A camera and a world coordinate frame are related as follows XcYcZc=RXwYwZw+T. (a) What is the origin of the camera coordinate system in the world frame? (b) What is the distance from the camera origin to the plane Yw=0 ? 1 (c) Assume that pixel coordinates relate to camera coordinates as u=fXc/Zc and v=fYc/Zc and that the columns of R are R=(r1,r2,r3). Assume the translation vector can be written as (Tx,Ty,Tz). Write the projection of a world point (Xw,Yw,Zw) to pixel coordinates (u,v) in matrix-vector form. Show then the projective transformation H from the plane Yw=0 to the pixel plane. (d) Is the resulting matrix H always a projective transformation? If not show a camera-world setup as a counterexample. (e) We discussed in class how it is risky to set the (3,3) element of a homography H equal to 1 . In the case handled here, is there any camera-world setup where the H33 vanishes? (f) What are the world coordinates of the point F in Yw=0 world plane that projects to the point (f,0) ? (g) What is the distance of F from the center of projection? (h) What are the coordinates of the vanishing point arising from parallel lines parallel to the Xw axis. The answer should be in terms of f and elements of the rotation matrix. (i) Repeat the same for parallel lines parallel to the Zw axis in the world. (j) What is the line equation of the horizon arising from the line at infinity in the plane Yw=0