Image-Based System for Measuring Dimension of Short Hollow Cylinders

Transcription

1 Proceedings of the 7th WEA Int. Conf. on ignal Processing, Computational Geometry & Artificial Vision, Athens, Greece, August 4-6, 7 3 Image-Based ystem for Measuring imension of hort ollow Cylinders Chin-Tun Chuang, Cheng-Chuan Chen, Ming-Chi Lu 3, and Chih-ung Chuang 4 epartment of Mechanical and Computer-Aided Engineering, t. John s University, Tamsui, Taipei County, TAIWA dashin@mail.sju.edu.tw epartment of Electrical Engineering, t. John s University, Tamsui, Taipei County, TAIWA 3 epartment of Electronic Engineering, t. John s University, Tamsui, Taipei County, TAIWA 4 epartment of Computer cience and Information Engineering, ational Taiwan University, Taipei, TAIWA Abstract: In this paper, a novel image-based method is prosed for measuring the dimension of short hollow cylinders without physical contact. The prosed method can measure the inner diameter, height, and thicness of the short hollow cylinder with one exposure by using a single digital camera. Because of a risedown platform of camera positioning control device develed in this paper, the aforementioned measuring method can reduce expenses and processing time during the measurement. It can perform 3 distance measuring based on a image frame. This measuring system is equipped with a function to automatically adjust the resolution. As a result, maximal image contour of an unnown short hollow cylinder picture can be obtained so as to achieve measuring results with highest resolution at each time. The effectiveness of the prosed approach in measuring the inner diameter, height and thicness of the short hollow cylinder has been validated by using gray scale chromatic aberration of the image contour regions. The measurement system not only increases the accuracy of the measuring results but is also applicable to any inds of digital cameras. Key-Words: circular plate of light transparent, gray scales concentric circle, short hollow cylinder. Introduction Most technicians or technical staffs usually use Vernier Calipers[]-[] for short hollow cylinder s dimension measuring. owever, it taes three times physical contact measuring to get the inner diameter, height and thicness. till, there is some short hollow cylinder s dimension measuring instruments still in use. Papers published of related researches mostly brought up the result that only measure a single function. It does not get the inner diameter, thicness and height of an unnown short hollow cylinder in one measuring. Even if there are many image type of quantity measuring system for an unnown short hollow cylinder s dimension[3]-[4], they are almost plane measuring and complete the test on inner diameter under the fixed measurement system (CC camera). Other non-contact measuring gauges such as ultrasonic waves and laser beams can be used for this measurement purpose. owever, they are claimed not being very user friendly[5]-[6]. Although ultrasonic waves and laser beams measuring gauges measured the distance between the sample and the measuring table, it needs twice measuring for the height of short hollow cylinder. And it is difficult to use accurate laser beams measuring gauge for inner diameter and thicness measuring of short hollow cylinder. There using P(Position ensing evice) or LVT(Linear Voltage ifferential Transformer) for measuring accurate distance[7]-[8]. Its contact-type function for distance measuring can also apply to measure the short hollow cylinder s dimension. But these measuring systems made up P or LVT have to do the measuring step for three times same as Vernier Calipers.

2 Proceedings of the 7th WEA Int. Conf. on ignal Processing, Computational Geometry & Artificial Vision, Athens, Greece, August 4-6, 7 4 As mentioned earlier, the goal of this research is to design a measuring method that allows us to do the measurement of the short hollow cylinder s dimension without any physical contact at one shot. We use the diameter of the circular plate of light transparent on the measuring table act as standard rule. In the capture digital image will get three different diameters of gray scales concentric circle image contour region cause of an unnown short hollow cylinder on measuring table. Calculated the total pixels of each round image contour region and get three different diameters. Following the simple formula derivatives the inner diameter, thicness and height, respectively. When adjusted the distance between CC camera place position and t of an unnown short hollow cylinder on the period of measuring. It will get high resolution of measuring cause of the suitable image contour region of an unnown short hollow cylinder. The second section will explain the theory of distance measurement and platform can be done in one shot. We continue to elaborate on the parameter of measuring formula in the third section. In the fourth section, we will prove theory illustration of short hollow cylinder s dimensions measuring. ection five will justify calculation process with an experiment and followed is the conclusion. Theory of measurement between measuring table and distance of two levels Adjusted nob CC high intensity LE lights c ( ) max h circle slab of pervious to light Fig. chematic diagram of measuring table The schematic diagram of measuring table is shown as Fig.. It is installed the high intensity LE lights below the ground glass. It would show conspicuous gray scales in the image contour picture because of the mean value brightness from the high intensity LE lights. In Fig., h is the height of the tic position, s is the diameter of the circular plate of light transparent and θ denotes the width viewed from horizontal angle of CC camera. The distance of capture level can be changed by adjusting the nob. V(max) V (max) P( i, j ) ( ) (max) (max) A ( ) (max) Fig. chematic image diagram of measuring table from the t (max) Figure shows the image contour region of P i, j A P i, j =. We shall measuring table from the t. When ( ) then P ( i, j ) =, otherwise ( ) express it as V A p ( i, j) ( ) = () i= j= As denotes the area of the round image contour region of the circular plate of light transparent. The total pixels, As(), would count the pixels based on As(). Then A ( ) ( ) = () π When we calculated the diameter of circular image contour from formula (), nown from the previous research[9]-[3], the distance of horizontal is a positive prortion to the value of pixels on the / V (max) horizontal scanning line. Then under the captured level,, and the horizontal view from the angle θ of CC camera gives (max) max ( ) = ( ) (3)

