The Hough transform for lines Consider the polar parameterization of a line $$x\ \cos\theta+y\ \sin\theta=\rho$$ (this parameterization is much more adapted to this problem than the Cartesian one). For each point $(x,y)$ of an image $I$, the Hough transform associates a sinusoid in the plane $(\rho,\theta)$, whose points have an amplitude equal to the intensity of the pixel $(x,y)$. So to all the points in $I$, the Hough transform associates a pencil of sinusoids which intersect themselves in the plane $(\rho,\theta)$. In other words, the HT performs integrations along lines on the image $I$, and the value of each integral is affected to the point $(\rho,\theta)$ corresponding to the parameters of this line. Therefore, if on the image $I$ some pixels with high intensities are concentrated along a straight line, we will observe in the domain $(\rho,\theta)$ a peak whose coordinates are directly related to the parameters of the lines. This method can be easily applied to other parametric curves, like hyperbola for example. This transform is computed in the file htl.m.
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