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a) (12/9) What's the entropy of the original data source (use 1st order
estimate)?
- a) (5/5) Identify at least two kinds of redundancy existed in this image. Briefly explain the redundancy.
- b) (10/5) Derive the probability of appearance (that forms the histogram) for each intensity level. Calculate the entropy of this image.
- c) (10/5) Derive the Huffman code.
- d) (5/0) Calculate the average length of the original code and that of the derived Huffman code.
- e) (5/0) Calculate the ratio of image size (in bits) between using the fixed length coding (size1) and Huffman coding (size2). Calculate the relative coding redundancy.
- f) (25/25) Choose one of the following problems and complete the whole compression process (i.e., complete all the three steps listed).
- i) Use bit-plane coding + run-length coding + Huffman coding to compress the image. Calculate the final image size (in bits) (size3).
- ii) Use predictive coding + bit-plane coding + RLC + Huffman coding to compress the image. Calculate the final image size (in bits) (size4). (Graduate students must "choose" this one)
- (15) Task 3.1: Implement DM lossy predictive coder and decoder.
- (5) Task 3.2: Show decompression results by using different delta values.
- (5) Task 3.3: Comment on the result.
b) (3/1) What's the average coding length if using fixed-length coding?
c) (20/20) What's the average coding length of Huffman coding? (Need to show details of Huffman coding)
d) (5/5) Comment on relationship between probability combination, entropy, amount of information, and uncertainty.
Here are the histogram information from three images:
| Pixel Level | Probability (Ex 1) | Probability (Ex 2) | Probability (Ex 3) |
| R0 | 0.15 | 0.32 | 0.125 |
| R1 | 0.11 | 0.16 | 0.125 |
| R2 | 0.19 | 0.09 | 0.125 |
| R3 | 0.15 | 0.05 | 0.125 |
| R4 | 0.08 | 0.14 | 0.125 |
| R5 | 0.02 | 0.15 | 0.125 |
| R6 | 0.2 | 0.01 | 0.125 |
| R7 | 0.1 | 0.08 | 0.125 |
(60/40) Task 2: Integrated Approach
The following figure shows an 8x8 image. Fixed-length coding (00, 01, 10, 11) is used for its four brightness levels. Answer the following questions: