Real Time Displacement Measurement of an image in a 2D Plane

Transcription

1 International Journal of Scientific Research Engineering & Technology (IJSRET), ISSN Volue 5, Issue 3, March Real Tie Displaceent Measureent of an iage in a 2D Plane Abstract Prashant Walia 1, Prof. Bhupal Singh 2 #1 M.Tech Research Scholar (A&R) ME Departent Ajay Kuar Garg Engineering College, Ghaziabad #2 HoD, Deapartent of Electrical Engineering Ajay Kuar Garg Engineering College, Ghaziabad A two diensional displaceent of an iage on a plane will be easured with one caera. However, the ensuration ethod desires the advanced standardization of the coordinate syste and of the caera states. The developed 2d displaceent ensuration ethodology can find the displaceents of several four-point LED (Light Eitting Diode) arkers, while not the advanced calibrations. With our ethodology, the caera paraeters, that characterize the caera standing, will echanically be deterined with four positions of the lighting LED on the native organization. The highresolution and high-speed caera was used for the event of code and for the displaceent ensuration. The resolution power for every onochroatic eight bits resolution, and therefore the sapling interval was one hundred ties per second. it was confired that our ethodology ight easure the displaceent with enough resolution power, for the ai of the displaceent ensuration by the big scale extensoeters. Key words: Displaceent Measureent, 2D Measureent, Real-tie Measureent, Iage Processing, LED Marker I. Introduction The easureent of positions, displaceent and strain with caera iage is useful for the evaluation of the structures, because of its non-destructive and noncontacting technique [1-4]. The authors developed the 3Dposition easureent syste with several high-speed caeras, and used it for the 3D-easureent of structures subitted to vibration testing [5, 6]. The 2D-easureent, by detecting the light-arkers, was also developed to detect the strain distribution on the wooden board, which suffered the shear force of the testing [7, 8].For the 3D easureent, the caera paraeters, which connect true 3D space and caera coordinates, should be precisely deterined before easureent. For the deterination of the caera paraeters, the relation between the 3D coordinates in true space, and 2D coordinates on the caera screen, was required at ore than six points. However, if the oveent of the target is liited to the plane, the caera paraeters can be deterined fro the position inforation of only four points. In this paper, the authors introduce the special arker with four LED lights to realize autoatic calibration of the caera paraeters for the 2D displaceent easureent, by iage processing. The experients for the evaluation of the accuracy of the experiental results, the usefulness of this easureent ethod was confired, for this type of testing. II. Principle of Measureent If the target points ove in a plane, the position of the target points are deterined by adopting the oblique/perspective coordinate syste on the caera screen as shown in Fig. 1. In general, the relation between the caera screen coordinates (X, Y) and the true 3D space coordinates (x, y, z) is given by the following equations: C 11 x + C 12 y + C 13 z + C 14 C 31 xx C 32 yx C 33 zx = X (1) C 21 x + C 22 y + C 23 z + C 24 C 31 xy C 32 yy C 33 zy = Y where, Cij (i=1,2,3; j=1,2,3,4) are eleven real nubers representing the linear caera paraeters. A. Deterination of caera paraeters There are eleven Cij real nubers representing caera paraeters. However, if the target point only oves in a x- y plane as shown in Fig.1, then the z-coordinate is zero and the Eqs.(1) are rewritten as follows: C 11 x + C 12 y + C 14 C 31 xx C 32 yx = X (2) C 21 x + C 22 y + C 24 C 31 xy C 32 yy = Y The equations (2) have eight Cij paraeters and they can be solved with four sets of relations of (x,y,0) and (X,Y). The authors suggest the target arker, which has four LEDs at the top of the diaond as shown in Fig.2. The lengths 2a and 2b ean the diagonal lengths of the diaond. The x-coordinate is set to the longer diagonal direction and the y-coordinate to the shorter diagonal direction. The local coordinates, with the origin in the center of the diaond, are set on each four points LED arker. The caera paraeters for each four-points arker Cij can autoatically be obtained fro the Eq.(3) fro the first caera iage of the arker a ax a 0 1 ay a ax a 0 1 ay 2 0 b b b b C X 0 C 12 C 11 1 Y X 2 0 C Y bx C 21 = 2 X by C Y by C 4 32 easureent were perfored in the laboratory. Fro our (3) bx 4 C31 X 4 Y 4

2 Volue 5, Issue 3, March where, (Xi, Yi ) (i = 1 4, and representing the arker s nuber) denote the positions of the four LED on the caera screen coordinates as shown in Fig. 3. It is assued that the target oves on the (x, y) plane twodiensionally. The displaceent (x, y) of each arker is calculated by Eqs.(2) substituting Cij to Cij. The process of calculation of the displaceent only needs the size of the arker s diaond (2a,2b). B. Calculation process of the arker displaceent The displaceent of the arker (x, y) is calculated by Eqs.(2) and (3). The caera paraeter Cij ust be obtained before the displaceent easureent, as an initialization process. a) Initialization process Before starting the easureent, the caera paraeters ust be deterined for each four-points arker. The following steps ust be carried out as an initialization processes: 1) Input the size of arker s diaond (2a, 2b) 2) Capture the iage at the zero displaceent state. 3) Search four-point diaonds on iage, and autoatically set their local coordinate. 4) Calculate Cij for each four-points arker with Eq.(3). b) Calculation process of displaceent After starting the easureent, the following processes ust be perfored for each frae. In our easureent, the frae speed (sapling speed) is 100 fraes per second. 1) Capture the iage. 2) Search four-point diaonds near the position of the four- points arkers on the iage. 3) Calculate the center of the four-points arkers on the iage, and obtain their 2D positions using Eqs.(2). The displaceent of the four-points arker corresponds to the average value of oveents of the four lights. III. Equipent and Measuring Method A) Equipent Two kinds of four-points arkers and one high-speed caera are used in the experients. Figure 4 shows the arkers and a caera. The sizes of the four-points arkers are (132.1, 91.4) and (69.5, 42.5), as (2a, 2b) in Fig.2. The size of the digital iage is 1024 x 768 pixels and the resolution for each pixel is 8 bits gray scale. The focus distance of the lens is 25. The real-tie tracking and easureent of the displaceent of several arkers are perfored by a Core i5, 3.2GHz coputer. The sapling interval is 0.01 second. The coputer has a 16bits 2channel D/A converter and two displaceents can be outputted as voltages in the -10V to 10V range. B) Detection of the four-points arker The LED points appear as the set of the high bright pixels of diaeter d (d is fro 4 to 10 pixels) on the iage, therefore the position of the LED points can be detected as the center of the set of those pixels [6],[7]. The positions of the four-points arkers are detected with the structure of the diaond shape. As two diagonals divide each other in half for the diaond, the four-points arkers can be autoatically found with the condition of the diaond shape. The autoatic search of the arkers ust be carried out at the initialization process. When the iss setting of the search occurs, the collection and the odification can be ade by anual labor. Fig. 3 Local coordinates of -th four-points arker Fig.1 Perspective coordinates on a caera screen (a) Large Marker (b) Sall Marker Fig. 2 Two kinds of four points LED arkers used in the experient (a) Two kinds of arkers (b) High-speed caera Fig. 4 Photographs of two kinds of four-points arkers (sall and large) and a high-speed caera

3 Volue 5, Issue 3, March C) Real tie processing To realize the real-tie easureent faster than 0.01 second for each frae, the search of each LED point of the arker follows the partial iage of its neighborhood. The iage data, that should be handled, becoes less than 10% of full iage by searching for only a partial neighborhood iage. D) Measuring ethod The displaceent can be easured fro any view position of the caera, theoretically. Each four-points arker has the individual local (x, y) coordinates, therefore it is possible to easure the displaceents of several fourpoints arkers at the sae tie. Figures 5 (a) and (b) show the conditions of two kinds of experients. Experient A, as shown in Figs.(a), is to check the independence of the caera view point. Large four-points arker is oved three different direction with a linear actuator. The accuracy of the linear actuator is better than Experient B, as shown in Figs.(b), is to exaine the accuracy and the resolution power of the easureent. Three sall four-points arkers are attached on the board and oved with the linear actuator. In this experient, the large four-points arker was used. Figure 6 shows the results of this experient. The easured results of three different directional oveents of the arkers are close each other, and the differences between the easured displaceent and the actuator s oveent are less than 5 % at 200 actuator s oveent. Therefore our ethod is independent of the installation position of the caera and the arkers, thus, it is easy to set the caera as well as the arkers, at convenient locations. The second experient is to exaine the accuracy of the easureent and possibility of the two directional displaceent easureents. Three sall four-points arkers were fixed on the board on the linear actuator. Figure 7 shows the photograph just after the autoatic initialization. The size of the arker (2a, 2b), in Fig.2 on the iage, is (90.11, 54.85) pixels. The local coordinates and the caera paraeters were deterined at this state. No.1 arker was inclined -30 degree fro the horizontal direction. No.2 arker was installed so that the longer diagonal line to be the vertical direction. No.3 arker was installed so that the longer diagonal line to be the horizontal direction. The directions of the local coordinates IV. Experiental Results In order to check the possibility of the displaceent easureent with the caera paraeter, the four-points arker was put on the linear actuator and oved three different directions, at an angle of 0, -45 and 45 degree, as shown in Figs.5 (a). The photograph of Fig.5 (a2) shows the caera iage of the condition of 45 degree direction.. (a1) (a) Experient A (a2) Fig. 6 Coparison of the easured results for three different directional view angles with the linear actuator oveent (b1) (b) Experient B (b2) Fig. 5 Two experients carried out in a laboratory to exaine the accuracy and resolution power of the displaceent easureent, and the iage (a2) shows the iage of the aker at the oving direction of 45 degree, and the iage (b2) shows the arkers index-nubers and their local coordinates Fig. 7 Auto-calibration of the caera paraeters of each the four-points arkers

