EBU7240 A Joint Programme Examinations 2020/21
EBU7240 Computer Vision
Time allowed 2 hours
Answer ALL questions
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Use Answer book to answer the questions.
NOT allowed: electronic calculators and electronic dictionaries.
INSTRUCTIONS
1. You MUST use the supplied Answer book to answer the questions.
2. You must NOT take question papers or answer books, used or unused, from the examination room.
3. Write only with a black or blue pen and in English.
4. Do all rough work in the answer book – do not tear out any pages.
5. If you use Supplementary Answer Books, tie them to the end of this book.
6. Write clearly and legibly.
7. Read the instructions on the inside cover.
Dr Changjae Oh, Dr Marie-
Copyright © Beijing University of Posts and Telecommunications & © Queen Mary University of London 2020
Filename: 2021_EBU7240_A
Before the start of the examination
Instructions
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EBU7240 Paper A 2020/21
Question 1
a) This question is about camera model.
i) Given the optical centre, 𝑂, at the origin, and the focal length 𝑓, and the image plane parallel to 𝑥𝑦-plane, 1) draw the pinhole projection model, including the 3D point 𝑃 = (𝑥1, 𝑦1, 𝑧1) and its projected 2D image point 𝑃′ = (𝑥′1, 𝑦′1). Also, 2) represent the coordinate 𝑃′ = (𝑥′1, 𝑦′1). in terms of 𝑥1, 𝑦1, and 𝑧1.
ii) Describe how depth of field is affected if aperture size becomes smaller.
b) This question is about image filtering.
(5 marks) (2 marks)
i) Given a 3 × 3 image, compute the output value of a centre pixel in grey by applying two different filters: 1) Uniform mean filtering with the 3 × 3 filter kernel, 2) Median filtering with the 3 × 3 filter kernel. (Show your calculations)
ii) Explain why the average mean filter is good at removing zero-mean additive white gaussian noise (AWGN) 𝑁 that has the following probability density function of a Gaussian random variable 𝑧.
1 𝑧2 𝑃(𝑧=𝑁) =√2𝜋𝜎exp(−2𝜎2)
iii) Explain the bilateral filtering including 1) its mathematical definition and 2) the advantages
over Gaussian filtering in image denoising.
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EBU7240 Paper A 2020/21
c) This question is about feature detection and matching.
[10 marks]
i) By using Harris corner detector with 3 × 3 window of equal weighting, the empirical constant k = 0.05, and differentiation kernel below (d/dx and d/dy), 1) find the Harris matrix, and 2) the corner response for the centre of the following image 𝐼1, and 3) determine whether the point is flat, edge, or corner.
55555 0 55555 𝑑/𝑑𝑥=[−1],𝑑/𝑑𝑦=[0 −1 1], 𝐼1 = 0 0 1 6 6 1 66666
[6 6 6 6 6]
ii) Describe how key point descriptor construction works in Scale Invariant Feature Transform. (4 marks)
iii) We have two sets of features {𝑓 |𝑖 = 1, … , 𝑁}, from a reference image 𝐼 , and {𝑔 |𝑗 = 1, … , 𝑀}, 𝑖1𝑗
from a target image 𝐼 . Given a reference feature, 𝑓 , describe how nearest neighbour matching
works on 𝑓 . 1
Question 2
a) This question is about fitting.
i) The figure below shows the pseudo code for estimating an affine transformation with RANSAC. Fill out the blanks in the code.
ii) Explain the Hough transform algorithm with illustrations.
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EBU7240 Paper A 2020/21
b) This question is about grouping.
i) The figure below shows the pseudo code for K-means algorithm. Fill out the blanks.
ii) State three advantages and two drawbacks of Mean-shift algorithm.
c) This question is about calibration.
State 1) the definition of camera calibration with 2) the illustration of image, camera, and
world coordinates.
d) This question is about stereo matching.
i) Explain the uniqueness constraint used for improving local stereo matching performance.
Provide your description with an illustration.
ii) In the figure below, derive the relationship between disparity, 𝑥 − 𝑥′ and depth 𝑧.
[8 marks] (3 marks)
[3 marks] (3 marks)
[6 marks] (3 marks)
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EBU7240 Paper A
Question 3
a) This question is about Tracking.
Kanade-Lukas-Tomasi (KLT) Tracker solves the objective function below:
min ∑[𝐼(𝑾(𝒙; 𝒑)) − 𝑇(𝒙)]2
where 𝒑 is warp parameters, 𝐼 is image intensity, 𝑾 is a warping function, 𝑇 is template image intensity, and 𝒙 is pixel coordinate. The figure below shows the procedure of KLT Tracker. Fill out the blanks with the proper notations.
4. Evaluate Jacobian [ 5. Compute Hessian [ 6. Compute ∆𝒑 = [
7. Update parameters [
1. Warp image [ 𝐼(𝑾(𝒙; 𝒑)) ]
2. Compute error image [ 𝐼(𝑾(𝒙; 𝒑)) − 𝑇(𝒙) ]
3. Compute gradient [ 𝐼(𝒙′) (𝒙′: coordinates of the warped image) ]
b) This question is about Recognition.
i) Describe semantic segmentation, instance segmentation and their difference.
[13 marks] (4 marks)
ii) Describe the training and testing phases in statistical learning framework with illustration.
iii) State the 1) two advantages and 2) two drawbacks of nearest neighbour classifier.
c) This question is about detection.
i) In Viola/Jones face detector, integral images are used for fast feature evaluation during testing. Find 1) the integral image of the figure below and compute 2) the sum of pixels in the grey region based on the integral image. (Show your calculations)
ii) Viola/Jones face detector employs boosting for feature selection. Describe the process, with illustration, of boosting round 1.
(4 marks) Turn over until you reach the “END OF PAPER” line Page 6 of 8
EBU7240 Paper A
Question 4
a) This question is about Backpropagation in Deep Learning.
The figure below is 2-layer neural network with batch size 1:
iii) In the above 2-layers neural net, the batch size is 1. Re-draw this figure when the batch size is 16. State the dimension of all variables clearly.
b) This question is about Feedforward process in deep learning.
The feed-forward process of the convolution is performed as below. Assume that matrix and vector multiplication is used for an efficient implementation on GPU. Note that the figure is drawn with BS = 1.
Input: [100x100x3]
Conv filter: 32 filters of [3x3x3]
Padding: 1
Batch size: BS
[10 marks]
where 𝒔 = 𝐖 𝒙 + 𝒃 , 𝒔 = 𝐖 𝒉 + 𝒃 , and the loss function 𝐿 = (𝒔 111222 2
And the sigmoid function is defined as below:
𝒉 = 𝜎(𝒔1) = 1 1+𝑒−𝒔1
i) Derive the following derivative, 𝜕𝐿 . 𝜕𝒔2
ii) Derive the following derivatives as a function of 𝜕𝐿 : 𝜕𝒔𝟐
1) 𝜕𝐿 ,2)𝜕𝐿 𝜕𝒃2 𝜕𝒉
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Page 7 of 8
EBU7240 Paper A 2020/21
i) Compute the size of output activation map when 𝐵𝑆 = 1. Use the formula for computing the size of activation map.
ii) Explain the feed-forward process of the convolutional layer in a form of O = WX + B. Assume that the batch size 𝐵𝑆 = 1 . Hint) Explain this by considering O as 32 × 10000 matrix. O should be reshaped into the output activation map.
c) This question is about Training a neural network.
i) Based on the loss curve in the figure below, state the problem and suggest the solution.
[8 marks] (4 marks)
ii) State two advantages and two drawbacks of neural networks.
END OF PAPER
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