Precision estimation of edge parameters in digital imagery

Edward Paul Lyvers, Purdue University

Abstract

As manufacturing processes become more automated, the need for automated inspection becomes even greater. Precision measurements of parameters in digitized images can be an important part of an automated inspection process. An edge operator based on spatial moments of a step edge is developed for both one-dimensional and two-dimensional cases. The one-dimensional operator estimates the parameters of edge location and edge step height. The two-dimensional operator additionally estimates edge orientation. The operator can be implemented for virtually any size window and can locate correctly modeled edges to hundredths of a pixel. This accuracy is unaffected by additive or multiplicative changes to the data values. Theoretical and experimental noise analysis shows the operator's accuracy is not severely degraded by moderate levels of noise. The operator is extended to accommodate non-ideal edge profiles and rectangularly sampled pixels. The effects of gray level quantization are also studied. The operator is shown to be optimum in this sense. The effects of a curved edge are also studied. The application of this technique to the measurement of imaged machined metal parts is also presented. A CCD based image acquisition system which provides the necessary match of image data to the underlying model, so that accurate subpixel measurements can be made, is developed. This system includes a modified CCD camera, a custom designed digitizer, and a custom interface to existing imaging hardware. The moment-based operator is simplified for use as a general-purpose edge detector. Its performance, for both for noiseless case and the case of additive gaussian noise, is compared to a variety of operators proposed in the literature. As an example of accuracies obtainable, under the assumption of an ideal edge at a random translation and orientation, with square-aperture sampling, and with no noise present, the maximum errors using a 3 x 3 Sobel operator are 7.93% in magnitude and 2.90$\sp\circ$ in angle. The 3 x 3 moment-based operator reduces this error to 0.91% in magnitude and 0.135$\sp\circ$ in angle. A Hough transform technique which uses both edge magnitude and edge orientation information is presented. This Hough transform also uses a Hough-domain smoothing technique which is very effective in locating straight line "clusters" in the Hough domain.

Degree

Ph.D.

Advisors

Mitchell, Purdue University.

Subject Area

Electrical engineering

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