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MIDTERM WED. OCT.21 October 6, 1998 1 Modified Hough Algorithm (More Efficient) • Note that for p-parameters a1,a2,…,ap containing 2 translation parameters that the accumulator array is now (p-2) dimensional. • Also note reduction in the number of pixels that are effectively visited: – Instead of examining all pixels as a possible ‘center’ for the shape we now only examine edge points as possible boundary points for the shape. October 6, 1998 2 GENERALIZED HOUGH ALGORITHM R-TABLE f 1 f2 (Xc,Yc) f October 6, 1998 f n r1,r2,…,,rn r1,r2,…,,rn r1,r2,…,,rn 1 3 BINARY SETS AND THEIR PROPERTIES October 6, 1998 4 S T S + T S - T October 6, 1998 5 MORPHOLOGICAL OPENING AND CLOSING OPENING S T = (S - T) + T CLOSING T = (S + T) - T S S T S T S T S T T October 6, 1998 6 EUCLIDEAN DISTANCE TRANSFORM • For a set S the Euclidean Distance Transform is the non-negative scalar function d(x,S) where x is a point in S and d(x,S) is the shortest distance from x to the boundary of S. October 6, 1998 7 “SKELETONS” AND THE MEDIAL AXIS TRANSFORM S Locus of centers of largest circles contained in S such that circles are tangent at 2 or more points. October 6, 1998 8 October 6, 1998 9