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Session 3565

Guided Tour of Hough Transforms on Elementary Patterns 1 John Schmeelk

Department of Mathematical Sciences Virginia Commonwealth University Doha, Qatar Campus

Abstract

Student motivation in elementary mathematics continues to be a major problem. The author recommends that one solution to this problem is through the integration of applications into the elementary courses that are consistent with student interests and experiences. This paper provides an introduction to problems in human vision research and provides applications of straight line slope concepts to problems in pattern recognition that are expected to be of general student interest. The notion of a vertical line having no slope in mathematics is substituted for an angle and distance using the Hough Transform.

I. The Hough Transform

The axiom in pattern recognition states that the essence of an image is contained in the edges of the image. This is, when for example we look at alphabets, E, F, H, L and N given in Figure 1, the edges contribute primarily to the recognition of the letters. The inside heavy black lines would not affect the recognition of the image. Therefore, the edges can be decomposed as a sequence of straight lines. However if we use the traditional description of lines given in all algebra courses implementing slopes, the problem of infinite slope presents itself when discussing a vertical line. Recall for vertical lines the change in the x-direction is zero giving us a meaningless slope.

One technique to overcome this problem is to use a parametric space using the angle of a normal line drawn from the origin to a given line of the image and the length of the normal measured from the origin to the given line. This is illustrated in Figure 2. The line segment denoted distance1 in Figure 2 represents the length of the normal line segment to the given line segment.

Figure1. The Alphabets, E, F, H, L, N

E F H L N 1 Funded by the Qatar Foundation, Doha, Qatar “Proceedings of the 2004 American Society for Engineering Education Annual Conferences & Exposition Copyright 2004, American Society for Engineering Education”

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Schmeelk, J. (2004, June), Guided Tour Of Hough Transforms On Elementary Patterns Paper presented at 2004 Annual Conference, Salt Lake City, Utah. 10.18260/1-2--13883