Using the Hough transform for analysis of images containing straight lines

Dachs, Andrew Francis

Using the Hough transform for analysis of images containing straight lines

Master Thesis

1990

Abstract

The Hough transform is a means for finding straight lines in an image. Since it is robust and efficient it is widely used in machine vision systems. The Hough transform has been shown to be a special case of the Radon transform. As a result, the Hough transform can be inverted using the inverse Radon transform. The Radon transform is important in the medical field, where its inverse, reconstruction from projections, is used to view "slices" through a patient in Computer Aided Tomography. The straight line Hough transform produces a two dimensional parameter space. A straight line in the image produces a peak in this space. Normally, the Hough transform extracts two parameters for each line in the image. Two parameters can describe a line mathematically, but a line segment requires four parameters since the end points must be defined. It is possible to avoid extending the Hough space to four dimensions and still extract line segments. The method presented here achieves this by filtering the two dimensional Hough space before inversion with the inverse Radon transform. The Hough, Radon and inverse Radon transforms are implemented on general purpose computers and the different algorithms for inverting the Radon transform are discussed. The "filtering in Hough space" method is applied to the problem of extracting polygons, or polyhedra, from images. The information extracted can be used by a Computer Aided Design (CAD) system to model the scene. Other uses of the forward transform I filter I inverse transform method are discussed. For example, linear features in images can be enhanced in this manner. This method can be used in a machine vision system in which straight lines must be extracted from an image. However, the computation times are too long for a real time system. In this case dedicated hardware would be required. Such dedicated hardware has been described in the literature. · It is possible to extend the Hough transform to other parametric curves, for example circles and ellipses. However, no inverse transform exists for these extensions. Therefore the filtering technique is limited to linear features at this stage.

Keywords

Electrical Engineering

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