Plane Segmentation from Two Views in Reciprocal-Polar Image Space

We present a new method of segmenting planar regions when an uncalibrated camera undergoes (near) pure translation. We show that, for pure translation parallel to a plane, the relation between the two views, when expressed in a reciprocal-polar ( 1 r , θ) space, is a pure shift in the ( 1 r ) dimension for a given value of θ. Furthermore, we show that the magnitude of these shifts follows a sinusoidal form along the θ direction over a maximum of π radians. This allows planar image motion to be accurately detected and recovered by 1D correlation. Simultaneous planar pixel grouping and recovery of the plane homography, thus amounts to a robustly fitting a sinusoid to shifts of maximum correlation in reciprocal-polar space. The phase of the recovered sinusoid corresponds to the orientation of the vanishing line of the plane and the amplitude is related to the magnitude of the camera translation.