4 Volue 5, Issue 3, March are shown in Fig.5 (b2). The oveent of the linear actuator starts fro the 0 position and the steps are as followings: The step differences are 100, , 2.0, 4.0, -4.0, -2.0, - 1.0, -0.5 and Figure 8 shows the results of this step oving experient. The step of 0.5 can be clearly obtained. Since No.1 arker was inclined 30 degrees, x1 and y1 displaceents were saller than the actuator s oveent. Figure 9 shows the coparison of the x3 (the x- displaceent of No.3 arker) with the oveent of the actuator. About 1.5 difference between the easured and ideal displaceent can be observed. Figure 10 shows the displaceent of No.2 and No.3 arkers fro the first step position. The horizontal axis eans the actuator s displaceent. The axiu difference between the easured results and the actuator displaceents is 0.29 at 7.5 displaceent. It is considered that the cause standard deviation and it was very sall. The experient, in which the actuator oves fro 0 to 300, with 3.0 /sec velocity, was perfored, and actuator s displaceent was easured in the sae conditions as in the Fig.5 (b2). The results were shown in Fig. 11. The values of y2 (the y-displaceent of No.2 arker), x3 (the x-displaceent of No.3 arker) and Sqrt(x1^2+y1^2) (absolute displaceent of the No.1 arker) can be expected to coincide with the actuator s displaceent. However, the difference between the easured results and the actuator s oveent can be observed at 300 position as a value of about 24 in the x-displaceent of the No.3 arker. This difference corresponds to an error of 8%. The error in the long distance oveent ay be caused by the distortion of the lens and the error of the easureent of the four light positions. V. Conclusions The authors introduce the diaond shape arker with four LED light to realize autoatic calibration of the caera paraeters for the 2D displaceent easureent by iage Fig. 8 Measured results for sapling fraes, Frae interval is 0.01 second, The notations x1, y1, y2 and x3 ean the x-directional displaceent of No.1 arker, and the y-displaceent of No.1 arker, the y-displaceent of No.2 arker and the x-displaceent of No.3 arker, respectively of this difference is due to the errors in the easureent of four light positions in. The noise of the easureent in a stop state was less than Fig. 10 The displaceent fro the first step of the sae experient fro the Fig.9 Fig. 9 Coparison of the x3 (the x-displaceent of No.3 arker) with the ideal displaceent of the linear actuator Fig. 11 The absolute displaceents of the four-points arkers

5 Volue 5, Issue 3, March processing. The experients for the evaluation of the accuracy of the displaceent easureent were perfored. The easureent results were copared with the actuator oveent in several displaceent conditions. Fro the experiental results, the usefulness of this easureent ethod was confired. The 2D displaceent (x, y) can be obtained easily by Eqs. (2). The search of the arker follows the partial iage of the arker neighborhood to realize real-tie processing. References [1] Tang, Z., Liang, J., Xiao, Z. and Guo, C.: Large Deforation Measureent Schee for 3D Digital Iage Correlation Method, Optics & Lasers in Engineering, 50 (2012), [2] Sierra, G., Wattrisse, B. and Bordreuil, C.: Structural Analysis of Steel to Aluinu Welded Overlap Joint by Digital Iage Correlation, Exp. Mech., 48 (2008), [3] Poissant, J. and Barthelat, F.: A Novel Subset Splitting Procedure for Digital Iage Correlation on Discontinuous Displaceent Fields, Exp. Mech., 50-3 (2010), [4] Tong, W.: Plastic Surface Strain Mapping of Bent Sheets by Iage Correlation, Exp. Mech., 44-5 (2004), [5] Fujita, S., Furuya, O., Niitsu, Y., Mikoshiba, T., Aikawa, S. and Fujiura, S.: Strudy on Measureent Method for Structural Fracturing and Breakdown Process in Shake Table Tests, PVP-Vo Seisic Engineering (2000), [6] Niitsu, Y., Iizuka, T. and Mikoshiba, T.: Theory of Pseudo 3D Position Measureent with One Caera Iage, Int. Conf. on Advanced Technology in Exp. Mech, No (2011), 155. [7] Iizuka, T., Mikoshiba, T. and Niitsu, Y.: Developent of Pseudo-3D Position Measureent with High Resolution Caera and its Application for Strain Measureent of Static Forced Wooden-Walls, Proc. of 5th World Conf. on Structural Control and Monitoring (2010), DVD-ROM. [8] Yasuoka, K., Iizuka, T., Araki, Y., Nagajia, S. and Niitsu, Y.: Strain and Displaceent Measureents of Shear Loaded CLT Panel by Iage Correlation Method,