3 Proceedings of the 7th WEA Int. Conf. on ignal Processing, Computational Geometry & Artificial Vision, Athens, Greece, August 4-6, 7 5 = ( ) cotθ h max ( ) = cotθ h (4) From formulae (3) and (4), it proved that we can measure the horizontal and vertical distances []- [3] at any height and width of the sensor by only one CC camera on IBM (Image-Based istance Measuring ystem). The measurement parameters of this measuring table system cotθ and h in formula (4) would be derived in the following section. 3 Measurement parameters cotθ and h Optical Axis c h cotθ = m m ( m) ( m) ( m m) ( m) ( m) (7) ( m) ( m) m ( m) m ( m) (8) ( ) ( ) = h = m m 4 measurement of short hollow cylinder s dimension In fig.4, W, WT and W denote the inner diameter, the thicness, and the height respectively. is the height from the measuring table of the CC camera. is the distance between the t of the short hollow cylinder and the position of CC camera. Knowing the distance of and, the height of short hollow cylinder W may be written in the form W = -. W (max) V c h m m G A C E F B (max) V ( ) max m ( ) max Fig.3 Illustration on acquiring the measurement parameters The position of CC camera can be placed at the height m and m, we will be able to get (m) and (m) by m and m, respectively. We can rewrite the formula (4) as ( m) ( ) = h (5) m cotθ = h (6) m cotθ m After finding the magnitudes cotθ and h from formulae (5) and (6), m EF ( ) C ( ) AB ( ) G ( ) (max) Fig.4 Operation of short hollow cylinder s dimension measuring In Fig. 5, G represents the diameter of the round image contour region formed by the circular plate of light transparent, with the captured distance,. EF is the diameter of the round image contour region formed by the bottom of short hollow cylinder. AB is the diameter of round image contour region formed by the outer diameter of short hollow cylinder, with captured distance,. C is the diameter of

4 Proceedings of the 7th WEA Int. Conf. on ignal Processing, Computational Geometry & Artificial Vision, Athens, Greece, August 4-6, 7 6 G A Optical Axis C E c max ( ) W F B h W Fig.5 Illustration of short hollow cylinder s dimensions measuring theory round image contour region formed by the inner diameter of short hollow cylinder. We then count the pixels in each round image contour region and calculate the diameter of each circle from formula (). From the previous research[3], the short hollow cylinder will form two round image contour region in different size because of its height. Then the inner diameter W will be equal to EF, which is the diameter of the round image contour region shown in Fig. 5. EF ( ) W = G ( ) (9) If the diameter on the t and the bottom of short hollow cylinder is the same, then the maximal horizontal distance, max(), pictured at the distance can be shown as: C ( ) max( ) = W () Once we get the value of from formula (4), the height, W, of an unnown short hollow cylinder can be shown as: ( ) ( ) W = W cotθ G C () ubtracting the inner diameter from the external diameter, we obtain the thicness, WT, shown as ( ) ( ) W W W AB T = C AB( ) ( ) ( EF = ) ( () C G ) o, as long as we counted the total pixels of each round image contour region from formulas () and (), and calculated the diameter of each round image contour region, we can now the value of inner diameter from formula (9), the value of height from formula (), the value of thicness from formula (). Thus, we realize the measurement of the inner diameter, the height and the thicness of an unnown short hollow cylinder s dimension without any physical contact by only one round image contour regions. 5 Experiment and Measurement () The digital camera used is PAAOIC Electric Industrial Co., Ltd. Lumix MC-FZ3 Type. () orizontal pixels of the circular plate of light transparent is G () = 37 pixels. (3) The diameter of the circular plate of light transparent is 6 mm. (4) Measurement parameters suggested by measure- ment frame h =. mm, cotθ =.. (5) etails of the sample measured as in Table, Table and Table 3. Result Fig.6 Images of short hollow cylinder Table Gauged height with same inner diameter and thicness ize of ample W = W = 8 W = W = W = W = 6 W * Error 5.84% 4.738% 5.743% * Error.86% -.786% -.3%

