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[SOLVED] Csci 576 assignment 3 question 1: dct coding (20 points) in this question you will try to understand the working of dct

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In this question you will try to understand the working of DCT in the context of JPEG. Below is
an 8×8 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)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 512×512 (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
explanationTypical 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 2
9 = 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 1This 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 ImplementationFor 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 levelDecoding 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.