cvpr maths -- 2

i want the below questions answered: We aim to create a 3D point-cloud from three different views of a scene. The following question will address the various steps involved in generating 3D from three views of the scene. 1st: Let’s consider affine transformations, which are any transformations that preserve parallelism. Affine transformations include not only rotations and translations, but also scaling and shearing. Given some vector p, an affine transformation is defined as: A(p) = Mp + b, where M is an invertible matrix. Prove that under any affine transformation, the ratio of parallel line segments is invariant, but the ratio of nonparallel line segments is not invariant 2nd: We want to calibrate the intrinsic parameters of all the 4 cameras. Describe a way to calculate the intrinsic parameters of the camera. Provide a derivation to estimate the intrinsic parameters for one camera. 3rd: Explain the stages involved in creating a 3D point cloud from these four views – give a 3-4 line description for each stage along with the equations. 4th: Write a derivation of estimating Fundamental matrix from 8 corresponding points for a pair of views. 5th:Explain how will you use the Fundamental matrix F and the Intrinsic parameters of each of the cameras to enforce Epipolar constraints to refine the correspondences to obtain the 3D point cloud. 6th: Now you have the 3D scene point cloud and you have obtained a new image of the scene with known intrinsic calibration. How will you establish correspondences between the 3D point cloud and the new 2D image of the scene.