Digital Image Processing Computer Assignment # 3 Problem 1. Download the file Square.tif and answer the following questions: i. Smooth the image with a 3x3 spatial filter. ii. Smooth the image with an implementation of Gaussian filter in frequency domain. Change the bandwidth of the filter and show how these changes affect the result. iii. Visualize that filtering in frequency domain can cause wraparound error in spatial domain and explain how can this interference be avoided. Apply your idea as a preprocessing step in part (ii) and display your results. iv. Sum up your conclusions in part (ii) and (iii), and List the Basic Steps required in DFT filtering. Implement all these steps in an M-file, named YOU M2 (replace YOU with your name). This file must get an arbitrary image as input, smooth the image with a Gaussian filter, and give the filtered image in output. The process of filtering should be done in frequency domain. Problem 2. Download the file CA03.jpg. 1. Add Gaussian noise N( 2=0, 0 =10/256) to the image and then apply Salt and Pepper noise with equal probability Pa = Pb = 0.1 to the result. Salt noise makes pixels the brightest and pepper makes pixels the darkest in the image. ii. There are some different approaches to remove noise: a) Applying a 3x3 mean filter. b) Applying a 3x3 median filter C) Applying a 3x3 mean filter at first and then applying a 3x3 median filter d) Applying a 3x3 median filter at first and then applying a 3x3 mean filter. Implement these approaches and remove noise using them. Show the result of each approach and discuss on results (a short and perfect discussion). Problem 3. Download the file porsch.tif. 1. Find or develop a program for adding Gaussian, and salt-and-pepper (impulse) noise to the image. The type of the noise should be determined through an input of the function. In the case of Gaussian white noise, mean and variance of the noise are the other inputs, and in the case of impulse noise, the probability of each of the two noise components should be specified. This is a generic project, in the sense that the program developed here is used in several of the next projects 2. Apply your noise generator function to porsch.tif. 3. Denoise the image of part (ii) by applying filtering techniques in frequency domain