Computer Vision Nptel Week 5 Assignment Answers
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Computer Vision Nptel Week 5 Assignment Answers (July-Dec 2025)
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Question 1. Consider a camera with calibration matrix K=[354135243]K = \begin{bmatrix} 3 & 5 & 4 \\ 1 & 3 & 5 \\ 2 & 4 & 3 \end{bmatrix}. It forms an image II of a world scene. The camera is rotated about its center by R=[0.360.48−0.8−0.80.600.480.640.6]R = \begin{bmatrix} 0.36 & 0.48 & -0.8 \\ -0.8 & 0.6 & 0 \\ 0.48 & 0.64 & 0.6 \end{bmatrix} and forms another image I′I’ of the same world scene. Compute the homography between II and I′I’.
a) [3201.252.25−0.251.251.75−1.25]\begin{bmatrix} 3 & 2 & 0 \\ 1.25 & 2.25 & -0.25 \\ 1.25 & 1.75 & -1.25 \end{bmatrix}
b) [0.360.4814.28−3.96−2.0446.561.2−0.36−3.24]\begin{bmatrix} 0.36 & 0.48 & 14.28 \\ -3.96 & -2.04 & 46.56 \\ 1.2 & -0.36 & -3.24 \end{bmatrix}
c) [5−1−152.8−0.24−7.81.2−0.36−3.24]\begin{bmatrix} 5 & -1 & -15 \\ 2.8 & -0.24 & -7.8 \\ 1.2 & -0.36 & -3.24 \end{bmatrix}
d) None of the above
Question 2. Compute the essential matrix EE, provided calibration matrices of two cameras in stereo set up as K=[134343243],K′=[234343334]K = \begin{bmatrix} 1 & 3 & 4 \\ 3 & 4 & 3 \\ 2 & 4 & 3 \end{bmatrix}, K’ = \begin{bmatrix} 2 & 3 & 4 \\ 3 & 4 & 3 \\ 3 & 3 & 4 \end{bmatrix} along with fundamental matrix F=[123214125]F = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 1 & 2 & 5 \end{bmatrix}.
a) [5672411121449914112967]\begin{bmatrix} 56 & 72 & 41 \\ 112 & 144 & 99 \\ 141 & 129 & 67 \end{bmatrix}
b) [1176492871119914112267]\begin{bmatrix} 117 & 64 & 92 \\ 87 & 111 & 99 \\ 141 & 122 & 67 \end{bmatrix}
c) [224642457411612414111175]\begin{bmatrix} 224 & 64 & 245 \\ 74 & 116 & 124 \\ 141 & 111 & 75 \end{bmatrix}
d) None of the above
Question 3. Consider the following matrix FF and the camera matrices PP and P′P’ (for left and right cameras). Which of the following statements (s) are true.
a) PP and P′P’ are compatible to FF as a fundamental matrix.
b) PP and P′P’ are not compatible to FF as a fundamental matrix.
c) Given the fundamental matrix FF, PP and P′P’ are the only pair of camera matrices.
d) PP and P′P’ provide a unique fundamental matrix given one of its non-zero element fixed to the value 1.
Question 4. Which of the following are valid steps in reconstructing a 3D line from its stereo image projections?
a) Compute the plane equations from the projection matrices and the image lines.
b) Use the intersection of the two image lines to define the 3D line directly.
c) Represent each plane as PTlP^T l and P′Tl′P’^T l’, and find the intersection of the planes.
d) Use only the fundamental matrix to recover the 3D line.
Question 5. Compute a homography induced by plane at infinity H∞H_\infty for camera matrices P=[423154320],P′=[243357342]P = \begin{bmatrix} 4 & 2 & 3 \\ 1 & 5 & 4 \\ 3 & 2 & 0 \end{bmatrix}, P’ = \begin{bmatrix} 2 & 4 & 3 \\ 3 & 5 & 7 \\ 3 & 4 & 2 \end{bmatrix}.
a) [0.150.6−0.151.15−0.4−0.650.60.4−0.1]\begin{bmatrix} 0.15 & 0.6 & -0.15 \\ 1.15 & -0.4 & -0.65 \\ 0.6 & 0.4 & -0.1 \end{bmatrix}
b) [0.150.640.251.170.87−0.850.680.49−0.40]\begin{bmatrix} 0.15 & 0.64 & 0.25 \\ 1.17 & 0.87 & -0.85 \\ 0.68 & 0.49 & -0.40 \end{bmatrix}
c) [0.0590.700.183.12−0.59−1.150.820.38−0.28]\begin{bmatrix} 0.059 & 0.70 & 0.18 \\ 3.12 & -0.59 & -1.15 \\ 0.82 & 0.38 & -0.28 \end{bmatrix}
d) None of the above
Question 6. Consider a plane induced homography H=[231122]H = \begin{bmatrix} 2 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix} of a stereo imaging set up. Epipole e′(3,5)e'(3,5) in right image plane and a point x(3,1) in left image plane are given. Compute the epipolar line l′l’ on which the corresponding point of x will lie in right image plane.
a) (-37, -19, 39)
b) (37, -17, -26)
c) (13, 13, 9)
d) None of the above
These are Computer Vision Nptel Week 5 Assignment Answers
Question 7. Suppose the motion of the cameras is a pure translation with no rotation and no change in the internal parameters. One may assume that the two cameras are: P=K[I∣0]P = K[I|0] and P′=K[I∣t]P’ = K[I|t]. If the camera translation is parallel to the x-axis, then e′=(1,0,0)Te’ = (1,0,0)^T. Can you compute fundamental matrix from the given information?
a) [0−10100000]\begin{bmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}
b) [01010−1010]\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \end{bmatrix}
c) [0−1010−1010]\begin{bmatrix} 0 & -1 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \end{bmatrix}
d) [00000−1010]\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0 \end{bmatrix}
Question 8. Assume that a stereo imaging setup has two image planes, left and right. Epipoles on left and right image planes are given as e and e’, respectively. Which of the following could be a possible right null vector of given fundamental matrix F=[−132110110]F = \begin{bmatrix} -1 & 3 & 2 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix}?
a) (2,2,14)
b) (1,-1,2)
c) (1,-1,-1)
d) (-2,1,-1)
Question 9. Given an affine fundamental matrix of the form FA=[00a00bdec]F_A = \begin{bmatrix} 0 & 0 & a \\ 0 & 0 & b \\ d & e & c \end{bmatrix}. Let FAF_A correspond to a stereo pair of affine cameras with parallel projection rays. Which of the following statements are true?
a) The right epipole is given by (−b,a,0)T(-b,a,0)^T.
b) The affine fundamental matrix has 7 degrees of freedom.
c) The left epipole is given by (−e,d,0)T(-e,d,0)^T.
d) The affine fundamental matrix must be full-rank (rank = 3).
**Question 10. Consider a stereo set-up with PP and P′P’ (camera matrices for left and right camera) as given below:
P=[500005000010],P′=[5001005000010]P = \begin{bmatrix} 5 & 0 & 0 & 0 \\ 0 & 5 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}, \quad P’ = \begin{bmatrix} 5 & 0 & 0 & 10 \\ 0 & 5 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}.
If the image coordinates of a 3-D point are (4,6) and (7.33,6) in left and right cameras, compute its depth (z-coordinate) in the 3D.**
a) 2.999
b) 2.762
c) 4.564
d) 3.003
These are Computer Vision Nptel Week 5 Assignment Answers