jpeg image compression technique discreate cosine transform

1. DARSHAN KAREKAR
51026
Created for -POM

2. CONTENTS
 What is JPEG?
 Basic JPEG Compression Pipeline
 JPEG examples
 Major Coding Algorithms in JPEG
 The Discrete Cosine Transform(DCT)
 Significance / Where is this used?
 Implementation Platform
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3.  JPEG: Joint Photographic Expert Group — an
international
 standard since 1992.
 Works with colour and greyscale images
 Up to 24 bit colour images (Unlike GIF)
 Target photographic quality images (Unlike GIF)
 Suitable for many applications
e.g., satellite, medical, general,photography...
What is JPEG?
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4. Continued..
 JPEG standard is a collaboration among :
 International Telecommunication Union (ITU)
 International Organization for Standardization (ISO)
 International Electrotechnical Commission (IEC)
 The official names of JPEG :
 Joint Photographic Experts Group
 ISO/IEC 10918-1 Digital compression and coding of
continuous-tone still image
 ITU-T Recommendation T.81
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5. Basic JPEG Compression Pipeline
 JPEG compression involves the following:
 Encoding
Decoding – Reverse the order for encoding
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6. JPEG examples
 note that the two images on the left look identical
 JPEG requires 6x less bits
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7. Major Coding Algorithms in JPEG
 The Major Steps in JPEG Coding involve:
 Colour Space Transform and subsampling (YIQ)
 DCT (Discrete Cosine Transformation)
 Quantisation
 Zigzag Scan
 DPCM on DC component
 RLE on AC Components
 Entropy Coding — Huffman or Arithmetic
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8. The Discrete Cosine Transform(DCT)
 In the same family as the Fourier Transform
 Converts data to frequency domain.
 Represents data via summation of variable frequency
cosine waves.
 Since it is a discrete version, conducive to problems
formatted for computer analysis.
 Captures only real components of the function.
 Discrete Sine Transform (DST) captures odd
(imaginary) components → not as useful.
 Discrete Fourier Transform (DFT) captures both odd
and even components → computationally intense.
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9. Significance / Where is this used?
 Image Processing
 Compression - Ex.) JPEG
 Scientific Analysis - Ex.) Radio Telescope Data
 Audio Processing
 Compression - Ex.) MPEG – Layer 3, aka. MP3
 Scientific Computing /
High Performance Computing (HPC)
 Partial Differential Equation Solvers
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10. Significance Cont.
 Image Processing Example
 Exhibits Energy Compaction
 Drop small amplitude coefficients
Original Image DCT Transformed
Image
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11. Implementation Platform
NVIDIA CUDA
Version 2.010/6/2013 11JPEG-DCT(POM)

12. EXAMPLE
JPEG-DCT(POM) 12
0 1 2 3 4 5 6 7
01234567
u
v
The 8x8 DCT basis
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13. JPEG-DCT(POM)
13
Example :
Y
the luminance of an image
W
H
8x8 values of luminance
48 39 40 68 60 38 50 121
149 82 79 101 113 106 27 62
58 63 77 69 124 107 74 125
80 97 74 54 59 71 91 66
18 34 33 46 64 61 32 37
149 108 80 106 116 61 73 92
211 233 159 88 107 158 161 109
212 104 40 44 71 136 113 66
8x8 DCT coefficiences
DCT
699.25 43.18 55.25 72.11 24.00 -25.51 11.21 -4.14
-129.78 -71.50 -70.26 -73.35 59.43 -24.02 22.61 -2.05
85.71 30.32 61.78 44.87 14.84 17.35 15.51 -13.19
-40.81 10.17 -17.53 -55.81 30.50 -2.28 -21.00 -1.26
-157.50 -49.39 13.27 -1.78 -8.75 22.47 -8.47 -9.23
92.49 -9.03 45.72 -48.13 -58.51 -9.01 -28.54 10.38
-53.09 -62.97 -3.49 -19.62 56.09 -2.25 -3.28 11.91
-20.54 -55.90 -20.59 -18.19 -26.58 -27.07 8.47 0.31
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