CSE 473/573 Homework Set #2
Programming languages: Python or MATLAB programming for the following problems is
preferred. However, solutions obtained via another programming language is also acceptable.
Submit your code and report via UBLearns.
Warning: You are NOT allowed to use library functions for applying convolution or
Fourier/inverse Fourier transform. You shall NOT receive credit if you use these library
functions directly.
Problem (1) (Fourier Transform) 50%
Pick an 𝑀 × 𝑁 image of your choice and convert it to 8-bit grayscale representation if needed
(a) Apply Fourier Transform on the image 𝐼𝑂 and display the Fourier Transform image
(b) Apply Inverse Fourier Transform to the output from (a) to obtain recovered image 𝐼𝑅
(c) Compute the Mean Square Error (MSE) between the original and the recovered image
based on the following:
𝑀𝑆𝐸 = ∑ ∑[𝐼𝑂(𝑖,𝑗) − 𝐼𝑅
(𝑖,𝑗)]
2
𝑁−1
𝑗=0
𝑀−1
𝑖=0
(d) Discuss why or why not the MSE may be non-zero
NOTE: You need to write your own code for this implementation. External libraries on Fourier
Transform can only be used for verification. Include all the images and results in your report.
Problem (2) (Laplacian Pyramid) 50%
Pick an 𝑀 × 𝑁 image of your choice and convert it to 8-bit grayscale representation if needed
(a) Generate 5-Level Laplacian Pyramid and display the images at each level
(b) Reconstruct the original image from its Laplacian Pyramid
(c) Compute the MSE between the original and the reconstructed image
(d) Discuss why or why not the MSE may be non-zero
NOTE: You need to write your own code for this implementation. Report all the images of 5-
Level Laplacian Pyramid of your image and the reconstructed image.
