Computer Vision Image Formation and Camera

Hi, I'm stuck on this problem for a computer vision course. What are the steps I need to take to solve this?

2 Image Formation 10 points In this problem we will practice rigid body transformations and image formations through the projective camera model. The goal will be to 'photograph' the four points X1 (-1,-0.5, 2) X2 (1,-0.5, 2) X3 (1, 0.5, 2) l, 0.5, 2) in the world coordinate frame. First, recall the following formula for rigid body transformation (2) RX t Cam where Cam is a point in the camera coordinate frame, X is a point in the world coordinate frame, and R and t are the rotation and translation that transform points from the world coordinate frame to the camera coordinate frame. Together, R and t are the ertrinsic camera parameters. Once transformed to the camera coordinate frame, the points can be photographed using the 3 x 3 camera calibration matrix K, which embodies the intrinsic camera parameters, and the canonical projection matrix Ilo Given K, R, and t, the image of a point X is x Cam KIRlt IX, where the homogeneous points x (Xcam, 1)T and X (X 1)T. We will consider four different settings Cam of focal length, viewing angles and camera positions below Camera Settings 1. No rigid body transformation Focal length 1. The optical axis of the camera is aligned with the z-axis, and pointing in the positive direction. There are no orientations of the camera. 2. Translation Focal length. 1. (0,0,2) The optical axis of the camera is aligned with the z-axis, and pointing in the positive direction. There are no orientations of the camera 3. [Translation and rotation]. Focal length 1. R encodes first a 60 degree rotation around the z-axis and then 45 degrees around the x-axis. t- (0,0, 2) 4. [Translation and rotation, long distance Focal length. 5. R encodes a 60 degrees around the z axis and then 45 degrees around the x-axis. t (0,0, 15) For each of these settings, calculate and report: (i) The matrix RIt containing the extrinsic camera parameters (ii) The camera matrix K containing the internal camera paramters. Note we will not use a camera calibration matrix that maps scene points to image points in pixels coordinates, but only parameterize this with the focal length f. In other words: the only parameter in the camera calibration matrix under the perspective assumption is f 2 Image Formation 10 points In this problem we will practice rigid body transformations and image formations through the projective camera model. The goal will be to 'photograph' the four points X1 (-1,-0.5, 2) X2 (1,-0.5, 2) X3 (1, 0.5, 2) l, 0.5, 2) in the world coordinate frame. First, recall the following formula for rigid body transformation (2) RX t Cam where Cam is a point in the camera coordinate frame, X is a point in the world coordinate frame, and R and t are the rotation and translation that transform points from the world coordinate frame to the camera coordinate frame. Together, R and t are the ertrinsic camera parameters. Once transformed to the camera coordinate frame, the points can be photographed using the 3 x 3 camera calibration matrix K, which embodies the intrinsic camera parameters, and the canonical projection matrix Ilo Given K, R, and t, the image of a point X is x Cam KIRlt IX, where the homogeneous points x (Xcam, 1)T and X (X 1)T. We will consider four different settings Cam of focal length, viewing angles and camera positions below Camera Settings 1. No rigid body transformation Focal length 1. The optical axis of the camera is aligned with the z-axis, and pointing in the positive direction. There are no orientations of the camera. 2. Translation Focal length. 1. (0,0,2) The optical axis of the camera is aligned with the z-axis, and pointing in the positive direction. There are no orientations of the camera 3. [Translation and rotation]. Focal length 1. R encodes first a 60 degree rotation around the z-axis and then 45 degrees around the x-axis. t- (0,0, 2) 4. [Translation and rotation, long distance Focal length. 5. R encodes a 60 degrees around the z axis and then 45 degrees around the x-axis. t (0,0, 15) For each of these settings, calculate and report: (i) The matrix RIt containing the extrinsic camera parameters (ii) The camera matrix K containing the internal camera paramters. Note we will not use a camera calibration matrix that maps scene points to image points in pixels coordinates, but only parameterize this with the focal length f. In other words: the only parameter in the camera calibration matrix under the perspective assumption is f