ELEC 5430/6430 Project #7 Spring 2009

Assigned: 4/22/09        Due: 4/29/09

Image Compression

This exercise is intended to familiarize you with some basic concepts related to image compression.

Exercises

1. Write a simple m-file function that computes an error image for the following DPCM prediction:

   
   

   $$\bar{y}(m,n) = 0.5 y(m,n-1) + 0.5 y(m-1,n)$$
   
   

   The error image is defined as

   
   

   $$e(m,n) = y(m,n) - \bar{y}(m,n)$$
   
   

   Include a listing of the m-file in your write-up.

2. Read in cameraman.tif. Compute the error image. Display a normalized version of the error image with imagesc(). Describe the image characteristics that cause the most error in the prediction.

3. Compute the histogram of the values in e(m,n) with hist. (Hint #1: You'll need to turn e(m,n) into a vector before finding the histogram. Hint #2: Use hist(x,[-255:255]) to compute the histogram.) Plot the histogram, and include it in your report.

4. Calculate the entropy to get the best lossless compression (in bpp) to be expected from this predictor. If p is a probability, use log2(p + eps) in the formula instead of log2(p) to prevent the result from being -Infty for p=0.

5. This exercise deals with JPEG transform coding.

   (a) Use imwrite(image,filename,'jpg','Quality',quality) to create lossy coded images. Determine the quality setting at which you can detect a difference between the coded image and the original. (The quality setting has a range [0,100], with 100 being the highest quality.) Describe the difference.

   (b) Determine the quality setting at which the image begins to look unnatural. What aspects of the image look unnatural?

   (c) Code the image at a quality factor of 20. Describe the problems with the image. Explain why the problems appear as they do.

   (d) Draw a rough plot of the number of bits versus quality factor. (You'll need to look at the image file sizes for each quality factor.) Is it a straight line? Why or why not?

   The following exercises are for ELEC 5430 only. NOTE: This portion will count as a supplemental assignment as described in the syllabus.

6. Write an m-file function that
   1. splits an image into 8x8 blocks, applies a 2-D DCT to each block, and returns the result in an image. Use the blkproc function.
   2. divides the entire image by 8 to normalize the DCT.
   3. given the standard JPEG quantization table and scale defined as follows:

      16	11	10	16	24	40	51	61
      12	12	14	19	26	58	60	55
      14	13	16	24	40	57	69	56
      14	17	22	29	51	87	80	62
      18	22	37	56	68	109	103	77
      24	35	55	64	81	104	113	92
      49	64	78	87	103	121	120	101
      72	92	95	98	112	100	103	99

      if quality < 50
          scale = 50 / quality;
      else
          scale = 2 - quality * 2 / 100;
      end
      

      multiplies each element by scale and rounds each result to the nearest integer, and then sets the minimum value to one (1). That is,
      

      NewQuantTable = max(ones(size(QuantTable)), round(scale * QuantTable));
      

   4. divides each block by the resulting quantization table and rounds to the nearest integer.
   5. multiplies each block by the same table and takes the 8x8 IDCT.
   6. Scales the result by 1/8.
   Congratulations! You've just implemented the basics of a JPEG coder/decoder!
7. Run your function on the cameraman image with a quality factor of 50. Compare to the result of saving and loading the image with the MATLAB JPEG format. What is the MSE of each result?
8. What is the MSE if you use a quality factor of 100?

Write a short report describing your findings following my format instructions. The report should contain a concise description of your results. Be sure to answer all questions. Please include in your report all the final image results you generated. Only email the specified image(s).

For further help:

• Matlab Primer

• Matlab Help Desk