# SIV864/PHM961 Special Module on Multimedia Processing and Communication

## Assignment 2: Image Compression

#### Due Date: Oct 16, 2017

**IITD students may submit their assignment by email to Mr Rajesh Kumar (email: rajeshk@cse.iitd.ac.in) and DEI sdudents may submit their assignment to the course coordinator Prof Vasantha Lakshmi **
**Part A:**

- Discrete Cosine Transform (DCT) founded by Ahmed et al [1] is widely used for transform coding. Please
read an interesting article [2] by Ahmed on how they came up with the DCT.
- Read a report on DCT by Syed Ali Khayam [3] and answer the following questions briefly:
- How does DCT perform in relatoin to its energy compaction
for the images which are correlated and decorrelated (not correlated)?
- In what ways the properties of separability and symmetry of DCT are useful?
- Consider the Table 1, what does reduction of entropy indicate? For example,
in case of Baboon it is shown that there is a drastic reduction of entropy.

- Please read the paper on JPEG [4]
and list its salient points which in your opinion add
to the class lectures on JPEG. Note that you are not required to write what is
written in the paper, but list (item wise) those parts which are different
and add to what was covered in the lectures.

** Part B:** Implement the following parts of the transform coding/decoding.

- Convert the image to gray scale (monochromatic) image using an in-built function
- Division of image to blocks (sub images)
- Transform of blocks
- Truncation or quantization (can try different strategies).
- Inverse transform and reconstruction of image from the retained
coefficents.
- Use Discrete Fourier Transform and Discrete Cosine Transform and compare and
show the error enountered for the same number of coefficients retained for each.

**Note:**

1. This assignment is meant for reading of material related to what has been covered in
the class and apply to some of the problems as above.

2. For the answers for the above problems if there is any sharing of information from
your friend/internet/other reference material, it is desired that you please
include/acknowledge the name of that reference.

3. You may submit the report of your assignment as a word or pdf
document.

For Part B, you may do the implementation in MATLAB or any other programming environment such as C/C++/Java

** References **
- [1] N. Ahmed, T. Natarajan and K. R. Rao, "Discrete Cosine Transform," IEEE Trans. Computers, 90-93, Jan. 1974.
- [2] N Ahmed, "How I Came Up with the Discrete Cosine Transform",
Digital Signal Processing, Vol 1, pp 4-5, 1991.
- [3] S A Khayam, "The Discrete Cosine Transform (DCT): Theory and Application", Technical Report, Michigan State University, 2003.
- [4] G K Wallace, "The JPEG Still Picture Compression Standard",a revised
version of the paper by the same author in Communication ACM April 1991.