Suppose we have two Cartesian coordinate systems: (X,Y,Z) and (X,Y,Z). Between these two coordinate systems, the rotation matrix is R and the translation vector is T. (a) Write the rigid transformation between these two coordinate systems. (b) Suppose (X,Y,Z) is the world coordinate system, and (X,Y,Z) is the camera coordinate system. The camera has a focal length f and pixel size s. Write the transformation that relates the a point (X,Y,Z) and its projection (u,v) on the camera image plane. (c) If the camera is rotated counter-clockwise by some degree along Z direction; derive the transformation between the original (u,v) and the new one. Problem 2: (25 points) Using [1,0,1] and its transpose to calculate the horizontal and vertical derivatives, and assuming flow vectors are constant in a 3-by-3 window, calculate the optical flow at the center position, from left image to the right one