Okamatsu, T. Matsumoto, T Hayashikawa, and X. He, Image analysis of damage and fracture process of CFRP beams under flexural loading, Proceedings of Hokkaido Chapter of the Japan Society of Civil Engineers, JSCE, Vol.68, A-22, 2011 (in Japanese). [4] N. Otsu, A thrshold selection method from gray-level histogram, IEEE transaction Systems, Man and Cybernetics, vol.9, pp. 62-66, 1979