HackMD- BK_0710·Last edited by BK_0710 on May 12, 2022Linked with GitHubContributed by
Log in to edit or delete your comments and be notified of replies.
There is no commentSelect some text and then click Comment, or simply add a comment to this page from below to start a discussion.Video Compression Homework2
1
a
其水平的頻率會由左而右逐漸增加，垂直方向的頻率會由上至下逐漸增加，對第 (u,v) 個 basis function 來說，可拆 8x8 個格子，其第(m,n)的值可寫成
可用dct_basis.py 產生下圖。
$ python dctbasis.py
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
b
DCT 可以把圖片中高頻跟低頻分離出來，因為人對於高頻也就是小範圍高複雜的辨認能力差，反之對於低頻較敏感，所以可以藉由 Quantization 把高頻部分壓縮，來達到犧牲掉肉眼不易分辨的資訊的效果。
2
Question
[[201. 192. 183. 180. 168. 154. 144. 128.]
[116. 96. 84. 70. 61. 56. 53. 52.]
[ 53. 42. 39. 37. 39. 39. 39. 38.]
[ 40. 65. 91. 55. 52. 125. 170. 168.]
[162. 140. 122. 90. 57. 58. 44. 59.]
[ 60. 74. 67. 61. 58. 61. 57. 56.]
[ 63. 63. 75. 61. 66. 53. 53. 53.]
[ 46. 46. 44. 50. 52. 47. 55. 57.]]
a
$ python dct_a.py
After DCT
[[642.5 50.44 34.22 -8.87 -15.25 6.27 7.48 1.99]
[164.75 31.96 9.13 10.85 -1.63 7.51 1.19 -1.95]
[ 57.92 37.42 -41.51 18.26 26.03 -4. -12.76 5.37]
[162.38 91.34 -15.61 3.39 6.5 -5.71 -0.63 -4.13]
[168.75 -14.62 21.4 -10.77 -13.5 7.98 3.31 -4.82]
[ 75.29 -94.95 -8.81 -10.69 -22.27 4.49 0.2 7.22]
[-24.8 -13.29 -19.76 9.06 6. -4.16 -8.99 -4.82]
[ -7.64 105.56 -12.45 11.6 27.59 -4.08 2.56 0.66]]
ZigZag Scan
[642.5 50.44 164.75 57.92 31.96 34.22 -8.87 9.13 37.42 162.38
168.75 91.34 -41.51 10.85 -15.25 6.27 -1.63 18.26 -15.61 -14.62
75.29 -24.8 -94.95 21.4 3.39 26.03 7.51 7.48 1.99 1.19
-4. 6.5 -10.77 -8.81 -13.29 -7.64 105.56 -19.76 -10.69 -13.5
-5.71 -12.76 -1.95 5.37 -0.63 7.98 -22.27 9.06 -12.45 11.6
6. 4.49 3.31 -4.13 -4.82 0.2 -4.16 27.59 -4.08 -8.99
7.22 -4.82 2.56 0.66]
n = 3
[642.5 50.44 164.75]
After Inverse ZigZag Scan
[[642.5 50.44 0. 0. 0. 0. 0. 0. ]
[164.75 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]]
After IDCT
[[117.62 116.29 113.83 110.62 107.14 103.92 101.46 100.13]
[113.27 111.94 109.48 106.27 102.79 99.57 97.11 95.78]
[105.24 103.91 101.45 98.23 94.75 91.54 89.08 87.75]
[ 94.74 93.41 90.95 87.73 84.25 81.04 78.58 77.25]
[ 83.38 82.04 79.58 76.37 72.89 69.68 67.22 65.89]
[ 72.88 71.55 69.09 65.87 62.39 59.18 56.72 55.39]
[ 64.84 63.51 61.05 57.84 54.36 51.14 48.68 47.35]
[ 60.49 59.16 56.7 53.49 50.01 46.79 44.33 43. ]]
MSE = 1629.8346
n = 10
[642.5 50.44 164.75 57.92 31.96
34.22 -8.87 9.13 37.42 162.38]
After Inverse ZigZag Scan
[[642.5 50.44 34.22 -8.87 0. 0. 0. 0. ]
[164.75 31.96 9.13 0. 0. 0. 0. 0. ]
[ 57.92 37.42 0. 0. 0. 0. 0. 0. ]
[162.38 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]
[ 0. 0. 0. 0. 0. 0. 0. 0. ]]
After IDCT
[[173.47 166.8 154.68 140.37 128.72 123.38 123.95 126.25]
[127.66 122.11 111.98 100.11 90.9 87.63 89.67 92.72]
[ 79.46 75.66 68.59 60.44 54.88 54.65 58.79 62.9 ]
[ 67.08 64.9 60.66 55.82 53.36 55.55 61.24 66.09]
[ 83.73 82.5 79.8 76.56 75.32 78.15 84.03 88.86]
[ 92.36 91.25 88.57 85. 82.91 84.5 89.15 93.21]
[ 73.88 72.37 68.82 63.79 59.77 59.24 62.03 65.01]
[ 49.09 47.19 42.82 36.59 31.05 28.94 30.41 32.63]]
MSE = 1106.754
b
$ python dct_b.py
n = 5
After Quantization
[[128. 10. 7. -2. -3. 1. 1. 0.]
