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CS/EE 545 Homework 8

Complete by Class 10

Parseval's Theorem

Parseval's Theorem, shown in class, is

State and prove Parseval's Theorem in the discrete case, that is, using the forward and inverse Discrete Fourier Transform in place of the forward and inverse Fourier Transform.

Compute the energy of an image -- your choice which image -- both ways. Do they agree?

Multiresolution Analysis

Write a program to produce a multiresolution pyramid, using a factor of 2 reduction at each step. To keep matters simple, use a 2x2 averaging filter before downsampling. Use the images of Io (io.img, io.tif, io.gif)

Show the images at 5 different levels of resolution reduction and also show the residual error images at each level. To display the residual error, treat an error of 0 as greylevel 128, etc.

E-mail your programs and solutions to cs545m_ta@cs.wpi.edu.


 
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