STEREO VISION AND LASER STRIPERS FOR THREE-DIMENSIONAL SURFACE MEASUREMENTS

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1 XVI CONGRESO INTERNACIONAL DE INGENIERÍA GRÁFICA STEREO VISION AND LASER STRIPERS FOR THREE-DIMENSIONAL SURFACE MEASUREMENTS BARONE, Sandro; BRUNO, Andrea University of Pisa Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione s.barone@ing.unipi.it, andrea.bruno@ing.unipi.it ABSTRACT In this paper, a 3D scanner, based on tracking a laser stripe by a stereo vision sensor, is presented. The system is composed of a pair of digital cameras, a laser stripe generator and software to control the hardware and process the images. The measurement procedure is based on detecting laser stripe locations in the digital images with subpixel resolution. Stereo vision principles are then used to correlated the data between the pair of images. The measurement process does not require the calibration of the laser light source. The use of a stereo vision system allows the integration with a photogrammetric procedure, developed in a previous research activity, to align multiple scans. In the work, experimental tests have been conducted with nominal models to analyse and verify usability and accuracy of the methodology. Key words: Reverse engineering, stereo-vision, surface modelling. 1. Introduction During the last decades, innovative optical technologies have proven to be very effective in providing non-contact techniques for measuring three-dimensional shapes [1]. The selection of a vision system is highly dependent on the type of applications and its practical limitations. Widely accepted measurement techniques are based on scanning a surface by controlled beams of radiation, typically laser [2] or white light [3], which interact with capturing devices (active systems). Geometric data about objects are extracted by processing grey intensity images. These methodologies require complicated calibration procedures to evaluate the parameters of the optical devices (i.e., sensors and light source), necessary for the measurement process.

2 Although very accurate, these techniques cannot be used as general purpose because optical adjustments are required for every specific application and, consequently, tremendous effort must be devoted to calibration aspects. This paper presents a research activity concerning the development of a versatile non-contact scanning system, which overcomes some of the limitations above described. The system uses a laser light source and a stereo image acquisition sensor, which is calibrated by simple procedures [4]. The measurement process is based on laser stripe tracking by using principles of stereo-vision. In particular, a procedure has been developed to detect peak positions with sub-pixel accuracy on the basis of light intensity constraints and fuzzy decision maker. The method comprehends algorithms for camera calibration, laser stripe detection and analysis, and 3D range-map reconstruction. In the paper, the methodology is described and laboratory applications are illustrated. 2. The experimental setup The optical system (Figure 1) is composed of two conventional monochrome digital cameras and a laser source (laser diode, wavelength 650 nm, output power 35 mw). For this work, all images were sampled with a matrix containing pixels and quantized with 256 grey levels (I(x,y)=0: black; I(x,y)=255: white). The laser light is a beam of circular cross-section with Gaussian intensity profile. The laser beam is spread by a cylindrical lens into a thin plane, so that the intensity profiles in the image planes of the cameras are practically still Gaussian across the stripes. This is used for detecting the stripe centres in the camera images with subpixel resolution. The light beam generated by the laser is deflected by a mirror and scanned on the object. Generally, all types of laser-based 3D range finders are based on calibrating an optical configuration, which includes sensors and light source [2]. In this paper, the 3D stripes are reconstructed by only using 2-D imagery, whereas the laser light source is not directly involved in the measurement process. There are certain advantages to using this approach. In particular, because the knowledge of the moving part positions is not needed in the triangulation process, the method lends itself to be simple, inexpensive and mechanically very robust. Moreover, the calibration of a stereo-vision system is now a well-established procedure, which can be easily carried out to adapt the stereo vision configuration to specific contexts. Figure 1: The stereo-vision system.

3 The calibration procedure [4] allows the calculation of the intrinsic (focal distances, coordinates of the principal points, radial and tangential distortions) and extrinsic (positions and orientations with respect to an absolute reference system) of the cameras. In particular, the parameters of the camera are obtained correlating the coordinates of known markers located on a calibrating sample, acquired in different positions, with the corresponding coordinates on the image planes. The procedure provides the translation vector and the rotation matrix of the reference system of the camera with reference to an absolute datum system. 3. Laser stripe detection The images acquired through the instrumentation above described are evaluated and the results are processed in order to obtain 3D point maps. Figures 2 show a pair of images acquired by the stereo-vision system. An image processing procedure is applied to detect the locations of laser stripe centres in the camera images. Naidu and Fisher [5] have proposed an interesting comparative analysis of five algorithms for determining the peak position of a laser stripe in an image with subpixel accuracy. In this work, the Blais e Rioux detector [6], which has been verified to be more noise-tolerant and equally computationally efficient, has been used. In the original image, the grey level transition across a laser line is gradual (Figure 3-a), in theory Gaussian, and this permits a sub-pixel evaluation of the line centres. The algorithm is based on the differentiation of the signal and the elimination of high frequency noise by using linear filters. In particular, the filtered signal at a pixel x,y is given by 2n th order linear operator defined as: I ( x, y) = sign( i) I( x + i, y) f n i= -n where I(x,y) is the grey level measured in the acquired images at a pixel x,y and -sign(i) is the sign operator. Typically, 6 th and 8 th order operators have provided good performances with stripe width of at least 3 pixels. It is remarkable that these operators act like a form of numerical derivative operator (Figure 3-b). Figure 4 shows the full field map of filtered signals obtained from Figure 2-a. Linear interpolation is then used to increase the precision of the zero crossing. In particular, the peak position is estimated with subpixel accuracy as: X I I f ( xc, y) (, ) ( + 1, ) = xc + δ = I x y I x y f c f c (1) Y I = y (2) where I f (x c,y) and I f (x c +1,y) are the filtered signals at the zero crossing zone. By this procedure the centres of the lines are determined with a resolution which depends on grid line width, grey level profile, grey level difference and system noise. In this paper, a resolution of 0.08 pixels was obtained applying a 6 th order operator to 10-pixel width lines and amplitude of the signal 130.

