# ECSE 415 Assignment 1: Image Filtering solution

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## Description

1 Thresholding (12 Points)
Thresholding is the simplest method of image segmentation. From a grayscale
image, thresholding can be used to create binary images. Here, each pixel in an
image is replaced with a foreground label (i.e. a white pixel with 255 value) if
the image intensity Ii,j is satisfies some pre-defined condition (Ex. if Ii,j > T),
or with a background label (i.e. a black pixel with 0 value) otherwise.
Simple Binary Thresholding:
Si,j =

255 if Ii,j > T; (1)
0 otherwise. (2)
Inverse Binary Thresholding:
Si,j =

255 if Ii,j < T; (3)
0 otherwise. (4)
Window Binary Thresholding:
Si,j =

255 if T1 > Ii,j > T2; (5)
0 otherwise. (6)
You are given an image named ”numbers.jpg” (Figure 1(a)) which contains
multiple different multi-digit numbers. Your task is to threshold the image using
the pre-defined conditions for thresholding defined above.
Note that you are not allowed to use the openCV cv2.threshold function
functions.
1. Threshold the image at three different thresholds 1) 55 2) 90 and 3) 150 using simple binary thresholding and inverse binary thresholding as defined
above. (3 points)
How many and which numbers are segmented at each threshold? (A number is considered as segmented if all digits of that number are considered
as foreground in the thresholded image) What else do you observe at each
threshold? (3 points)
3. Threshold the image using Window binary thresholding using three different range of thresholds. 1) T1=55 and T2=90, 2) T1=90 and T2=150,
3) T1=55 and T2=150. Write your observations. How many and which
numbers are segmented at each threshold? (3 points)
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(a) (b)
Figure 1: (a) Input image for thresholding, (b) Example of output image of
thresholding. Note that only numbers ”123” and ”549” are segmented (foreground pixels).
4. In a practical application, we vary the value of the hyper-parameters (here,
the threshold values) for any of the above mentioned thresholding methods, such that we get the desired output. Find a threshold value such
that only numbers ”123” and ”549” are segmented (i.e. considered as
foreground – white pixel – 255 value). See Figure 1(b). Report your finding for at least three different threshold values, and write how it helped
you in narrowing down the desired hyper-parameter value. (3 points)
2 Denoising (18 Points)
You are given a clean image named ‘lighthouse’ (Figure 2(a)) and an image
corrupted by additive white Gaussian noise (Figure 2(b)). You are allowed to
use OpenCV/Scikit-learn functions for this section.
Apply the following filtering operations:
1. Filter the noisy image using a 5 × 5 Gaussian filter with variance equal to
2. (3 points)
2. Filter the noisy image using a box filter of the same size. (3 points)
3. Compare the Peak-Signal-to-Noise-Ratio (PSNR) of both of the denoised
images to that of the clean image and state which method gives the superior result. (Use the PSNR function provided by opencv) (3 points)
You are also given an image corrupted by salt and pepper noise (Figure 2(c)).
Apply the following filtering operations:
4. Filter the noisy image using the same Gaussian filter as used in the previous question. (3 points)
5. Filter the noisy image using a median filter of the same size. (3 points)
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(a) (b) (c)
Figure 2: Input images for denoising. (a) clean image (b) image corrupted with
Gaussian noise (c) image corrupted with salt and pepper noise.
6. Compare the PSNR of both of the denoised images to that of the clean
image and state which method gives a better result. (3 points)
3 Sobel edge detector (16 Points)
In this question, you will assess the effect of varying the kernel size on the
results of an edge detection algorithm. You will detect edges in a clean image
named, ‘cameraman’ (Figure 3(a)). You are allowed to use OpenCV/Scikit-learn
(a) (b)
Figure 3: Input image for edge detection. (a) clean image (b) image corrupted
with Gaussian noise.
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functions for this section.
• Apply a Sobel edge detector with the kernel size of 3×3, 5×5 and 7×7 to
the image. Threshold the filtered image to detect edges. Use two values
of thresholds: 10% and 20% of the maximum pixel value in the filtered
image. (4 points)
• Comment on the effect of filter size on the output. (2 points)
Next, you will evaluate the effect of denoising prior to edge detection. For
the following questions, you will use noisy image as shown in Figure 3(b).
• Apply a Sobel edge detector with the kernel size of 3 × 3. Threshold the
filtered image to detect edges. Use two values of thresholds: 10% and 20%
of the maximum pixel value in the filtered image. (4 points)
• Denoise the image with a 3 × 3 box filter and then apply the same Sobel
edge detector, with the same values of the thresholds, from the previous
question. (4 points)
• Comment on the effectiveness of using denoising prior to edge detection.
(2 points)
(a) (b)
Figure 4: (a) Input image for canny edge detection (b) expected output.
4 Canny Edge Detection (12 Points)
For this section, experiments will be performed on the ’dolphin.jpg’ (Figure
4(a)) image.
1. Briefly describe the 4 main steps of Canny edge detection. (2 points)
2. As you saw in Tutorial-2, the 3 main hyperparameters of Canny Edge
detection are the Gaussian Smoothing Kernel size (K), and the Lower (L)
and Higher (H) Thresholds used for Hysteresis. In this section, we will
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observe the effect of changing these hyperparameters. You will experiment on 3 different values for all 3 parameters (K = 5,9,13, L = 10,30,50,
H = 100, 150,200). Vary the values of each hyper-parameter and keep
other hyper-parameters constant. Do this procedure for all combination of
hyper-parameters mentioned above. This should results in total 27 triplets
of hyper-parameters. E.g. (K,L,U) = (5,10,100), (5,10,150), (9,10,200),
…. Use canny edge detection (cv2.GaussianBlur and cv2.Canny) for each
of these triplets. (4 points)
3. Comment on how changing values of each hyper-parameters (K,L,U) effects the overall edge detection. Is there is any relationship between any
hyper-parameters? (3 points)
4. Find a value of each hyper-parameter such that only dolphin edges are
detected. (Figure 4(b)) (3 points)
(a)
(b)
Figure 5: (a) checkerboard input image and expected harris corner output (red
dots represents detecteed harris corners) (b) shapes image.
5 Harris Corner Detection (12 points)
Implement the Harris corner detector as described in class (lecture-5 slide-48
and tutorial-2) using numpy (5 points). This has the following steps:
1. Compute Image derivatives (optionally, blur first)
2. Compute Square of derivatives
3. Apply Gaussian Filtering on the output of step-2
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4. Get Cornerness function response (Determinant(H)-kTrace(H)2), where
k=0.05. (You can vary value of k for your application)
5. Perform non-maxima suppression (as in the Canny edge detector)
You will apply Harris Corner Detector for three different images:
1. Checkerboard image Figure 5(a) (Input image). Change value of threshold
to get detected corners similar to Figure (a) (Harris Corner). Observe and
report affect of changing threshold values (3 points)
2. Shape image Figure 5(b). Try different value of thresholds and report