Assignment 1: Image Processing Solution

This assignment covers topics discussed in the rst two weeks of class. The assignment is divided into two main parts: (1) mathematical and theoretical questions, (2) gentle Python programming for computer vision introduction. This assignment is designed to refresh the students of what they already know, as well as provide a quick background in case they are not familiar with the topics.







Instructions are provided rst for a reason.




Please read the instructions carefully.










Instructions



1.1 Submission Package




All assignments are submitted to your git repository located on git.engr.uvic.ca. The




last submitted entry, or (b) the submission with "Final submission" in the commit com-ments will be considered your submission entry. Marking will commence 72 hours after the deadline on entries that do not have "Final submission" comments for students who are using their late hours. A GIT tutorial is posted on the course page.



1.2 Assignment Report




Reports will be submitted in pdf format as assignX report.pdf. Any other format will not be accepted.







Do not explain or submit code in your assignment report. Reports are for discussing results when appropriate. You should provide comments in your code for the marking TA but deductions will not applied if no comments are provided. However, comments may aid the TA in understanding your code if you have provided an incorrect solution.




1.3 Code




All assignments should be in Python 3. Code that fail to run on Python 3 will receive a 20% deduction on the nal score. IPython or Jupyter notebooks are not accepted. Please do not change the provided script names, which have been provided for you.




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ECE 471/536: Computer Vision Assignment 1: Image Processing










It is strongly encouraged to follow PEP8. It makes your code much more readable for the marking TA. You will not, however, be marked on the quality of your code.




1.4 Delayed submission




Each student has a bank of 72 late hours which they may use for any assignment. No deduction for lateness will be applied while you have late hours. These are deducted in 30 minutes segments. Otherwise, you will receive a deduction of 20% per day.




1.5 Use of open source code




Short snippets of code on public websites such as StackOver ow may be used without an explicit license, but proper attribution should be given even in such case. This means that if you embed a snippet into your own code, you should properly cite it through the comments.




Please note that without proper attribution, it will be considered plagiarism.




We will be using the OpenCV 3 open source library available through the python pip package manager. However, the use of APIs/classes that perform the bulk for the assignment task will be prohibited. If you are unsure if an OpenCV library is prohibited, just message me on Slack.




In addition, as the assignments are intended for you to learn, (1) if the external code implements the core objective of the task, no points will be given; (2) code (including pseudo code) or written answers from other ECE471/ECE536 students will count as plagiarism.




To be more clear on (1), with the assignment, we will release a requirements.txt le, that you can use with pip to setup your environment.







Theoretical (50 points)



2.1 Preliminaries




2.1.1 Linear Algebra (29 points)




NOTE: We will not cover this in class.




Q1) Given the following vector and matrix de nitions, answer the following questions (show your work):

v =
1 2 3 u =
23
43
A =
2 4 5 63




1
2


1
2
3
45
65


4 7
8
9 5
v + 1 (1 mark)
v + vT (1 mark)
v vT (dot product) (3 marks)
v u (cross product) (3 marks)



v u (matrix multiplication) (3 marks) [NOTE: treat u as a multiple vector matrix (i.e. each row is a separate vector)]



v vT (Hadamard product) (3 marks)
Calculate the eigenvalues for matrix A (15 marks)















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ECE 471/536: Computer Vision Assignment 1: Image Processing










2.1.2 Statistics (16 points)




NOTE: We will not cover this in class.




Q2) Short answer - De ne and explain the following in 2-3 sentences (math de nitions are not required, but may be used to expand on your answer) and/or by sketching where appropriate.




What is mean and variance? (2 marks)



What is the Central Limit theorem? (3 marks)



What is the curse of dimensionality and how does it apply to Computer Vision? (5 marks)



What are the three properties of a probability density function f(x) for a continuous random variable X? (6 marks)



2.1.3 Linear Filtering (5 points)




Q3) Cross-correlation and convolution are similar operations, but convolution is associative and commutative while, in general, correlation isn't. How might this improve computation time (how fast the program will run)?







Programming (50 points)



3.1 Setting up a python virtual environment (no points)




You may skip this section if you are already familiar with how Python virtual environments work, and you already know how to set it up. However, it is encouraged to setup a new environment for the assignments, as we will test your Python scripts in a virtual environment with the packages speci ed in the requirements.txt le.




This step-by-step guide will rst go through the process of installing pip the Python package manager, and then installing virtualenv, and then nally setting up the your virtual environment.




3.1.1 Installing Python 3 and pip




In many cases Python 3 may not be installed in your OS. Installing Python 3 is highly dependent on the operating system. For this process, you will need root access.




