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Fast Hough transform is a widely used algorithm in pattern recognition. Thealgorithm relies on approximating lines using a specific discrete line modelcalled dyadic lines. The worst-case deviation of a dyadic line from the idealline it used to construct grows as $O(log(n))$, where $n$ is the linear size ofthe image. But few lines actually reach the worst-case bound. The present paperaddresses a statistical analysis of the deviation of a dyadic line from itsideal counterpart. Specifically, our findings show that the mean deviation iszero, and the variance grows as $O(log(n))$. As $n$ increases, the distributionof these (suitably normalized) deviations converges towards a normaldistribution with zero mean and a small variance. This limiting result makes anessential use of ergodic theory.

Analyzing Deviations of Dyadic Lines in Fast Hough Transform