Site REU Program in CVIP Summer 2006 Lab 6 Exercise on Filter Techniques in Frequency Domain
The extra notes related to frequency domain can be downloaded at the following website: http://www.cs.usu.edu/~xqi/Teaching/REU06/Notes/Supplements.pdf
Problem 1: Exercises on Low-pass and High-pass Filters in the Frequency Domain a) Design a butterworth low-pass filter of order 2 with a cutoff frequency of 80 in the frequency domain. Obtain the filtered image by filtering the original image Sample with the designed butterworth filter. Display the original image, the butterworth low-pass filter (treat it as an image), and the filtered image in figure 1 with the appropriate titles. b) Repeat the step a) by using the corresponding high-pass filter. Display the corresponding images (original image, high-pass filter, and filtered image) in figure 2 with the appropriate titles. c) Close all figures and all variables in the workspace. Problem 2: Exercise on Certain Operations in the Frequency Domain a) Take the FT (Fourier Transform) of the two images Sample and NewCapitol (Note: You need to do the centering so the DC component will be in the center). Display the magnitude and the phase of the two FTed images in figure 1 with the appropriate titles. Conduct an inverse FT on each FTed image by using only its magnitudes. Conduct an inverse FT on each FTed image by using only its phases. Display the four corresponding reconstructed images in figure 2 with appropriate titles. Exchange the phase components of the two FTed images and take an inverse FT. Display the two corresponding reconstructed images in figure 3 with appropriate titles. b) Take the FT of the Lena image. First, set the phase equal to zero, and take the inverse FT. Display the reconstructed image in figure 4 and explain why the resulting image looks nothing like the original via display command. Then, let the phase be the original one and respectively set the magnitude equal to 100 and equal to the average of the original magnitude values and take the inverse FT. Display the two reconstructed images in figure 5 and explain the effect of the different magnitudes via display command. Problem 3: Remove Additive Cosine Noise The noisy image boy_noisy.gif has been generated by adding some noise in the form of a cosine function. Your is goal to remove the cosine interference. This can be done as follows: a) Compute the DFT of the noisy image. b) Compute the magnitude and find the frequencies corresponding to the four largest distinct magnitudes (do not consider the magnitude at the center - very large values) c) Replace each one of these magnitude values by the average of its 8 neighbors (do this averaging both for the real and imaginary parts). d) Take the inverse DFT transform and display the original image and the resulted image side-by-side in figure 1 with the appropriate titles. e) Explain why the four largest distinct values of the magnitude were chosen to do the processing via Matlab display command. f) Close all figures and all variables in the workspace. Problem 4: Preliminary Wavelet Transform 1
a) Apply a maximum-level db2 wavelet decomposition on Lena.jpg by using appropriate Matlab function(s). You need to use an appropriate Matlab function to get the maximum decomposition level. Apply the inverse wavelet transform to restore the image. Use if-else statement to compare your restored image with the original image so the appropriate message indicating the equality or inequality between these two images should be displayed. b) Apply a three-level db2 wavelet decomposition on Lena.jpg by using appropriate Matlab function(s). For each subband image at the horizontal, vertical, and diago...