3. (Old Exam) Two identical security cameras are mounted in a room as shown in the...

   

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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 C1 and C2. In the following, PW, P and P 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 z = 1, i = 1,2, respectively. X X2 2 (a) Let E1 and E2 be the epipoles in camera 1 and 2 respectively. Find the camera coordinates E and E2 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 f = (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 C1 and C2. In the following, PW, P and P 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 z = 1, i = 1,2, respectively. X X2 2 (a) Let E1 and E2 be the epipoles in camera 1 and 2 respectively. Find the camera coordinates E and E2 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 f = (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.