Assignment 3

Question 1: DCT Coding (20 points)

In this question you will try to understand the working of DCT in the context of JPEG. Below is an 8x8 luminance block of pixel values and its corresponding DCT coefficients.

188
180
155
149
179
116
86
96
168
179
168
174
180
111
86
95
150
166
175
189
165
101
88
97
163
165
179
184
135
90
91

96
170
180
178
144
102
87
91

98
175
174
141
104
85
83
88

96
153
134
105
82
83
87
92

96
117
104
86
80
86
90
92
103

    • Using the 2D DCT formula, compute the 64 DCT values. Assume that you quantize your DCT coefficients using the luminance quantization table K1 on page 143 of the uploaded ITU-T JPEG standard. What does your table look like after quantization? (5 points)

    • In the JPEG pipeline, the quantized DCT values are then further scanned in a zigzag order. Ignoring your DC value, show the resulting zigzag scan AC values. (2 points).

    • For this zigzag AC sequence, write down the intermediary notation (5 points)

    • For these are luminance values, write down the resulting JPEG bit stream. You will need to consult standard luminance code tables on page 150 of the ITU-T JPEG standard. (6 points)

    • What compression ratio do you get for this luminance block? (2 points)

Programming on DWT Compression (80 points)

This programming assignment will help you gain an understanding of issues that relate to image compression using wavelets. You will read an RGB file and convert the image pixel to a DWT representation (as used in the JPEG2000 implementation) for each channel. Depending on the second parameter n you will decode both the representations using only n levels of the low pass coefficients and display the output. Remember all input files will have the same format as explained to the class website. They will be of size 512x512 (intentionally square and a power of 2 to facilitate easy encoding and decoding). Your algorithm, whether encoding or decoding, should work on each channel independently.

Input to your program will be 2 parameters where:

    • The first parameter is the name of the input image rgb file. (file format is similar to previous assignments).

    • The second parameter n is an integral number from 0 to 9 that defines the low pass level to be
used in your decoding. For a given n, this translates to using 2n low pass coefficients in rows and columns respectively to use in the decoding process . Additionally, n could also take a value of -1 to show progressive decoding. Please see the implementation section for an explanation

Typical invocations to your program would look like

MyExe Image.rgb 9

This the level 9 or the highest level and as such corresponds to your entire image. Here you are making use of 29 = 512 coefficients in rows and 512 coefficients in columns, which essentially is the input image itself and so the output should look just like the input.

MyExe Image.rgb 8

This is level 8 and the first level of the wavelet encoded hierarchy in rows and columns. Here you are making use of 28 = 256 low pass coefficients in rows and 256 low pass coefficients in columns,

MyExe Image.rgb 1

This is level 1 and the eight level in the wavelet encoded hierarchy in rows and columns . Here you are making use of 22 = 4 low pass coefficients in rows and 4 low pass coefficients in columns,

Encoding Implementation

For the DWT encoding process, convert each row (for each channel) into low pass and high pass coefficients followed by the same for each column applied to the output of the row processing. Recurse through the process as explained in class through rows first then the columns next at each recursive iteration, each time operating on the low pass section until you reach the appropriate level

Decoding Implementation:

Once you reach the appropriate level, zero out all the high pass coefficients. Then perform a recursive IDWT from the encoded level upto level 9 which is the image level. Yu need to appropriately decode by zeroing out the unrequested coefficients (just setting the coefficients to zero) and then perform an IDWT.

Progressive Encoding-Decoding Implementation

This is when n = -1. In this case you will go through the creation of the entire DWT representation till level 0. Then decode each level recursively and display the output. The first display will be at level 0, then level 1 and so on till you reach level 9. You should see the image progressively improving with details.




What should you submit?

    • Your source code, and your project file or makefile. Please confirm submission procedure from the TAs. Please do not submit any binaries or data sets. We will compile your program and execute our tests accordingly.

    • Along with the program, also submit an electronic document (word, pdf, pagemaker etc) for the written part and any other extra credit explanations.