Linux: If you are using a Linux distribution, use your package manager to install Python 3 and pip. For example, on Ubuntu/Debian/Mint, it should be as simple as typing in the terminal:




sudo apt install python3 python3-pip




OSX: Use Homebrew. Install Homebrew by visiting brew.sh, and type in the terminal:




brew install python3 (This also installs pip)




Windows: For Windows version, please install a Linux Virtual Machine using Virtual Box, or use a Linux server. Then follow Linux instructions. Alternatively, for Windows 10, install the required packages by following this Youtube video.




The following command-line commands should work for Windows 10 PowerShell (don't use the cmd terminal), but is currently untested.







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ECE 471/536: Computer Vision Assignment 1: Image Processing










3.1.2 Installing and setting up your virtual environment




After installing pip, you can easily install your virtual environment by opening a terminal and typing:




pip3 install --user virtualenv




Here, we have the {user ag as we are installing this for the current user. This way we wont need root privileges.




Then, you need to specify a directory for your virtual environments. For example, it could be /myvenvs. We will use this directory for the time being, for easy explanation, but any directory is ne. Create that directory, and then all you need to do is:




virtualenv --python=$(which python3) /myvenvs/a1




On Windows you may need to replace $(which python3) with the path to you Python3 executable.




Note that we are setting up the virtual environment with python3 by designating the python executable. To work in (activate) this virtual environment, type:




source /myvenvs/a1/bin/activate




To leave the virtual environment, type deactivate. In most cases, you will see something on the left of your command prompt, showing that you are inside a virtual environment. Once inside a virtual environment, you should now be able to install the exact environment that you will be evaluated through:




pip3 install -r <path-to-requirements.txt




For example, if you are already in the directory which you extracted the assignment package, you can type:




pip3 install -r requirements.txt




To check if everything is okay, you can try which python, that would return something like:




/home/adash/myvenvs/a1/bin/python




where /home/adash/ is your home folder, that is, /. Also, at this point you should also have ipython, which is a prettier version of the python command line interface. Go ahead to try importing numpy after launching ipython to try things out.




3.1.3 Python IDE




You may use any IDE or text editor you prefer. I prefer PyCharm, Spyder (which can be installed through pip) or Vim (not for the faint of heart). PyCharm has built-in git integration while Spyder does not; however, Spyder is less resource-heavy and I like its ipython terminal. Sublime is another popular IDE.




























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ECE 471/536: Computer Vision Assignment 1: Image Processing










3.2 Basic Image Handing (15 points)




3.2.1 Reading, display, and save an image




See provided boilerplate code. The code uses argparse to parse command-line arguments. You do not need to provide any arguments as the code will use default values, but is given as an example.




Your script will perform the following:




Reads pear.png provided in the assignment package, or any image your pass via the command-line.



Displays the image using matplotlib or OpenCV as a grayscale image.



Save an image as sharpened.png.



Your nal submission will save the result of imfilter2d. For testing, I suggest saving the result of cv2.filter2D for debugging purposes.




Hint: Keep a careful eye on the data-types for each of your arrays. Matplotlib handles images of oat type di erently than unsigned integer { it assumes that oat images are in the range of [0,1]. OpenCV doesn't like oat type images for displaying at all. When saving an image, you should make sure your image is in the range of [0,255].




Useful functions:




cv2.imread, cv2.imwrite cv2.imshow, cv2.waitKey




plt.imshow, plt.show, plt.plot




Useful reads:




Numpy ndarray documentation Matplotlib image tutorial




Numpy tutorial by Justin Johnson







3.3 Image Filtering (35 points)




3.3.1 Sharpen image using an approximate Laplacian of Gaussian )LoG) lter







See provided boilerplate code and lecture notes. Use the code from the previous section to display and save your output. You should submit your saved result with your nal submission.




Your script will perform the following:




Reads pear.png provided in the assignment package, or any image your pass via the command-line



Create an approximate LoG lter (see Lecture notes) of size 9x9



Apply a border to the input image



Apply the lter to the image using convolution



Save the result of the convolution to an result array



Clip the result (i.e. values less than 0 are set to 0) so the image is in the range [0,255]



Save an image as sharpened.png. Your nal submission will save the result of imfilter2d



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ECE 471/536: Computer Vision Assignment 1: Image Processing










8. BONUS: Write your code to handle any size of kernel




Hint: A Gaussian kernel is a linear kernel and is therefore separable and should sum to 1. You may use any border padding before performing convolution, but cv2.BORDER REFLECT is set by default.




Useful functions:




cv2.getGaussianKernel np.zeros, np.ones




np. oat32, np.uint8 cv2.copyMakeBorder




Prohibited functions:




cv2. lter2D (you can use it to test your imfilter2d)




Useful reads:




OpenCV image ltering documentation







Final Submission



Your nal submission in GitLab should include the following:




a1/




solution.py




assign1 report.pdf







sharpened.png




































































































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