Abstract
The Hough transform is commonly used for detecting linear features within an image. A line is mapped to a peak within parameter space corresponding to the parameters of the line. By analysing the shape of the peak, or peak locus, within parameter space, it is possible to also use the line Hough transform to detect or analyse arbitrary (non-parametric) curves. It is shown that there is a one-to-one relationship between the curve in image space, and the peak locus in parameter space, enabling the complete curve to be reconstructed from its peak locus. In this paper, we determine the patterns of the peak locus for closed curves (including circles and ellipses), linear segments, inflection points, and corners. It is demonstrated that the curve shape can be simplified by ignoring parts of the peak locus. One such simplification is to derive the convex hull of shapes directly from the representation within the Hough transform. It is also demonstrated that the parameters of elliptical blobs can be measured directly from the Hough transform.
Highlights
Introduction to the Hough TransformA common task in many image processing applications is the detection of objects or features
The converse relationship is true; it is well known that a point in parameter space maps to a line in image space
This paper demonstrates that the line Hough transform has more utility than just detecting lines within an image
Summary
A common task in many image processing applications is the detection of objects or features (for example lines, circles, etc.). Any noise points effectively vote at random locations within parameter space It requires many co-linear noise points to build a significant peak. J. Imaging 2020, 6, 26 the number of votes within a peak, but as long as there are sufficient edge points detected to form a significant peak, the shape can be detected and reconstructed from the parameters. With each detected pixel voting on a linear trace in parameter space This is effective for approximately horizontal lines, as the line becomes more vertical, both the slope and intercept tend towards infinity. The voting trace within parameter space for Equation (2) follows a sinusoidal curve This voting approach can be extended to detect any parameterised shape, for example circles [4,6] and ellipses. Detection implies the ability to reconstruct key features of the curve, or the curve in its entirety
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