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ENGN6528 Final Exam S1 2020








The Australian National University College of Engineering and Computer Science Final Examination, First Semester 2020

ENGN6528 Computer Vision

Question Booklet

Reading time: 15 minutes
Writing time: 3 hours
Uploading time: 15 minutes




















Instructions on next page



2
Allotted Time

You will have 3 hours to complete the exam plus 15 minutes of reading time. An additional 15
minutes has also been allowed to accommodate the additional task of uploading your completed
exam to the final exam turnitin submission portal on the ENGN6528 Wattle site. Thus you have 3
hours and 30 minutes to complete the exam. NO late exams will be accepted. You may begin the
exam as soon as you download it.
Minimal requirements:

You may attempt all questions

You SHOULD NOT include an assignment cover sheet

You must type your ANU student identification number at the top of the first page of your submission

You must monitor your own time (i.e. there is no invigilator to tell you how many minutes are left).

Your answers must be clear enough that another person can read, understand and mark your
answer. 11 or 12 point font with 1.5 spacing is preferred. Scanned images of handwritten equations
or diagrams must be legible and of a suitable size.

Numbering questions
● You must specify the question you are answering by typing the relevant question number at
the top the page
● Each question should begin on a new page
● Multi-part questions (e.g. question 1 parts a and b) may be addressed on the same page but
should be clearly labelled (e.g. 1a, 1b )
● Questions should be answered in order

You must upload your completed answers in a single document file within the allotted time using a
compatible file type for Turnitin (Preference: MS Word’s .doc or .docx format) It is the student’s
responsibility to check that the file has uploaded correctly within Turnitin. No late exams will
be accepted.
Academic integrity

Students are reminded of the declaration that they agree to when submitting this exam paper via
Turnitin:
I declare that this work:
● upholds the principles of academic integrity as defined in the University Academic Misconduct
Rules;
● is original, except where collaboration (for example group work) has been authorised in
writing by the course convener in the course outline and/or Wattle site;
● is produced for the purposes of this assessment task and has not been submitted for
assessment in any other context, except where authorised in writing by the course convener;
● gives appropriate acknowledgement of the ideas, scholarship and intellectual property of
others insofar as these have been used;
● in no part involves copying, cheating, collusion, fabrication, plagiarism or recycling.

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There are 10 questions in total.
(Q1-Q10)

Please name your submission as
ENGN6528_exam_u1234567.docx

































Questions on the next page

4

Q1: (10 marks) [basic concepts]

Answer the following questions concisely. Each question must be answered in no
more than 5 lines of text. Longer answers will be penalized.

(1) According to David Marr, computer vision can be separated into three layers,
low-level, mid-level and high-level vision. Image processing, filtering, and low-
level edge detection such as the Sobel filter are regarded as low-level vision.
Give an example of a mid-level vision task. [1 mark]



(2) Consider the HSV colour space. What does H, S, and V stand for? [1 mark]
Describe the information that the H channel contains.




(3) What does SVM stand for? What does RANSAC stand for? [2 marks]




(4) Using the PCA technique, any face image can be represented as a linear
combination of some so-called “eigenfaces”, plus a noise image. The eigenfaces
can be computed by using eigen-value decomposition of certain covariance
matrix A. The representation then uses the top K Eigen faces in its
representation. Describe how the top K eigenfaces are chosen? [2 marks]





(5) We can represent a face image by a feature vector (w1,…,wk), which is obtained
by projecting it to the face space (u1, u2,… , uk). Mathematically, it is defined as
(w1, …, wk) = (u1T(x – µ), … , ukT(x – µ)).

Explain the process of evaluating a novel face and determining if the novel face
image is one of the faces in the training dataset. You can choose to do this by
explaining the terms u1, x, and µ and their usage, or some other way if you prefer. [4
marks]
.


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Q2: (21 marks) [3D SFM and Image formation question]

Answer the following questions concisely. Write down working, and if you are
unsure about some part along the way, state your best assumption and use it for the
remaining parts. Similarly, if you think some aspect is ambiguous, state your
assumption and write the answer as clearly as you can.

