On the magic of SLIDE

Subspace-based line detection (SLIDE) is a novel approach for straight line fitting that has recently been suggested by Aghajan and Kailath. It is based on an analogy made between a straight line in an image and a planar propagating wavefront impinging on an array of sensors. Efficient sensor array processing algorithms are used to detect the parameters of the line. SLIDE is computationally cheaper than the Hough transform, but it has not been clear whether or not this is a magical free bonus. In particular, it has not been known how the breakpoints of SLIDE relate to those of the Hough transform. We compare the failure modes and limitations of the two algorithms and demonstrate that SLIDE is significantly less robust than the Hough transform.