Homework 3 Digital Image Processing

Homework 3
ECE 253
Digital Image Processing

Make sure you follow these instructions carefully during submission :

• All problems are to be solved using MATLAB/Python unless mentioned otherwise.
• You should avoid using loops in your MATLAB/Python code unless you are explicitly permitted to do so.
• Submit your homework electronically by following the two steps listed below -
1. Upload a pdf file with your write-up on Gradescope. This should include your answers
to each question and relevant code snippet. Make sure the report mentions your full
name and PID. Finally, carefully read and include the following sentences at the top of
your report:
Academic Integrity Policy: Integrity of scholarship is essential for an academic community. The University expects that both faculty and students will honor this principle and
in so doing protect the validity of University intellectual work. For students, this means
that all academic work will be done by the individual to whom it is assigned, without
unauthorized aid of any kind.
By including this in my report, I agree to abide by the Academic Integrity Policy mentioned above.
2. Upload a zip file with all your scripts and files on Gradescope. Name this file:
ECE 253 hw3 lastname studentid.zip. This should include all files necessary to run
your code out of the box.
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Problem 1. Canny Edge Detection (15 points)
In this problem, you are required to write a function that performs Canny Edge Detection. The
function has the following specifications:
• It takes in two inputs: a grayscale image, and a threshold te.
• It returns the edge image.
• You are allowed the use of loops.
A brief description of the algorithm is given below. Make sure your function reproduces the
each step as given.
1. Smoothing: It is inevitable that all images taken from a camera will contain some amount
of noise. To prevent noise from being mistaken for edges, noise must be reduced. Therefore
the image is first smoothed by applying a Gaussian filter. A Gaussian kernel with standard
deviation σ = 1.4 (shown below) is to be used.
k =
1
159
·






2 4 5 4 2
4 9 12 9 4
5 12 15 12 5
4 9 12 9 4
2 4 5 4 2






2. Finding Gradients The next step is to find the horizontal and vertical gradients of the
smoothed image using the Sobel operators. The gradient images in the x and y-direction, Gx
and Gy are found by applying the kernels kx and ky given below:
kx =


−1 0 1
−2 0 2
−1 0 1

 , ky =


−1 −2 −1
0 0 0
1 2 1

 .
The corresponding gradient magnitude image is computed using:
|G| =
q
G2
x + G2
y
,
and the edge direction image is calculated as follows:
Gθ = arctan(
Gy
Gx
).
3. Non-maximum Suppression (NMS): The purpose of this step is to convert the thick
edges in the gradient magnitude image to ”sharp” edges. This is done by preserving all local
maxima in the gradient image, and deleting everything else. This is carried out by recursively
performing the following steps for each pixel in the gradient image:
• Round the gradient direction θ to nearest 45◦
, corresponding to the use of an 8-connected
neighbourhood.
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• Compare the edge strength of the current pixel with the edge strength of the pixel in the
positive and negative gradient direction i.e. if the gradient direction is north (θ = 90◦
),
then compare with the pixels to the north and south.
• If the edge strength of the current pixel is largest; preserve the value of the edge strength.
If not, suppress (remove) the value.
4. Thresholding: The edge-pixels remaining after the NMS step are (still) marked with their
strength. Many of these will probably be true edges in the image, but some may be caused by
noise or color variations. The simplest way to remove these would be to use a threshold, so
that only edges stronger that a certain value would be preserved. Use the input te to perform
thresholding on the non-maximum suppressed magnitude image.
Evaluate your canny edge detection function on geisel.jpg for a suitable value of te that retains
the structural edges, and removes the noisy ones.
Things to turn in:
• The original gradient magnitude image, the image after NMS, and the final edge image after
thresholding.
• The value for te that you used to produce the final edge image.
• Code for the function.
Problem 2. Butterworth Notch Reject Filtering in Frequency Domain (15 points)
This problem will follow Figure 4.64 in section 4.10.2 Notch Filters of Gonzalez & Woods 3rd
Edition.
(i) Read in the image Car.tif, pad the image to 512x512 (using zero padding on all four sides of
the image), and display the 2D-FFT log magnitude (after moving the DC component to the
center with fftshift):
MATLAB:
imagesc(-256:255,-256:255,log(abs(imFFT))); colorbar;
xlabel(‘u’); ylabel(‘v’);
Python: Please refer to this link and check Fourier Transform in Numpy section.
You should see symmetric “impulse-like” bursts which we suspect is the cause of the Moire
Pattern (the dot pattern from the newspaper image). We would like to filter out this pattern
in the frequency domain using a Butterworth Notch Reject Filter given by:
HNR(u, v) = Y
K
k=1
?
1
1 + [D0/Dk(u, v)]2n
? ? 1
1 + [D0/D−k(u, v)]2n
?
(1)
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where
Dk(u, v) =
(u − uk)
2 + (v − vk)
2
1/2
(2)
D−k(u, v) =
(u + uk)
2 + (v + vk)
2
1/2
(3)
Here, we have slightly modified the definition from the textbook slightly in that we removed
M/2 and N/2 from the equation so that the center of the DFT image is 0 rather than
(M/2, N/2).
The parameter K is the number of “impulse-like” bursts you would like to remove (excluding
their symmetric counterparts since the HNR equation already includes it), e.g. 4 for this
image rather than 8. The parameters n and D0 are scalar values that you may choose to
control the transition and radius of the notch filters. The parameter uk and vk is the location
of the k
th “impulse-like” bursts in the 2D DFT magnitude image. u and v are all possible
(u, v) coordinate pairs that you want to generate HNR for:
MATLAB:
[u,v] = meshgrid(-256:255);
Python:
x_axis = np.linspace(-256,255,512)
y_axis = np.linspace(-256,255,512)
[u,v] = np.meshgrid(x_axis,y_axis)
(ii) Repeat for Street.png, except for K=2 and remove the burst along the u = 0 axis and the
v = 0 axis.
Things to turn in:
• All images should have colorbars next to them
• All DFT magnitude images should have the DC frequencies in the center of the image
• 4 images from 2(i): 1 unpadded original image, the corresponding 2D DFT log-magnitude,
the butterworth Notch Reject Filter in frequency domain HNR(u, v), the final filtered image
• 10 parameters for 2(i): n, D0, u1, v1, ..., u4, v4
• 4 images from 2(ii): 1 unpadded original image, the corresponding 2D DFT log-magnitude,
the butterworth Notch Reject Filter in frequency domain HNR(u, v), the final filtered image
• 6 parameters for 2(ii): n, D0, u1, v1, u2, v2
• Code for 2(i), 2(ii)
Problem 3. PyTorch tutorial and questions (5 points)
After seeing some awe-inspiring machine learning results, do you want to try some yourselves?
Let’s start with some basic practice of machine learning framework: PyTorch. Please follow the
tutorial for cifar10 classifier (cifar10 tutorial ) and answer the following questions.
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(i) Login to the server for CPU/GPU resources. (0 point)
• https://datahub.ucsd.edu/ (Jupyterhub)
• Select environment (with or without GPU. You don’t need gpus in this homework.)
• Launch environment.
(ii) How many images and batches are used to train the network?
(iii) Do we normalize the images? What do we do in the example?
(iv) The losses are dropping! Can you plot out the training loss?
(v) Now the network is done training. Can you check some successful cases and some failure cases
(show some images classified by the network)?
(vi) Can you visualize the output of the 1st layer of CNN using one image from the training set?
Congratulations! Pytorch can be more powerful than that! Feel free to go through some tutorials
and get cool models!
References:
• deep learning 60min blitz
• pytorch with examples
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