(a) Given two calibrated cameras, C1 and C2, C1 has focal length of 500 in x and 375
in y, the camera has resolution 512x512, and the camera centre projected to image
is at (251, 252), with no skew. Suppose C2 has the same resolution and focal
length as C1, but the camera centre projected to image is at (250, 250). Write
down the calibration matrix K1 and K2 for C1 and C2 respectively. [3 marks]

(b) Suppose that a 3D world coordinate system ((X,Y,Z) coordinates as in the below
diagram from the lecture notes) is defined as aligned with the camera coordinate
system of C1. More specifically, the world origin is at the camera centre of C1,
the Z axis is aligned with the optical(principal) axis and the X and Y world
coordinate systems aligned parallel with the x and y axes of the image of C1.
Write down the matrices K[R|t] which define the projection of a point in world
coordinate system to the image of C1. [3 marks]


(c) Suppose that the scene has a point, P1, that in the world coordinate system defined
above that lies at (0.240, 0.232, 0.100). Note that the points in world coordinate
system are measured in m. What location (to the nearest pixel) will that world
point (P1) map to in the image of C1? [2 marks]

(d) Suppose that with respect to the world coordinate system that is aligned with
camera C1, camera C2 begins being aligned to C1, and is then rotated by 45
degrees about its vertical axis (Y-axis)(as shown below), and subsequently the
centre of C2 is translated by 0.2 m to the left of C1 (along the X axis of C1). The
two camera centres both remain on the same (X, Z) plane

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Write down the matrices K[R|t], which define the projection of points in the world
system (i.e, the same coordinate system of C1) to the image of C2. [3 marks]



(e) What is the location (to the nearest pixel) that P1 maps to in the image of Camera
C2? [2 marks]

(f) Define the term epipole. [2 marks]


(g) For camera C1, there is an epipole (or epipolar point) that relates to Camera C2.
For the two-camera setup for predicting structure from motion, what is the
position of the epipole in camera C1 of camera C2? (Hint: It is a point in the
image coordinates of Camera C1.)[2 marks]

(h) Given a point P2 that appears in camera C1 at image location (x1, y1), and in
camera C2 at image location (x2, y2). How would you find the world coordinates
of point P2? [4 marks]

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Q3 [Camera models and SFM] (10 marks)
(a) The first image below is taken from the course lecture notes. It shows a
pinhole camera model, where all rays from the scene are blocked by a barrier,
except those from a single direction that pass through a pin-hole, resulting in
the projection of an image (of a tree here) onto a film or ccd/CMOS sensor of
a camera. However, as shown in the second image below, many cameras
include a thin lens rather than simply a pin-hole barrier. How is the pin-hole
model a good model for a camera with a lens? Explain in two or three
sentences at a maximum, and/or with a diagram. [3 marks]

(b) Given two cameras with an unknown distance between them that view the
same scene. Suppose that you know the intrinsic parameters of both cameras,
and they both view a common object, for which a large number of accurately
matched points are available in both images.
What information can you recover about the cameras and the scene from this
configuration up to scale? Describe what the parameters are to be recovered,
and how many parameters there are. [3 marks]

(c) Suppose that you do know the intrinsic calibration parameters of both
cameras, describe a method for recovering camera and scene information
given a set of point matches where a small number of the points maybe
mismatched. [4 marks]

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Q4: (10 Marks) [Shape-from-X, Stereo]

(1) Shape-from-Shading approaches predict the 3D shape from the brightness of
image pixels. Given a point light source at infinity (distant light source), write
down the equation that defines the brightness at an image pixel assuming that
the camera views a Lambertian surface, Please also define the terms of the
equation. [2 marks]

(2) Suppose that we have used some other methods to know the brightness of the
lighting, its lighting direction and the reflectance properties of the surface in the
above scenario, but we only have intensity information about this particular
pixel for this surface, what can we say about the surface orientation? [2 marks]

(3) Suppose we have three images of this point from the same camera position,
each taken by moving the light source to different locations. What could we then
say about the surface orientation at this point? [2 marks]

(4) The images (a and b) shown below are the left, and the right image of an ideal
stereo pair, taken with two identical cameras (A and B) mounted at the same
horizontal level and with their optical axes parallel.



Draw a planar-view (i.e., a top-down bird-eye's view) of the scene showing
roughly what the spatial arrangements of the three objects are. Only relative
(rather than accurate) positions are required. [4 marks]
(a) (b)
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Q5: (5 Marks) [Image Filtering and histogram modification]

Suppose that we have a histogram modification function as follows: (colour
image)

M(v) = cv^, where 0 <= v <= 255 (assuming pixel values for the camera are in
the range of [0,255], where = 0.4, and c is 1.

