The Hough transform estimator

The Hough Transform Estimator∗

This paper pursues a statistical study of the Hough transform; the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose objective is to find the line that “best” fits a set of planar points. In particular, we establish strong consistency, rates of convergence and characterize the ...

The Cascaded Hough Transform

When using the original slope-intercept parameter-isation for the Hough transform, the resulting parameter space actually corresponds to the dual space. Indeed , lines are transformed into points, and for every point there is also a corresponding line. This paper presents a way of exploiting this special property, by the introduction of the Cascaded Hough Transform, or CHT for short. This allow...

Statistical properties of the Hough transform estimator in the presence of measurement errors

The Coherent Circle Hough Transform

We introduce a novel formulation of the Circle Hough Transform that we call the Coherent Circle Hough Transform. The technique uses phase to code for radii of circles. The usual simplifications of the Circle Hough Transform (CHT) are used in which lines pointing away from edge points are plotted rather than circles. Intersections of these "spokes" accumulate edge magnitude, or edge "energy", ne...

On the Inverse Hough Transform

ÐIn this paper, an Inverse Hough Transform algorithm is proposed. This algorithm reconstructs correctly the original image, using only the data of the Hough Transform space and it is applicable to any binary image. As a first application, the Inverse Hough Transform algorithm is used for straight-line detection and filtering. The lines are detected not just as continuous straight lines, which i...