1. CSc 461/561 Multimedia Systems Part B: 2. Lossy Compression

2. Summary (1) Why is lossy compression possible? (2) Distortion measure
(3) Quantization
(4) Transformation
(5) Introduction to JPEG- Part I
(6) Introduction to MPEG-Part I

3. 1. Why is lossy compression possible?
some information is more important than others for human
keep the important one
Original
Compression Ratio: 7.7
Compression Ratio: 12.3
Compression Ratio: 33.9

4. 2. Distortion measure Rate Distortion Rate vs distortionB
Rate
# of bits per source symbol
Distortion
one measure: mean square error (MSE)
x: original value; y: reconstructed value
MSE = [(x1-y1)2+(x2-y2)2+…+(xN-yN)2]/N
Rate vs distortion
lower rate, higher distortion

5. 3. Quantization (1) Quantization (recall audio A/D)
use a discrete value to represent a value range
information loss!
The smaller range, the less distortion
granular distortion
Quantization steps
uniform: all ranges have the same size
non-uniform: otherwise

6. 3. Uniform quantization (2)
Quantization step: uniform
Two constructions: midrise, midtread
∆ 2∆ 3∆ Input
-3∆ -2∆ -∆
Reconstruction
3.5∆
2.5∆
1.5∆
0.5 ∆
-0.5∆
-1.5∆
-2.5∆
-3.5∆
Uniform Midrise Quantizer
-2.5∆ -1.5∆ -0.5∆ 3∆ 2∆ ∆ -∆
-2∆
-3∆
Uniform Midtread Quantizer
0.5∆ 1.5∆ 2.5∆ Input

7. 3. Signal-to-quantization-noise ratio (3)
n bits; 2n steps for [-Xmax,Xmax]
step size: delta = 2Xmax / 2n
granular distortion:
SQNR in dB
10 log10 signal_energy / noise_energy
=10 log10 [(2Xmax)2/12]/[delta2/12]=20n log102
One more bit adds 6 dB to SQNR

8. 3. Non-uniform quantization (4)
Recall u-law or A-law voice compander
How to choose quantization steps?
Int f(x) dx = 1/2n
xi+1 xi
f(x)
f(x)
Uniform
Non-uniform x x xi
xi+1 xi
xi+1

9. 3. Non-uniform quantization: more (5)
How to represent a range?
Int f(x) dx = 1/2n+1
when uniform: yi=(xi+xi+1)/2 yi xi
f(x)
f(x)
Uniform
Non-uniform x x xi
xi+1 xi
xi+1 yi yi

10. 4. Transformation (1) Transformation Inverse transformation
represent information in anther space
identify and remove (hard-to-remove) correlation, i.e., redundancy, in the original space
information loss!
e.g., time/space => frequency (FFT)
Inverse transformation
represent the info back in the original space

11. 4. Discrete Cosine Transform (2)
Recall: a wave is of many waves
“Any signal can be expressed as a sum of multiple signals that are sine or cosine waveforms at various amplitudes and frequencies.”
Cosine transform: using cosine waveforms
DCT: integer indexes
widely used in image compression (e.g., JPEG)

12. 4. DCT: more (3) 2-D DCT (8x8); C(x)=1/sqrt(2) when x=0
Inverse 2-D DCT (IDCT); C(x)=1 otherwise

13. 4. DCT: examples (4) Original values of an 8x8 block
DC Component
Original values of an 8x8 block
(in spatial domain)
Corresponding DCT coefficients
(in frequency domain)

14. 5. Introduction to JPEG-Part I (1)
Joint Photographic Experts Group (JPEG)
ISO standard (1992)
widely used (.jpeg, .jpe, .jpg; C/R: 10~20)
The family of JPEGs
lossless JPEG: prediction-based compression
lossy JPEG: DCT-based compression
M-JPEG: motion JPEG
JPEG2000: discrete wavelet transform; new!

15. 5. Introduction to JPEG-Part I (2)
JPEG compression guidelines
Brightness vs color sensitivity
RGB => YUV/YIQ
chroma subsampling (4:2:0)
Spatial correlation among nearby pixels
slice an image into 8x8 blocks (bad for text)
Remove redundancy in frequency domain
discrete cosine transform (DCT)
coarse quantization for high freq coefficients

16. 5. Introduction to JPEG-Part I (3)
Sequential mode
Progressive mode
low quality first, then differential data added
DC first, then AC; or MSB first, then LSB
Hierarchical mode
lowest resolution first and then higher resolutions
Lossless mode
prediction and entropy encoding

17. 5. Introduction to JPEG-Part I (4)
We will revisit the topic later.

18. 6. Introduction to MPEG-Part I (1)
MPEG-1 (1991): VCD (VCR+CD quality)
352x240, 1.2Mbps video CBR, 256Kbps audio
progressive scan only (1x CD-ROM)
MPEG-1 video compression
similar to H.261, with a few differences
more formats, flexible slices, quantization table
I-frame: JPEG-like compression
P-frame: prediction-based; B-frame

19. 6. Introduction to MPEG-Part I (2) MPEG-1: more
I B B P B B P B B
Bi-directional search
search both previous and next frames for similar macro-blocks
MPEG-1 GOP
I-frame, P-frame, B-frame
display order: IBBPBBPBBPBBPBBI (M=3, N=15)
coding order: IPBBPBBPBBPBBIBB; timestamps
D-frame: for search through the video, DC only

20. 6. Introduction to MPEG-Part I (3) MPEG-2
MPEG-2 (1994): DVD, HDTV, etc
also adopted as ITU-T H.262
many video formats and data rates; better audio
profiles: simple (4:2:0, I/P), main (+B), SNR (+variable quality), spatial (+variable resolution), high (+4:2:2)
levels: low (352x288), main (720x576), high (1440x1152), high (1920x1152)
support interlaced video (broadcasting!)

21. 6. Introduction to MPEG-Part I (4) MPEG-2 scalability
Layered encoding
base layer: independent for basic quality
enhancement layer: dependent on the base layer
E.g., SNR scalability
base: low SQNR (coarse quantization)
enhance: high SQNR (fine Q on actual-base)
E.g., spatial scalability
base: low resolution; enhance: high resolution

22. 6. Introduction to MPEG-Part I (5) MPEG-4
MPEG-4 (1999): content-based, object-oriented
based on H.263, initially for low bit-rate apps
video sequence: a collection of media objects
objects: still image, moving object, audio, etc
how to decompose is NOT specified (encoder)
VOP: video object plane
GOV: I-VOP, P-VOP, B-VOP
VOP is divided into many macro-blocks
motion estimation: bounding box; padding

23. 6. Introduction to MPEG-Part I (5): MPEG-4: object oriented

24. 6. Introduction to MPEG-Part I (6) MPEG-4: more
Fine gain scalability
spatial scalability
temporal scalability
quality scalability
MPEG-4 audio
general audio (2~64Kbps)
speech (2~4Kbps: HVXC; 4~24Kbps: CELP)
synthesized (e.g., MIDI, TTS)

25. 6. Introduction to MPEG-Part I (7)
We will revisit the topic later.