Chapter 3

THREE-DIMENSIONAL VISION BASED ON

BINOCULAR IMAGING AND APPROXIMATION

NETWORKS OF A LASER LINE

J. Apolinar Muñoz-Rodríguez*

Centro de Investigaciones en Optica, A. C. Leon, Gto, 37150 Mexico.

Abstract

We present a review of our computer vision algorithms and binocular imaging for shape detection optical metrology. The study of this chapter involves: laser metrology, binocular image processing, neural networks, and computer vision parameters. In this technique, the object shape is recovered by means of laser scanning and binocular imaging. The binocular imaging avoids occlusions, which appear due to the variation to the object surface. A Bezier approximation network computes the object surface based on the behavior of the laser line. By means of this network, the measurements of the binocular geometry are avoided. The parameters of the binocular imaging are computed based on the Bezier approximation network. Thus, the binocular images of the laser line are processed by the network to compute the object topography. By applying Bezier approximation networks, the performance of the binocular imaging and the accuracy are improved. It is because the errors of the measurement are not added to the computational procedure, which performs the shape reconstruction. This procedure represents a contribution for the stripe projection methods and the binocular imaging. To describe the accuracy a mean square error is calculated.

* E-mail address: munoza@foton.cio.mx. Tel: (477) 441 42 00.

This technique is tested with real objects and its experimental results are presented. Also, the time processing is described.

Keywords: Binocular imaging, laser line, Bezier approximation networks.

1. Introduction

In computer vision, optical systems have been applied for shape detection. The use of structured illumination makes the system more reliable and the acquired data are easier to interpret. A particular technique is the laser line projection [1-3]. When a laser line is projected on an object, the line position is shifted in the image due to the surface variation and the camera position. From the line position and the geometry of the optical setup, the object contour is deduced. The main aim of the line projection is the detection of the line behavior in the image [4-6]. Also, the geometry of the setup is measured to obtain the object topography. When the surface variation produces an occlusion, the line position can not be detected. Therefore, in the area of the line occlusion the topographic data are not retrieved [7-8]. In the proposed technique here, occluded areas are retrieved by binocular imaging. To extract the object surface, the object is moved in the x-axis and scanned by a laser line. Based on the line behavior in the image, the object shape is retrieved. In each step of the scanning, a pair of binocular images of the line is captured. When the surface produced a line occlusion, the occluded area appears only one of the two images. Thus, the data missed in each image can be retrieved from each other. In this manner, the line occlusion is avoided by the binocular imaging. Typically, the disparity is needed to retrieve the object depth in a binocular system [9]. In the proposed technique, the disparity is determined by detecting the line position in each pair of the binocular images. In the proposed setup, the position of the line disparity is proportional to the object depth. By means of a Bezier network, a mathematical relationship between the line position and the object depth is generated. In this manner, the measurements of the focal length, and the distance between the two cameras are avoided. The Bezier network is constructed using the disparity of the line, which is projected on the objects with known dimensions. The disparity is detected measuring the position of the line displacement in the image. Thus, the network calculates the depth dimension for a position of a stripe displacement given. The line position is detected by means of Bezier curves with a resolution of a fraction of pixel. This position is processed by the network to determine the object shape. In this manner, all steps of the proposed technique are performed automatically by

camera is indicated by ac and ec, respectively. When a laser line is projected on the surface, the line position is moved from ao to ap in the image plane of the camera a. At the same time, the line position is moved from eo to ep in the camera e. The line displacement in the image plane for each camera is represented by

By means of the positions ep and ap, the line displacement respect to the reference point “o” is given by as(x,y) for the camera a and es(x,y) for the camera e. Based on the pinhole camera model [10], the surface zi in a binocular system is deduced by

from this equation, δ+ε is the disparity. The distances of the disparity are deduced by δ = ac- ap and ε = ec – ep, respectively. To compute the surface zi by means of Eq.(3), the constants F, d, ac, ec and camera orientation should be known. Typically, the parameters d and F are obtained by an external procedure to the contouring. Then, these parameters are given to the computer system to reconstruct the object shape. This means that Eq.(3), can not be computed in the image processing of the laser line. For the proposed technique, the object depth h(x,y) is computed directly in the image processing of line position. In this procedure, a Bezier network provides a function that computes the object depth based on the line displacement. Also, this network provides information of the camera orientation, the focal lens, the center coordinates, the distance between tow cameras, disparity and center coordinates. Thus, the performance for object contouring is improved. In our contouring system, the object depth is computed by the network based on the line position using only one camera of the binocular system. This means that the network produces the depth h(x,y) using as(x,y) or es(x,y). The image processing provides a least one of the two displacements. When a line occlusion appears in the camera a, as(x,y) is missing. Then, the ep of the line disparity is used to compute the object depth h(x,y). In this manner, the occlusion problem of the laser line is solved by the binocular imaging. To detect the disparity, the line position is measured in every row of the binocular images. This position is computed by detecting the maximum of the line intensity in each

row of the image. The intensity projected by a laser diode is a Gaussian distribution in the x-axis [11]. The intensity in every row of the image is represented by (x0, z0), (x1, z1), (x , z2),.......,(xn, zn), where xi is the pixel position and zi is the pixel intensity. To detect the line position, the maximum intensity measured in the image. To carry it out, Bezier curves and peak detection are used. The nth-degree Bezier function is determined by n+1pixels [12]. The nth-degree Bezier function is determined by two parametric equations, which are described by

Eq.(4) represents the pixel position and Eq.(5) represents the pixel intensity. To fit the Bezier curve shown in figure 3, x0, x1, x2,......,xn, are substituted into Eq. (10) and z0, z1, z2,....,zn, are substituted into Eq. (5). Then, these equations are evaluated in the interval 0≤ u≤1. In this case, the second derivative z”(u) > 0 in the interval 0≤ u≤1. Therefore, the maximum is detected by the first derivative equal to zero z´(u)=0 [13] via bisection method. Beginning with a pair of values ui = 0 and us =1, because z(u) is defined for the interval 0 ≤ u ≤ 1, u* is halfway between ui and us. If z´(u) evaluated at u = u* is positive, then ui = u*. If z´(u) evaluated at u = u* is negative, then us=u*. Next, u* is taken as the mid point of the last pair values that converges to the root. The value u* where z´(u) = 0 is substituted into Eq.(5) to obtain maximum position x*. The result is x* = 34.274 and the stripe position is ap = 34.274 pixels, which is shown in figure 3. The procedure of stripe detection is applied to all rows of the image. Then, the line position is processed by the network to obtain the object contour.

Figure 1. Experimental setup.

Figure 2. Geometry of the experimental setup.0.