(a) Suppose that we apply this to the following image. Describe what the effect
will be on the modified histogram? [2 marks]



(b) Suppose we now use a different function that operates as follows:

M(v) = cv^ , where v < 50
M(v) = c(v-20)^ , where 50 <= v < 70
M(v) = cv^ , where v >=70

where = 0.4, and c is 1.

Suppose that we apply this to (the histogram of) an image. What will be the effect
on the histogram of the image? What will be the change to the output image? [3
marks]


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Q6: (11 marks) [ Image filtering]
(a) Consider the 4 x 5 image below. The pixel grey values are indicated by the
values in the cells.
4 4 4 4
6 4 7 3
8 3 5 5
3 10 6 8
8 6 8 7

Apply the following filter to the image defined above. Note that to avoid
problems at
boundaries of the image you only need to calculate the filtered values for the 2x3
centred region. [4 marks]

Note: in solving this problem, please use a “correlation” rather than “convolution”
operator to implement the image filtering.


(b) The following is a separable filter. What does it mean to be a separable filter? [2
marks]
1 2 1
2 4 2
1 2 1
(c) Write down the separate components of the above filter. [4 marks]


(d) What is the difference between correlation and convolution? [1 mark]


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Q7: (13 marks) [ Basic algorithms ]

(a) Suppose that a linear support vector machine was used to classify the
following points (red vs blue are two classes Which line (among a, b, c and d)
below defines the classifier computed based on a linear support vector
machine. Your answer may be (a-d), or multiple or all of these? [1 mark]

(b) Explain (in a few words or a sentence) why you selected your answer. [2
marks]
























(c) The Integral Image is a part of the Viola-Jones face detector that makes feature
computation more efficient. Given an input image below, write down the
corresponding integral image? [4 marks]
4 4 4 4
6 4 7 3
8 3 5 5
3 10 6 8
8 6 8 7




a
b c d
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(d) Both the Viola-Jones face detector and the Histogram of Oriented Gradients
detector use gradients as their basis for detection. What is the advantage of
gradients over some other low-level descriptor (such as colour)? [2 marks]

(e) The Histogram of Oriented Gradients detector applies a window to determine
if a pedestrian occurs at a particular location in an image. This is broken up
into 15x7 individual cells. What information does the descriptor include for
each of these cells? [2 marks]

(f) The SIFT algorithm is not sensitive to the scale of the appearance of the
locations that it matches. Describe (in a few sentences) how SIFT achieves
being able to match regions at a variety of scales. [2 marks]


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Q8: (8 marks) [basic design problem]

Given below is a single node in a neural network. Supposing that d is 4,
x={4,2,5,2}, and w={0.2,0.3,0.4,0.1}, b=0.1, and that the activation function is a
standard ReLU, that is =max(0,x), where x is the input to the activation function.


(a) What is the output of this node? [2 marks]

(b) Describe the difference between, recognition and detection in terms of how you
would use a Deep Convolutional Network to solve the problem? [2 marks]

(c) In the VGG convolutional neural network, the first layer (CONV1) adopts a set
of 3x3 filters for convolution, followed by a ReLU, then the second layer
(CONV2) similarly adopts 3x3 Convolution filters, followed again by a ReLU.
For the output of a single location (node) in CONV2, how many pixels of the
input image would impact on the result? (i.e., if you changed the pixel values).
[2 marks]

(d) You could remove one of these layers from the network, perhaps modifying the
other. Would this have an impact on the quality of the learning? Explain your
answer in at most a few sentences. (Note that multiple answers are possible to
this question, state any assumptions you make). [2 marks]



14
Q9: (2 marks) (questions with short answers) Given a dataset that consists of images
of the Eiffel Tower, your task is to learn a classifier to detect the Eiffel Tower in new
images. You implement PCA to reduce the dimensionality of your data, but find that
your performance in detecting the Eiffel Tower significantly drops in comparison to
your method on the original input data. Samples of your input training images are given
in the following figures. Why is the performance suffering? [hints: describe in two
sentences.]


Figure 1. Images in the dataset


15
Q10: (10 marks) (algorithm design) Turn your phone into a GPS in an art museum or a
library. GPS usually does not work well in an indoor environment. The goal of
designing this algorithm is to localise your position by taking a few images around you
in the museum. Please Briefly describe the key steps of your method.


Localize yourself


======= END of ALL QUESTIONS in the EXAM ===========


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