## Guided Tour Of Hough Transforms On Elementary Patterns

Conference

2004 Annual Conference

Location

Salt Lake City, Utah

Publication Date

June 20, 2004

Start Date

June 20, 2004

End Date

June 23, 2004

ISSN

2153-5965

Conference Session

Potpourri of Engineering Mathematics

Page Count

8

Page Numbers

9.650.1 - 9.650.8

DOI

10.18260/1-2--13883

Permanent URL

https://peer.asee.org/13883

419

#### Abstract NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

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”

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

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2004 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015