1200 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 12, NO. 12, DECEMBER 1990 RE FER EN c E s [l] P. D. Hyde and L. S. Davis, “Subpixel edge estimation,” Partern Recog- nition, vol. 16, no. 4, pp. 413-420, 1983. [2] I. Overington and P. Greenway, “Practical first-difference edge de- tection with subpixel accuracy,” Image Ksion Comput., vol. 5, no. 3, [3] C. A. Berenstein, L. N. Kanal, D. Lavine, and E. C. Olson, “A geometric approach to subpixel registration accuracy,” Comput. Vision, Graphics, Image Processing, vol. 40, no. 3, pp. 334-360, 1987. [4] Q. Tian and M. N. Huhns, “Algorithms for subpixel registration,” Com- put. Vision, Graphics, Image Processing, vol. 35, no. 2, pp. 220-233, 1986. [5] J. W. Hill, “Dimensional measurements from quantized images,” in Machine Intelligence Research Applied to Industrial Automation (SRI 10th Report for NSF Grant DAR78-27128), D. Nitzan et al., 1980, pp. 75- 105. [6] H. S. Ranganath, “Hardware implementation of image registration algo- rithms,” Image Vision Comput., vol. 4, no. 3, pp. 151-158, 1986. [7] C. Ho, “Precision of vision system,’’ in 1982 Workshop Industrial Applications ofMachine Vision Conj Rec., IEEE Cat. No. 82CH1755-8, pp. 217-224, 1987. pp. 153-159. Stereo Ranging with Verging Cameras Eric Krotkov, Knud Henriksen, and Ralf Kories Absfract-We present a novel method to compute absolute range from stereo disparities with verging cameras. The approach differs from others by concentrating, through both analysis and experiment, on the effects caused by convergence, rather than on the general camera calibration problem. To compute stereo disparities we first extract linear image features and then match them using a hypothesize-and-verify method. To compute range we derive the relationship between object distance, vergence angle, and disparity. Experimental results show the precision of the range computation, excluding mistaken matches, to be approximately 5% for object distances up to three meters and a baseline distance of 13 cm. Including mistaken matches results in performance an order of magnitude worse, leading us to suggest methods to identify and model them. Index Terms-Binocular stereo, stereo matching, stereo reconstruction, three-dimensional computer vision, vergence. I. INTRODUCTION Computing range from stereo requires first matching the images taken by two cameras to determine disparities (differences in the positions of corresponding features), and then transforming these into absolute distances. A great deal of research in computer vision, robotics, photogrammetry, psychology, and neurophysiology has ad- dressed both of these problems. Our contribution to this research is to develop and analyze a novel method for absolute stereo ranging with a pair of verging cameras. Manuscript received December 10, 1986; revised April 19, 1990. Recom- mended for acceptance by 0. D. Faugeras. This work was performed in the Grasp Laboratory at the University of Pennsylvania and was supported in part by NSFDCR, U.A. Air Force, DARPNONR, U.S. Army, NSFICER, DEC Corp., IBM Corp., Lord Corp., and the German Federal Ministry of Defense. E. Krotkov is with the Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213. K. Henriksen is with the Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen, Denmark. R. Kories is with the Deutsche Bundespost Telekom, D-6110 Dieburg, Germany. IEEE Log Number 9040026. Fig. 1. The agile camera system. The agile camera system allows two cameras to translate horizontally and vertically, and to rotate by panning and tilting. Motors mounted in the camera housings allow control of the lenses by independently adjusting their focusing distance, focal length (zoom), and aperture diameter. Fig. 1 illustrates the physical camera system, which is described in detail elsewhere [9]. Two cameras mounted on a platform can translate horizontally and vertically, and rotate left-right and up- down. Motors mounted on each lens adjust the focal length, focusing distance, and aperture diameter. Further, the two cameras can verge, by rotating towards each other (converging) or away from each other (diverging). Fig. 2 illustrates the vergence mechanism; the travel from minimum to maximum vergence angle is approximately 6”, covering 90 000 motor steps. Potential advantages of vergence include increasing the field of view common to two cameras, and constraining the stereo disparity. We model each lens as a pinhole, assuming that to first order all lines of sight intersect at a unique lens center. The lens centers are separated by a baseline distance b, and both lenses have focal length f. Associated with the cameras are reference frames L and R, with origins at the lens centers, and Z-axes coincident with the optic axes, positive in the direction of the scene. We define a Cyclopean reference frame W with origin at the midpoint of the baseline, Z-axis normal to the baseline, and X-axis coincident with the baseline (Fig. 3). We address the following problem: identify the three-dimensional position of an object point P = [Xw. Yu. ZW]~ in the Cyclopean frame from its projections (TL. y~) and (zn, y~) onto the left and right image planes, respectively, using verging cameras. In addition, we are interested in the uncertainty on the measurement of ZW. This correspondence presents a novel method to compute ZW that differs from classical approaches to stereo ranging that involve solving the camera calibration problem [5], [11]-[13] or related orientation problems [7, p. 3111. The approach differs by concentrat- ing, through both analysis and extensive experiments, on the effects caused by convergence. The correspondence is organized as follows. In Section I1 we describe a method for computing stereo disparities based on extracting and matching lines. We present in Section I11 the method for comput- ing range as a function of disparity and vergence angle, and describe in Section IV a procedure to identify the parameters required for the 0162-8828/90/120O- 1200$01 .OO 0 1990 IEEEIEEE TRANSACTIONS ON PAlTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 12, NO. 12, DECEMBER 1990 1201 ./ I kl 1 Fig. 2. Vergence
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