3. (Old Exam) Two identical security cameras are mounted in a room as shown in the figure below. The world coordinate system W is at one corner of the room, and each camera has its own coordinate system Ci and C2. In the following, Pw, Pl and P2 represent the coordinates of a point P with respect to the world coordinate system W, the camera 1 coordinate system C and the camera 2 coordinate system C2, respectively. The world coordinates of the centers of projection C" and C are (2,2, 4) and (4,3,3), respectively. The focal length of the cameras is 1 and their image planes are located at i = 1, 1 = 1, 2, respectively. X C .Z 2 1 (a) Let E, and E2 be the epipoles in camera 1 and 2 respectively. Find the camera coordinates E and Ez of the epipoles expressed in their respective camera systems. (b) The cameras capture images of a fly in the room. Let fi and f2 be the images of the fly in the first and second camera, respectively. The camera 1 coordinates of the image in the first camera are fi = (0,2.1). Find the equation of the epipolar plane containing the fly, expressed in the camera 2 coordinate system. Hint: find f first. (c) The fly flies following a straight line with constant velocity with respect to the world coor- dinate system(-3, -2, -1). Find the camera coordinates of the FOE in camera 1. 3. (Old Exam) Two identical security cameras are mounted in a room as shown in the figure below. The world coordinate system W is at one corner of the room, and each camera has its own coordinate system Ci and C2. In the following, Pw, Pl and P2 represent the coordinates of a point P with respect to the world coordinate system W, the camera 1 coordinate system C and the camera 2 coordinate system C2, respectively. The world coordinates of the centers of projection C" and C are (2,2, 4) and (4,3,3), respectively. The focal length of the cameras is 1 and their image planes are located at i = 1, 1 = 1, 2, respectively. X C .Z 2 1 (a) Let E, and E2 be the epipoles in camera 1 and 2 respectively. Find the camera coordinates E and Ez of the epipoles expressed in their respective camera systems. (b) The cameras capture images of a fly in the room. Let fi and f2 be the images of the fly in the first and second camera, respectively. The camera 1 coordinates of the image in the first camera are fi = (0,2.1). Find the equation of the epipolar plane containing the fly, expressed in the camera 2 coordinate system. Hint: find f first. (c) The fly flies following a straight line with constant velocity with respect to the world coor- dinate system(-3, -2, -1). Find the camera coordinates of the FOE in camera 1
