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## Description

Instructions for submission: Please write a document in a pdf or doc file with your solutions (include pictures where needed), and submit through MarkUS. Please include your code and specify the question to which it corresponds.

1. (a) [0.5 point] Given an n n image I, and m m filter h, what is the computational cost of computing h I if h is not separable?

1. [0.5 point] What is the computational cost if h is separable?

1. [1 points] What are the steps of Canny edge detection? Please explain in detail the purpose of each step, and briefly describe how to implement each step.

1. [1 point] Explain why Laplacian of Gaussian can be used to detect edges.

1. [1 point] Write your own function M yCorrelation that implements the correla-tion operation. The input of the function includes: an input grayscale image I, a filter h, and a string mode. The function outputs the filtering results J. The mode parameter can be ’valid’, ’same’ or ’full’. The output must match what is specified by mode.

1. [0.5 point] Implement your own function M yConvolution that implements the convolution operation, based on the function M yCorrelation. The input and output is the same as M yCorrelation.

1. [1 point] Many camera apps provide “portrait mode”. It tends to make back-ground objects out of focus. We can generate such effect with the knowledge in image filtering. Please select an appropriate portrait photo you like, and change it to “portrait mode”.

Please provide the type, parameters of the filter you choose, and explain the reasons for using it. Please inlcude the original image and the processed image in your answer.

(Hint: you can mannully segment out the foreground masks.)

1. [1 point] Please breifly explain what is a separable filter.

1. [1 point] Please implement a function isSeparableF ilter, which takes a filter as input and outputs a bool number indicating whether it’s seperable. If it’s seperable, print the corresponding horizontal and vertical filters.

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1. [0.5 point] Please implement a function AddRandN oise to add uniformly dis-tributed random noises on a given image. The input includes: a grayscale image I, the magnitude of random noises m. The output is the image with noises.

Use AddRandN oise to add noises to gray:jpg. Rescale the range of image to [0; 1] and set the range of noises to [ 0:05; 0:05]. Show the image with noises in your answer.

1. [1 point] Select appropriate linear filters to remove the noises. Please provide the type, parameters of the filter you choose, and explain the reasons for using it. Show the filtered image in your answer.

2. [1 point] Please implement a function AddSaltAndP epperN oise to add salt-and-pepper noises on a given image. The input includes: a grayscale image I, the density of noises d. The output is the image with noises.

Set the density salt-and-pepper noises to 0.05 (5% of pixels affected) and add noises to gray:jpg. Show the image with noise in your answer.

1. [1 point] Try using the filter you choose in (b) to remove the noises in (c). Does it still work now? If not, can you find a way to remove the noises? You can either implement from scratch or use existing libraries. Briefly explain the method you use and why it can work. You should demo the results in your answer.

2. [1 point] Use AddSaltAndP epperN oise with density as 0.05, to add noises to each channel of color:jpg. Then you will get an image similar as shown in the middle of Fig. 1.

If we apply the filtering method in (d) to each channel, and then concatenate them, there will be flaws in the result. As shown in the right of Fig. 1, many noisy color blocks occurs, and the color doesn’t exist in the local region of original

New

colors!

Figure 1: From left to right: Original image, image with noises, and artifacts when applying filtering to each channel. Zoom in to have a better view.

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