[ 33. 6. 2. 2. -0. 2. 0. -0.]
[ 12. 7. -8. 4. 5. -1. -3. 1.]
[ 32. 18. -3. 1. 1. -1. -0. -1.]
[ 34. -3. 4. -2. -3. 2. 1. -1.]
[ 15. -19. -2. -2. -4. 1. 0. 1.]
[ -5. -3. -4. 2. 1. -1. -2. -1.]
[ -2. 21. -2. 2. 6. -1. 1. 0.]]
After Inverse Quantization
[[640. 50. 35. -10. -15. 5. 5. 0.]
[165. 30. 10. 10. -0. 10. 0. -0.]
[ 60. 35. -40. 20. 25. -5. -15. 5.]
[160. 90. -15. 5. 5. -5. -0. -5.]
[170. -15. 20. -10. -15. 10. 5. -5.]
[ 75. -95. -10. -10. -20. 5. 0. 5.]
[-25. -15. -20. 10. 5. -5. -10. -5.]
[-10. 105. -10. 10. 30. -5. 5. 0.]]
After IDCT
[[199.97 190.94 180.01 179.95 167.19 154.63 146.53 128.81]
[115.79 97.18 83.85 69.48 61.38 53.52 54.98 52.66]
[ 52.22 41.95 37.44 37.16 38.99 35.95 37.5 40.29]
[ 39.9 64.84 91.72 58. 52.33 124.58 169.57 166.06]
[161.45 138.44 122.8 88.76 54.17 57.07 41.48 59.1 ]
[ 57.82 75.57 65.05 59.8 57.45 61.41 56.99 54.13]
[ 62.77 64.08 72.38 61.32 64.82 52.28 49.88 53.91]
[ 45.04 49.02 43.87 49.62 52.7 48.62 55.87 56.95]]
MSE = 2.1344829
n = 20
After Quantization
[[32. 3. 2. -0. -1. 0. 0. 0.]
[ 8. 2. 0. 1. -0. 0. 0. -0.]
[ 3. 2. -2. 1. 1. -0. -1. 0.]
[ 8. 5. -1. 0. 0. -0. -0. -0.]
[ 8. -1. 1. -1. -1. 0. 0. -0.]
[ 4. -5. -0. -1. -1. 0. 0. 0.]
[-1. -1. -1. 0. 0. -0. -0. -0.]
[-0. 5. -1. 1. 1. -0. 0. 0.]]
AFter Inverse Quantization
[[ 640. 60. 40. -0. -20. 0. 0. 0.]
[ 160. 40. 0. 20. -0. 0. 0. -0.]
[ 60. 40. -40. 20. 20. -0. -20. 0.]
[ 160. 100. -20. 0. 0. -0. -0. -0.]
[ 160. -20. 20. -20. -20. 0. 0. -0.]
[ 80. -100. -0. -20. -20. 0. 0. 0.]
[ -20. -20. -20. 0. 0. -0. -0. -0.]
[ -0. 100. -20. 20. 20. -0. 0. 0.]]
After IDCT
[[196.31 201.76 184.36 176.26 166.87 152.59 143.57 118.77]
[126.75 101.65 72.6 68.21 66.94 54.88 45.27 35.34]
[ 57.15 42.79 36.97 36.65 44.04 48.91 41.36 39.37]
[ 37.51 70.15 84.78 47.28 51.67 116.81 159.43 177.31]
[158.74 140.37 122.46 84.52 62.2 59. 45.57 47.07]
[ 65.89 72.66 75.66 59.88 51.65 57.43 56.42 55.94]
[ 70.51 72.58 66.91 65.37 61.12 55.81 58.09 55.18]
[ 42.62 50.23 41.75 46.12 46.68 45.78 61.39 60.07]]
MSE = 34.86187
