Computer Vision Nptel Week 4 Assignment Answers
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Computer Vision Nptel Week 4 Assignment Answers (July-Dec 2025)
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Question 1. Compute the homography matrix H.
a) [113011010]\begin{bmatrix}1&1&3\\0&1&1\\0&1&0\end{bmatrix}
b) [01113013−1]\begin{bmatrix}0&1&1\\1&3&0\\1&3&-1\end{bmatrix}
c) [010001310]\begin{bmatrix}0&1&0\\0&0&1\\3&1&0\end{bmatrix}
d) [011031031]\begin{bmatrix}0&1&1\\0&3&1\\0&3&1\end{bmatrix}
Question 2. For a given epipole e′=(1,0)e’=(1,0) in the right image, and a point x=(3,5)x=(3,5) in the left image, determine the epipolar line l′l’ in the right image along which the corresponding point xx must lie.
a) (−6, 6, −7/3)(-6,\,6,\,-7/3)
b) (6, 6, −6)(6,\,6,\,-6)
c) (6, 6, 6)(6,\,6,\,6)
d) (3, 6, −3)(3,\,6,\,-3)
Question 3. For the given stereo imaging set up, find the fundamental matrix FF.
a) [0−1−1120011]\begin{bmatrix}0&-1&-1\\1&2&0\\0&1&1\end{bmatrix}
b) [00−22−26222]\begin{bmatrix}0&0&-2\\2&-2&6\\2&2&2\end{bmatrix}
c) [01−10110−1−1]\begin{bmatrix}0&1&-1\\0&1&1\\0&-1&-1\end{bmatrix}
d) [100110011]\begin{bmatrix}1&0&0\\1&1&0\\0&1&1\end{bmatrix}
Question 4. Given a point p1=(3,5)p_1=(3,5) in the left image. Compute the epipolar line.
a) (−1, 4, 6)(-1,\,4,\,6)
b) (4, 8, 6)(4,\,8,\,6)
c) (1, 6, 4)(1,\,6,\,4)
d) (8, 4, 1)(8,\,4,\,1)
Question 5. Given another point p2=(3,2)p_2=(3,2) in the left image, find the right epipole e′e’.
a) (−6, −6, 12)(-6,\,-6,\,12)
b) (6, −21, 15)(6,\,-21,\,15)
c) (6, −6, 21)(6,\,-6,\,21)
d) (6, −6, 12)(6,\,-6,\,12)
Question 6. Given rotation R=[10001000−1]R=\begin{bmatrix}1&0&0\\0&1&0\\0&0&-1\end{bmatrix} and translation t=(0,1,1)t=(0,1,1), compute the Essential matrix EE.
a) [010−10000−1]\begin{bmatrix}0&1&0\\-1&0&0\\0&0&-1\end{bmatrix}
b) [0−100−1110−1]\begin{bmatrix}0&-1&0\\0&-1&1\\1&0&-1\end{bmatrix}
c) [011−10101−1]\begin{bmatrix}0&1&1\\-1&0&1\\0&1&-1\end{bmatrix}
d) [100−10001−1]\begin{bmatrix}1&0&0\\-1&0&0\\0&1&-1\end{bmatrix}
Question 7. Consider a stereo imaging set up with two cameras P=[300003000010]P=\begin{bmatrix}3&0&0&0\\0&3&0&0\\0&0&1&0\end{bmatrix} (left) and P′=[300003000010]P’=\begin{bmatrix}3&0&0&0\\0&3&0&0\\0&0&1&0\end{bmatrix} (right). If the image coordinates of a 3‑D point are (19,3)(19,3) and (9,3)(9,3) in left and right cameras, compute its depth (z‑coordinate) in 3D.
Question 8. Find the fundamental matrix FF and camera centre. Answer till two decimal places.
a) F=[22.28−14 4−6−60−18]F=\begin{bmatrix}22.28&-14&\;\;4\\-6&-60&-18\end{bmatrix}, Centre (4, 3, −4), (4, −1, −7)(4,\,3,\,-4),\; (4,\,-1,\,-7)
b) F=[22.28−14 4−6−60−18]F=\begin{bmatrix}22.28&-14&\;\;4\\-6&-60&-18\end{bmatrix}, Centre (4, 4, 3), (a, t, i)(4,\,4,\,3),\; (a,\,t,\,i)
c) F=[22.28−14 4−6−60−18]F=\begin{bmatrix}22.28&-14&\;\;4\\-6&-60&-18\end{bmatrix}, Centre (4, 4, −3), (a, t, −17)(4,\,4,\,-3),\; (a,\,t,\,-17)
d) F=[22.28−14 4−6−59−18]F=\begin{bmatrix}22.28&-14&\;\;4\\-6&-59&-18\end{bmatrix}, Centre (4, 4, 3), (a, −1, −7)(4,\,4,\,3),\; (a,\,-1,\,-7)
Question 9. Find the right epipole e′e’. Answer till two decimal places.
a) (0.5, 3.69, 0.07)(0.5,\,3.69,\,0.07)
b) (−0.5, 0.5, 0.07)(-0.5,\,0.5,\,0.07)
c) (0.69, −3.69, −0.07)(0.69,\,-3.69,\,-0.07)
d) (−0.69, 3.69, −0.07)(-0.69,\,3.69,\,-0.07)
Question 10. Assume a stereo imaging setup has two image planes, left and right. Which of the following could be a possible left null vector (right epipole for the corresponding stereo setup) of F=[21208−759−433−177]F=\begin{bmatrix}2&1&20\\8&-7&59\\-4&33&-177\end{bmatrix}?
a) (1, −3, 1)(1,\,-3,\,1)
b) (−1, 3, 1)(-1,\,3,\,1)
c) (−1, 3, −1)(-1,\,3,\,-1)
d) (1, 3, 1)(1,\,3,\,1)
These are Computer Vision Nptel Week 4 Assignment Answers