Subpixel Precision of Straight-Edged Shapes for Registration and Measurement
|
Abstract—The precision by which a region is located or measured on the image plane is limited by the sampling density. In this paper, the worst-case precision errors are determined for calculating the average image location of an edge, line, and straight-edged region. For each case, it is shown how the worst-case error can be minimized as a function of the geometric parameters. These results can be used to determine the worst case error by which the location of a known shape is measured. Another application is to design shapes for use in registration, such as fiducial marks used in electronic assembly. The main conclusion of this paper is that, to achieve better precision, measurement of a straight-edged region should be made at an angle askew to the sampling axis (not 0, 45, or 90 degrees) and this should be at a certain length that is a function of this skew angle.
[1] 746 D.I. Havelock,“Geometric precision in noise-free digital images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 10,1,065-1,075, 1989.
[2] D.I. Havelock, “The Topology of Locales and Its Effect on Position Uncertainty,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 380-386, Apr. 1991.
[3] J.W. Hill, "Dimensional Measurements from Quantized Images," D. Nitzan, S. Barnard, R. Bolles, R. Cain, J. Hill, W. Park, and R. Smith, Machine Intelligence Research Applied to Industrial Automation, SRI 10th Report for NSF Grant DAR78-27128, pp. 75-105, 1980.
[4] L. Dorst and A.W.M. Smeulders, "Discrete Representation of Straight Lines," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 4, pp. 450-462, July 1984.
[5] C.A. Berenstein,L.N. Kanal,, and D. Lavine,“A geometric approach to subpixel registration accuracy,” Computer Vision, Graphics, and Image Processing, vol. 40, pp. 334-360, 1987.
[6] Z. Kulpa, "On the Properties of Discrete Circles, Rings, and Disks," Computer Vision, Graphics, and Image Processing, vol. 10, pp. 348-365, 1979.
[7] A. Nakamura and K. Aizawa, "Digital Circles," Computer Vision, Graphics, and Image Processing, vol. 26, pp. 242-255, 1984.
[8] Q. Tian and M.N. Huhns, "Algorithms for Subpixel Registration," Computer Vision, Graphics, and Image Processing, vol. 35, no. 2, pp. 220-233, 1986.
[9] H.K. Nishihara and P.A. Crossley, "Measuring Photolithographic Overlay Accuracy and Critical Dimensions by Correlating Binarized Laplacian of Gaussian Convolutions," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, no. 1, pp. 17-30, Jan. 1988.
[10] C. Bose and I. Amir, “Design of Fiducials for Accurate Registration Using Machine Vision,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 12, pp. 1,196-1,200, Dec. 1990.
[11] L. O'Gorman, A.F. Bruckstein, C.B. Bose, and I. Amir, "Subpixel Registration Using a Concentric Ring Fiducial," Proc. 10th Int'l Conf. Pattern Recognition, pp. 249-253,Atlantic City, 1990.
[12] L. O'Gorman, A.M. Bruckstein, C.B. Bose, and I. Amir, "A Comparison of Fiducial Shapes for Machine Vision Registration," Proc. IAPR Workshop on Machine Vision and Applications (MVA '90), pp. 253-256,Tokyo, Nov. 1990.
[13] A. Efratand and C. Gotsman, "Subpixel Image Registration Using Circular Fiducials," Int'l J. Computational Geometry and Applications, vol. 4, no. 4, pp. 403-422, 1994.
[14] I. Niven and H.S. Zuckerman, An Introduction to the Theory of Numbers, fourth edition. New York: John Wiley and Sons, chapter 2, 1980.
[15] A.M. Bruckstein, L. O'Gorman, and A. Orlitsky, "Design of Shapes for Precise Image Registration," unpublished manuscript.
Index Terms:
Registration, precision, fiducial marks, machine vision, image processing, metrology, subpixel precision.
Citation:
Lawrence O'Gorman, "Subpixel Precision of Straight-Edged Shapes for Registration and Measurement," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 7, pp. 746-751, July 1996, doi:10.1109/34.506796
PURCHASE ARTICLE: $19
IEEE Xplore Subscribers
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb