Homework 2 due Monday October 5.
Submit Matlab parts via email to ee528homeworks AT gmail.com
Homework 2a, EE 528 Fall 2009
For Matlab problems, if needed, use as the image, I(m,n), either
a chessboard image
or a fence image.
- Problems 5.2, 5.9, 5.11,
5.12 of AK Jain
- Verify problem 5.11 using Matlab
- Find an application of the 2D-DFT and implement it. This can be
from your research area or be any standard application, e.g. use of DFT
to detect regions and times where there is fast
motion:
apply DFT to image differences and look for high frequency regions or
the use of Fourier descriptors to represent contours or the use of
Fourier slice theorem for tomography (this will be taught later)
- Just for your understanding
(need not submit): look at the 2D-DFT of a few different images
- natural and man-made.
Homework 2b, EE 528 Fall 2009 due
Monday Oct 5.
- Problems 5.16
- Problem 5.24 (do only
for DFT, DCT, Hadamard and can use Matlab for it).
- Either prove or verify using Matlab that the DCT matrix
approximately diagonalizes the matrix given in Equation 2.68 of the
book when rho is close to 1.
- Extra (not graded but for your own sake): also verify this by
generating zero mean stationary Markov sequences and estimating their
correlation/covariance matrix
- Extra: So now consider a 2D-DCT. Tell me what type of images does
it approximately diagonalize? See Example 5.6 in the book.
- Extra: Problem 5.23