4 The detection of laser stripe centres can be disturbed by the presence of undesirable elements in the scene. Figure 5 show the plots of the intensity levels and the filtered signals measured across three different lines of the acquired image (Figure 2-a) and the filtered map (Figure 4). It is apparent that the signal peaks are not always due the presence of a laser stripe, rather, spurious elements in the scene can also induce forms of signal variations. The use of pass-band interference filters can partially avoid these drawbacks. However, this solution does not allow the use of a multi-scan procedure based on photogrammetric routines integrated to the measurement process as proposed in [3]. In this paper, a fuzzy-based algorithm has been developed and applied to the filtered maps (Figure 4) in order to optimise the peak detection process. In particular, the filtered maps are row-wise scanned; for each row, the filtered signal is measured and a fuzzy decision maker [7] is employed to resolve whether the light variations are due to the laser stripe or spurious image features. The fuzzy algorithm is an ordered set of conditional fuzzy statements, which upon execution yield an approximate solution to the recognition problem reproducing human inference way. Each statement deals with fuzzy variables, which are defined to distinguish peaks of intensity. The fuzzy procedure is based on detecting the highest (I M ) and smallest (I m ) values of each filtered signal distribution (Figure 4). Then, five variables, named a, b, c, d, e, are defined as: a = I M + I m (3) b = I M I m (4) c = I M I m (5) d = x M x m (6) e= x x (7) M m where x M and x m are the pixels where I M and I m occur, respectively, a takes into account the difference of intensity between the peak and his neighbourhood, b takes into account the symmetry of the peak distribution, c, d and e control the distribution and the position of the signal peak. The five variables are modelled by means of fuzzy membership functions (Figure 5) with different shapes and chosen on the basis of a trial and error method. The modelling procedure provides the basis for the set of fuzzy rules, which are processed by a Sugeno-style inference and the weighted sum as a defuzzification method. The fuzzy algorithm coupled to camera adjustments (i.e., gain and shutter-time) provide high robustness to the peak detection process, even in non-controlled working environments.

5 (a) (b) Figure 2: Example of acquired left (a) and right (b) images: measurement of a rectified plane. (a) (b) Figure 3: Grey level distributions (a) and filtered signals (b) across a laser stripe. Figure 4: Full filed map of the filtered signals obtained from the image of Figure 2-a.

6 Figure 5: Plots of intensity levels and filtered signals measured in three different rows of the acquired filtered images. 4. Stereo image correlation Figure 6: Scheme of the fuzzy inference system. The 3D measurement using stereo vision requires the matching of conjugate image points. The correlation process is typically based on similarity constraints (feature-based or intensity-based). However, a point in image I 1 can be correlated with many points in image I 2 (false matches), and this problem is particularly evident in measuring free-form surfaces due to the absence of peculiarities in the scene to be used as similarity constraints. The measurement system presented in this paper solves the matching problem by combining the laser stripe detection (intensity-based constraint) with the epipolar geometry (stereo vision constraint) (Figure 7). In particular, given a point m 1 on the

7 image I 1 (camera 1), its conjugate m 2 on the image I 2 (camera 2) belongs to the epipolar line defined as intersection of the image plane with the plane through m 1 and the focuses of the two optical devices. On the basis of the perspective projection theory, the coordinates of conjugate points m 1 e m 2 are defined by the following equations: m = P w i = 1,2 (8) i i where P i (i = 1, 2) is the perspective projection matrix and w the coordinate vector of a generic 3D point. The mathematical expressions of the optical rays through w and the focus c 1, or c 2, can be written as: wλ = ci + λ wi = ci + λ P + i mi i = 1,2 (9) where λ is a scalar parameter, w i represents the direction of an optical ray and P is the pseudo-inverse perspective matrix. + i The epipolar line l 2 corresponds to the projection of the optical ray w-c 1 on to the image plane of the second camera (I 2 ) with respect to the optical centre c 2. Its expression can be determined considering the projections of c 1 on to I 2 (corresponding to the epipole e 2 ) and infinite point of the optical ray w-c 1. These points are defined as: e2 = P2 c 1 (10) e = P P m (11) The equation of the epipolar line of m 1 can then be written as (in homogeneous coordinates): l = e + λ e (12) 2 2 e 2 2 Considering that an equation in homogeneous coordinates of a line through two points can be written as the external product of the points, the epipolar line of m 1 can be expressed as: l = e e = e P P m = F m (13) The matrix F, named the Fundamental Matrix (a 3 3 square matrix), depends on the epipolar parameters and the perspective projection matrixes of the optical devices, which can be obtained by the calibration routines. However, considering that the point m 2, conjugate of m 1, belongs to the epipolar line l 2, the following relation can be written (Longuet-Higgins equation): m T 2 F m1 0 1 = (14)

