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Information about exercise 3 for the image processing course ece547, taught by prof. Thomas huang. The exercise includes problems on compression ratio calculation for mp3 images, finding the ifs and fractal dimension for a given fractal image, and finding different ifss with the same attractor. Students are encouraged to use matlab or other software to help with the problems.
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ECE547 Image Processing Sept 25, 2008
Lecturer: Prof. Thomas Huang Due: Oct 9, 2008
Compute the compression ratio that you achieved in MP3. Assume that it takes the original image was 128 × 128 with 8 bits per pixel. Suppose that it takes 7 bits to encode each row and column value, 3 bits to encode a, and 8 bits to encode b. What is the compression ratio for blocksize= and blocksize=8?
For these problems, it would be really helpful to have some program which draw can draw an IFS. The easiest way is probably to use plotifs.m, which you should be able to obtain online at http://courses.ece.uiuc.edu/ece547/exercises/plotifs.m^1. In MATLAB, you can turn on the grid using grid on.
Below is an image of a simple 2-D fractal. Find the corresponding IFS and its fractal (Hausdorff) dimension.
−1/2−1/2 −1/3 −1/6 0 1/6 1/
−1/
−1/
0
1/
1/
(^1) Other choices include using FRACTINT, if you can get a copy which runs on your system. You may also search for Java IFS applets on the web.
Find two different IFSs that have the following diagram as an attractor. (For example, there is one which has two transforms and at least two which have three.) Show that both formulations give the same fractal dimension.
−1/6 0 1/6 1/3 3/8 1/
0
1/
1/
1/
This is a variation of the “standard” fractal tree. Find its IFS. Why can we not estimate its fractal dimension with the technique we covered in class?
(0, 0.275)
−0.3−0.25−0.2−0.15−0.1−0.05 0 0.05 0.1 0.15 0.2 0. 0