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The 2D Least Median of Squares (LMS) is a popular tool in robust regressionbecause of its high breakdown point: up to half of the input data can becontaminated with outliers without affecting the accuracy of the LMS estimator.The complexity of 2D LMS estimation has been shown to be $\Omega(n^2)$ where$n$ is the total number of points. This high theoretical complexity along withthe availability of graphics processing units (GPU) motivates the developmentof a fast, parallel, GPU-based algorithm for LMS computation. We present a CUDAbased algorithm for LMS computation and show it to be much faster than theoptimal state of the art single threaded CPU algorithm. We begin by describingthe proposed method and analyzing its performance. We then demonstrate how itcan be used to modify the well-known Hough Transform (HT) in order toefficiently detect image lines in noisy images. Our method is compared withstandard HT-based line detection methods and shown to overcome theirshortcomings in terms of both efficiency and accuracy.

GPU-Based Computation of 2D Least Median of Squares with Applications to Fast and Robust Line Detection