8 The Fundamental Matrix is obtained on the basis of an optimisation procedure, considering a number of known conjugate points higher than the number of unknowns. In the method developed in this paper, the epipolar constraint is applied to the points belonging to the laser stripes. The matching problem of conjugate points is straightforward considering that, in each image plane, a conjugate point belongs both to a laser line and to an epipolar line (Figure 7): given a laser line point m 1 on the image (I 1 ), its conjugate m 2 is obtained as intersection between the epipolar line and the laser stripe on the image (I 2 ). Then, from the knowledge of the conjugate pair m 1, m 2, the corresponding 3D point w is determined by a triangulation procedure. The correlation procedure does not require any operator s intervention. The combination of two constraints, i.e. laser line and epipolar line belongings, guarantees the matching problem has always a unique solution. Moreover, this methodology can efficiently used to measure free-form shapes, which typically do not present peculiarities usable by classical correlation procedures. Figure 7: Schematic diagram of the stereo vision set-up. 5. Laboratory applications Experimental tests have been carried out to measure nominal shapes to verify the accuracy of the proposed methodology. In particular, two nominal samples, i.e. a rectified stepped surface and a cylinder (radius of 125 mm), have been captured with working distances of 1800 mm and 3000 mm. Figure 8-a shows the three-dimensional points determined for the stepped surface. The experimental points have been compared with planes of best fit. The analysis of deviations has yielded an average error of 0.15 mm and a standard deviation of 0.07

9 mm with a working distance of 1800 mm, and an average error of 0.27 mm and a standard deviation of 0.18 mm with a working distance of 3000 mm. Figure 8-b shows the three-dimensional points determined for the cylindrical surface. The experimental points have been compared with a cylinder of best fit. The analysis of deviations has yielded an average error of 0.1 mm and a standard deviation of 0.05 mm with a working distance of 1800 mm, and an average error of 0.19 mm and a standard deviation of 0.1 mm with a working distance of 3000 mm. It is possible to note the results for the cylinder are more accurate than those obtained for the stepped surface. This is probably due the better surface quality of the cylinder, which showed negligible reflection phenomena. It is interesting to evidence that the procedure directly yields sets of ordered points, which can better support the successive process of surface modelling. (a) (b) Figure 8: Acquisition of rectified stepped surface (a) and a cylindrical surface (b). (a) (b) Figure 9: Deviations from the nominal geometries of Figures 8 as obtained by the proposed method for the rectified stepped surface (a) and the cylindrical surface (b).

10 6. Conclusions In this paper, a stereo vision system for shape measurement applications has been developed. The methodology is based on using light stripe, generated by a laser beam deflected by a mirror and scanned on the object, and a stereo vision system. A procedure has been developed to detect peak positions with sub-pixel accuracy on the basis of light intensity constraints and fuzzy decision maker. The 3D stripes are reconstructed by only using 2-D image information, whereas the laser light source is not directly involved in the measurement process. This solution reduces the influence of the mechanical moving parts on the accuracy and the stability of the system. Moreover, the optical configuration can be easily adapted to specific applications calibrating the stereo vision system by wellestablished procedures. Experimental applications concerning shape measurements of nominal models have evidenced the accuracy and the easy of use of the proposed technique. References [1] VÀRADY T., MARTIN R.R., COX J., Reverse engineering of geometric models an introduction, Computer Aided Design, 29(4), 1997, [2] ELLI ANGELOPOULOU, JOHN R. WRIGHT, Laser Scanner Technology, Philadelphia, PA , GRASP Laboratory University of Pennsylvania [3] BARONE S., CURCIO A., RAZIONALE A., A structured light stereo system for reverse engineering applications, Proceedings of the IV Italo-Español Seminar on Reverse Engineering Techniques and Applications, Naples 2003, [4] GRUEN A., HUANG T.S., Calibration and Orientation of Cameras in Computer Vision, Springer, Berlin, [5] TRUCCO E., FISHER R.B., FITZGIBBON A.W., NAIDU D.K., Calibration, data consistency and model acquisition with laser stripers, International Journal of Computer Integrated Manufacturing, 11(9), 1998, [6] BLAISE F., RIOUX M., "Real-Time Numerical Peak Detector." Signal Processing, 1986, 11, [7] KASABOV N.K., Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering, A Bradford Book, 1996, Cambridge, Massachusetts, The MIT Press.