Answer Happy

(b) Consider the problem of detecting arcs of circles that pass through the origin of the x-y coordinate system. The equation of the circle is given by: (x-a)²+(y-b)² = a² + b² where (a, b) are the coordinates of the centre of the circle. (1) In a given image, the pixels Pi's that lie on a circle have been determined by an edge operator, how would you use the Hough Transform to determine the coordinates of the center of the circle? (ii) If we know not only the coordinates (xį, y¡), but also the slope mi at each point Pj, derive the expressions for a and b in terms of xi, y¡ and mi.