Harris-Stephens' combined corner/edge detector
Frank Nielsen · 2008
We summarize Harris-Stephens 1 combined corner/thin edge detector that does not depend on rotation nor shift or ane change of intensity. LetI(x;y) denote the intensity pixels of ImageI. Harris-Stephens extended the principle of Moravec’s corner detector by considering the local auto-correlation energy E(x;y) = P u;v wu;v (I(x +u;y +v) I(u;v)) 2 , where (u;v) denote a neighborhood of (x;y). Traditionally, wu;v = 1 if and only ifjx uj s andjy vj s, with 2s 1 being the size of the square window patch. In order to be invariant to rotations, Harris-Stephens considered a smooth Gaussian circular window with wu;v = exp( u 2 +v 2 2 2 ) (and u 2 +v 2 s 2 , with s denoting the radius size). Observe when a window patch is: enclosed into an almost constant shaded region, shifts in every direction result in a small change of energy. straddling an edge, the shift along the edge yields a small variation of energy while moving perpendicular to that edge results in signicant change. at a corner (including isolated points), then every direction yields a large change of energy. Approximate the energy function at (x;y) by the bilinear form E(u;v) = [u v]Mx;y[u v] T , where Mx;y is a 2 2 positive denite matrix computed as