5 Proceedings of the 7th WEA Int. Conf. on ignal Processing, Computational Geometry & Artificial Vision, Athens, Greece, August 4-6, 7 7 W * Error -.775% 5.633%.663% Table Gauged thicness with same height ize of ample Result Result W = = W = W = W = W = 3 = 4 W = W * Error 6.4% 4.738% 3.95% * Error 3.88% -.786% -3.35% W * Error -.4% 5.633%.75% Table 3 Gauged inner diameter with same thicness and height ize of ample W = 6 W = 8 W = W = 8 W = 6 W = 8 W * Error 5.488% 5.84% 5.48% * Error -.59%.86% -3.43% W * Error 5.675% -.775%.388% Proved from the above, the method brought up in this paper is practical. And the aim of this paper is to devel a rise-down platform of camera positioning control device. In the future, though, the improvement in the accuracy of measurement depends on a more perfect distinction in gray, it will reduce expenses and processing time during the measurement. 6 Conclusion As demonstrated in this paper, the prosed approach is capable of measuring dimension of short hollow cylinder without physical contact based on round image contour region from a single CC camera. Measurement of inner diameter, height, and thicness of the short hollow cylinder can be obtained via the prosed approach using only a single CC camera for 3 gauged dimension of round image contour region. In the future, we will improve the measurement accuracy and design a reliable rise-down platform for projecting beams of light. The methodology prosed in this article has revealed the potential to allow height and perimeter measuring for irregular objects. It is hed that the measuring system prosed in this paper will mae contributions for the mechanical fabrication industry. References: [] Type Result Form.aspx type=3. [] Type Result Form.aspx type=36. [3] A. Torralba and A. Oliva, epth estimation from image structure, IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 4, Issue 9, pp. 6-38, ept.. [4] Qilong Zhang; Pless, R,; Fusing video and sparse depth data in structure from motion, 4 International Conference on Image Processing, Volume 5, 4-7 Oct. 4, pp [5]. Pellegrini, G.. Buller, and A.M. Wallace, Laser depth measurement using picosecond resolution time correlated single-photon counting, Lasers and Electro-Optics Eure Conference, -5 ept., pp.. [6] E.A. Wulf, J. Ampe, W.. Johnson, R.A Kroeger, J..Kurfess, and B.F. Philips, epth measure- ment in a strip detector, IEEE uclear cience ymposium, Volume, ov., pp [7] G.Y. Tian, Z.X. Zhao, R.W. Baines, and P. Corcoran, The design of miniaturised displacement transducers for deep hole diameter measurement, Mechatronics, pp.37 37, 999. [8] G.Y. Tian, Z.X. Zhao, R.W. Baines, and P. Corcoran, A miniaturised sensor for deep hole diameter measurement, Precision Engineering 3, pp.36 4, 999. [9] M.-C. Lu, W.-Y. Wang, and.-. Lan, Imagebased height measuring system for Liquid or particles in tans, in Proc. IEEE Int. Conf. etworing, ensing and Control, vol., 4, pp.4-9. [] M.-C. Lu, W.-Y. Wang, and C.-Y. Chu, Optical-Based istance Measuring ystem (OM), The Eighth International Conference on Automation Technology, 5, pp.8-83.

6 Proceedings of the 7th WEA Int. Conf. on ignal Processing, Computational Geometry & Artificial Vision, Athens, Greece, August 4-6, 7 8 [] M.-C. Lu, Image-based height measuring system for Liquid or particles in tans, ROC patent of invention, o. 536, 4. [] Ming-Chih Lu, Wei-Yen Wang, and Chun-Yen Chu, Image-Based istance and Area Measuring ystems, IEEE ensors Journal, vol. 6, no., pp , April 6. [3] Chin-Tun Chuang, Ming-Chih Lu, Chen-Chien su, and Yin-Yu Lu, iameter and epth Measurement of oles by a ingle Camera, WEA Transactions on ystems, Volume 6, Issue 5, pp , May 7.