(ECSE 415) Assignment 1: Image Filtering

Please submit your assignment solutions electronically via the myCourses assignment dropbox. The submission should include: a report in PDF format and ve jupyter notebooks corresponding to ve subquestions. More details on the format of the submission can be found in the last section. Submissions that do not follow the format will be penalized 10%. Attempt all parts of this assign-ment. The assignment will be graded out of total of 65 points. Students are expected to write their own code. (Academic integrity guidelines can be found at https://www.mcgill.ca/students/srr/academicrights/integrity). Assign-ments received up to 24 hours late will be penalized by 30%. Assignments received more than 24 hours late will not be graded.

    • Filtering

1.1    Denoising

You are given a clean image named, ‘peppers’ (Figure 1(a)) and an image cor-rupted by additive white Gaussian noise (Figure 1(b)). Apply following ltering operations:

    1. Filter the noisy image using a 7 7 Gaussian lter with variance equals to 2. (3 points)

    2. Filter the noisy image using a box  lter of the same size. (3 points)

    3. Compare the PSNR of both of the denoised images to that of the clean image and state which method gives the superior result. (3 points)

You are also given an image corrupted by salt and pepper noise (Figure 1(c)).

Apply the following    ltering operations:

    4. Filter the noisy image using the same Gaussian lter as used in the pre-vious question. (3 points)

    5. Filter the noisy image using a median  lter of the same size. (3 points)

    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)


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1.2    Sharpening

Sharpening is de ned as follows:


sharpened image = original image + details

details = original image    blurred image

    1. Sharpen the given image ‘rice’ (see Figure 2(a)) where,

the blurred image is generated using 5  5 box  lter. (3 points)

the blurred image is generated using 5 5 Gaussian lter with vari-ance = 2. (3 points)

    2. Which of the two methods is expected to give better results and why? Can you observe expected result? (4 points)











(a)    (b)    (c)

Figure 1: Input images for denosing. (a) clean image (b) image corrupted with Gaussian noise (c) image corrupted with salt and pepper noise.

















(a)    (b)

Figure 2: Input images for sharpening and edge detection. (a) rice (b) woman.



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    • Edge detection

2.1    Sobel edge detector

    1. E ect of sharpening on edge detection

Apply a Sobel edge detector to the image ‘rice’ (Figure 2(a)). Use following thresholds: 150 and 200. Use kernel size of 3. (4 points)

Apply a Sobel edge detector to the two previously-sharpened images with the same threshold. (4 points)

Comment on the e ectiveness of using sharpening prior to the edge detection. (3 points)

    2. E ect of denoising on edge detection

Apply a Sobel edge detector to the image ‘woman’ (see Figure 2(b)). Use two values of thresholds: 10% and 20% of the maximum lter response. (4 points)

First denoise image with a 3 3 box lter and then apply a Sobel edge detector. Use the same values of threshold. (4 points)

Comment on the e ectiveness of using denoising prior to edge detec-tion. (3 points)

2.2    Laplacian of Gaussian

    1. Apply a 5 5 Laplacian of Gaussian edge detector to the image ‘woman’. (6 points)

    • Template Matching

In this problem we will look at how to nd a template pattern in a clut-tered scene. In order to make it more fun we will use ‘Where is Waldo?’ (https://en.wikipedia.org/wiki/Where%27s Wally%3F) puzzle. You are given a scene of an amusement park shown in Figure 3(a) and you have to nd Waldo, shown in Figure 3(b).


    1. Given a reference image (scene of an amusement park) and a template image (face of Waldo), iterate over all pixel locations of reference image and compare the local patch with template image using sum of square distance (SSD) metric. Display SSD for whole image. Find the location ((x; y) coordinate) where the SSD is minimum and see if you can nd Waldo there! (7 points)

    2. Repeat above process with the noisy template as shown in Figure 3(c). (2 points)



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(b)





(c)

(a)

Figure 3: (a) Cluttered scene of an amusement park (b) template face of Waldo (c) noisy template face of Waldo

    • Instruction for the Report

Please recall submissions that do not follow the format will be penalized 10%.

4.1    Report

    1. Write answers section-wise.

    2. Numbering of answers should match exactly as the questions.

    3. Paste output images in the answers of programming questions.

    4. Answers to reasoning questions should be brief but comprehensive. Un-necessarily lengthy answers will be penalized.

4.2    Code

    1. Title ve jupyter notebooks as (i) denoising (ii) sharpening (iii) sobel edge (iv) LoG edge (v) template matching, each corresponding to one subsec-tion.

    2. Comment your code appropriately.

    3. Assume images are kept in a same folder as codes. Make sure that the submitted code is running without error. Add a README le if required.

    4. If external libraries were used in your code please specify its name and version in the README le.

    5. Do not submit input/output images.




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