# CS作业代写|CS-512 Assignment Camera Calibration

### 什么是OpenCV？

OpenCV 代表开源计算机视觉。简单地说，它是一个用于图像处理的库。事实上，它是一个巨大的开源库，用于计算机视觉应用、人工智能或机器学习算法驱动的领域，以及完成需要图像处理的任务。因此，它在当今系统的实时操作中具有重要意义。使用 OpenCV，可以处理图像和视频以识别物体、面部，甚至是人类的笔迹。

OpenCV 最初由英特尔开发，后来得到 Willow Garage 和 Itseez 的支持，后来又被英特尔收购。第一个 OpenCV 版本是 1.0。这个跨平台库在 BSD 许可下发布，在开源 Apache 2 许可下可免费用于学术和商业用途。它具有 C++、C、Python、Java 和 MATLAB（一种提供良好数值计算环境的专有多范式编程语言）接口，这些接口的 API 可以在在线文档中找到。OpenCV 还支持 Windows、Linux、Mac OS、iOS 和 Android。最初，创建 OpenCV 的主要目的是提高计算效率的实时应用程序。自 2011 年以来，OpenCV 还为实时操作提供 GPU 加速。在与其他库（例如 NumPy）集成后，Python 可以处理 OpenCV 数组结构进行分析。识别图像模式及其几个特征需要使用向量空间并对这些特征进行数学运算。

### 下面是一个OpenCV的计算机代写案例：

##### Review questions

• Camera calibration 1
(a) Given the projection equation p = MP explain the problems of: forward projection, calibration, and reconstruction. Which problem is the easiest? Which is the most difficult?
(b) Explain what is the necessary input for camera calibration.
(c) Explain the steps in the non-coplanar calibration algorithm.
(d) Given a known projection matrix with rows (1)2)3)4)(1)0)3)4)(1〉1〉111) and a world point Pi = (1,2)3) what are the 2D image coordinates of Pi after projecting it. Make sure to convert Pi to homogeneous coordinates before projecting it.
(e) Given the corresponding world-image points: — (100, 200) write the first two lines of
the matrix that needs to be formed for solving for the unknown projection matrix M.
(f) What is the minimal number of points that is necessary to be able to find a unique solution for M. How is the solution obtained?
(g) Explain the principal that is used to extract the unknown camera parameters from the projection matrix M.
(h) Explain how to compute the quality of the projection matrix M estimate.
(i) Explain the principal of planar camera calibration. How does planar camera calibration differ from non-coplanar one?
(j) Explain the difference between the homography (2D projective map) H and the projection matrix M. What is the assumption that is used to make sure we deal with homography matrices?
• Camera calibration 2
(a) Given a pair of corresponding image and world points (1)2) (3, 4)5) respectively, write the first two rows of the matrix that has to be constructed to solve for the unknown coefficients of the projection matrix.
(b) Given the estimated projection matrix M with rows (2)3)4,5)> and (3)4)5)6), findthe camera parameters UQ and VQ (coordinates of principal point) of the camera.
(c) Given a pair of corresponding image and world points (1)2) ⑶ 4)5) respectively, and estimated projection matrix M)with rows (1,2)3)4))(2)3)4,5，and 3)4)5)6))Find the projection error of the matrix M.

(d) After performing calibration, let the obtained rotation of the world with respect to the camera be given by / + Q where 7 is a 4×4 identity matrix and Q is a 4×4 matrix having in its (0)0) element the number 5 and zeros elsewhere. Let the obtained translation of the world with respect to the camera be given by the vector (1)2)3). Compute the rotation and translation of the camera with respect to the world.
(e) Given a pair of corresponding image and world points (1)2) ⑶ 4,0) respectively, that are used for planar calibration, write the first two rows of the matrix that has to be constructed to solve for the unknown coefficients of the homography matrix.

• Multiple view geometry 1
(a) Explain the difference between sparse and dense stereo matching. What are the advantages/disadvantage of each approach?
(b) Explain how normalized cross correlation (NCC) and sum of square distances (SSD) can be used for point matching. What is the isk in allowing the search space to be the entire image? How can the search space be reduced to a line?
(c) Given an axis aligned stereo pair with corresponding points (100, 200) and (103,200) in the left and right images respectively, compute the depth (z-coordinate) of the 3D point that produced this projection. Assume that the focal length of both cameras is 10. that the baseline is 100, and that we are working in camera coordinates.
(d) Explain the ambiguity problem in stereo matching.
(e) Given R』and Rr ^ Tr (rotation and translation of left/right cameras with respect to world)? Write the expression for the rotation and translation of the right camera with respect to the left camera.
• Multiple view geometry 2
(a) Given an axis aligned stereo system with focal length of 10mm)and baseline 20mmi compute the depth of a point with disparity of 30mm.
(b) Let A and B be the vectors (2)3,4), respectively. Write the matrix that if multiplied by B will result in the cross product AxB
(c) Let F be a fundamental matrix with rows (1,2,3), (2,3,4), (3,4,5). Let (1,2) and (2, 3) be corresponding left and right points. Compute the value of Fpi.
(d) Given corresponding left and right points (1)2)⑵ 3), respectively, write the respective row the in the matrix that has to be formed to solve for the fundamental matrix.

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