Digital Image Processing

Course Nos. ECE.09.452 and ECE.09.552

Laboratory Project 4: Digital Image Compression

Objective

The objective of this project is to study the use of the Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT) and the Karhunen-Loeve Transform (KLT) as tools for performing image compression. This project has three parts.

For this project, download the Mandrill (Baboon) image from the USC- SIPI Image Database, which you will use as the standard image to test your algorithms.

Note: In all of the image compression studies that you will perform, you must provide pictures of (a) the reconstructed image and (b) the squared error image. At the top of each page, also provide a picture of the original image, in order to facilitate comparison.

Part 1

In this part, you will compare the image compression capabilities of the three image transforms indicated earlier.

Import the Mandrill image into MATLAB, convert to grayscale (monochrome).
Subdivide the original sized image into sub-images of size 8 x 8. Compute, for each sub-image, the DFT, DCT and KLT coefficients. Perform image compression by using threshold masks of various sizes, i.e. choose only the k < 64 most significant transform coefficients of the 8 x 8 sub-images. For the DFT and DCT, this is done by retaining the k largest transform coefficients in the sub-image and setting the remaining elements of the sub-image to zero. For the KLT, choose the transform coefficients that correspond to the k largest eigenvalues.

Hint 1: Use the blkproc function in MATLAB for computing the transform coefficients for the sub-images. Do >>help blkproc for details, or check out the MATLAB Image Processing Toolbox User's Manual.
Hint 2: You are welcome to modify and use the code given in Hotelling or Karhunen-Loeve Transform demo, for computing the KLT coefficients.

Reconstruct the original sized image from each of the truncated 8 x 8 transform images. The blkproc function in MATLAB is again useful for this. Compute the mean squared error between the original and reconstructed image.
Vary k and compute the mean squared error resulting from image compression for each case. Obtain a graph of the mean squared error vs. k for image compression performed using each of the three transforms. Comment on your results.

Part 2

In this part, you will investigate the effect of varying the sub-image size and type of truncation mask, while performing image compression using the Discrete Cosine Transform.

Choose sub-images of sizes 2 x 2, 8 x 8, 16 x 16, 64 x 64, 128 x 128 and 256 x 256 and entire image.
For each of these sub-images, perform image compression using both threshold and zonal masks such that approximately 25% of the DCT coefficients are retained.
Calculate, for each case, the mean squared error in the reconstructed image. Obtain a graph of the mean squared error vs. sub-image size, for both types of masks. Comment on your results.

Part 3

Based on your investigations in Parts 1 and 2, implement what you decide is the "best" image compression for the given Mandrill image. What criteria (visual, mathematical, etc.) have you used to arrive at this answer? What is the compression ratio?

Your report should be in the usual format.

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