Download - DPCM - Overview
Bernd Girod: EE398B: Image Communication II DPCM no. 1
DPCM - Overview
Principle of Differential Pulse Code Modulation (DPCM)Characteristics of DPCM quantization errorsPredictive coding gainAdaptive intra-interframe DPCMConditional Replenishment
Bernd Girod: EE398B: Image Communication II DPCM no. 2
Principle of DPCM
quantizer entropy coder
predictor
+
+
-
+ e'
s'
einput channel
s
+
+predictor
entropy decoder
s' e'output
s
channel
s
decoder
coder
Prediction error Reconstruction Reconstruction error =quantization error
e = s − ˆ s ′ s = ′ e + ˆ s ′ s − s = ′ e − e = q
Bernd Girod: EE398B: Image Communication II DPCM no. 3
Quantization error feedback in the DPCM coder
Assuming a linear predictor, the DPCM coder is equivalent to the following structure:
Transfer function of the prefilter:
Transfer function of quantization error feedback:
quantizers e+
- -
s (s) s (q)
q (e)
-
+
e e'~
predictor predictor
transfer function of the predictor
˜ E (Ω) = 1− P(Ω)[ ]S(Ω)
′ E (Ω) = ˜ E (Ω) + 1− P(Ω)[ ]Q(Ω)
Ω - abbreviation for frequency vector,e.g., ω x,ωy( )
Bernd Girod: EE398B: Image Communication II DPCM no. 4
Power spectrum of the DPCM quantization error
Power spectral density of the quantization error q measured for intraframe DPCM with a 16 level quantizer
ωx
ωy
π
π
−π
−π
00
Bernd Girod: EE398B: Image Communication II DPCM no. 5
Signal distortions due to intraframe DPCM coding
Granular noise: random noise in flat areas of the pictureEdge busyness: jittery appearance of edges (for video)Slope overload: blur of high-contrast edges, Moire patterns in periodic structures.
Bernd Girod: EE398B: Image Communication II DPCM no. 6
Example of intraframe DPCM coding
original
granular noise Linear predictor:
Lloyd-Max quantizersFixed-length coding
1/2
0 1/4 1/4
2 bit/pixel 3 bit/pixelprediction error coding
1 bit/pixeledge busyness
slope overload
4 bit/pixel
Bernd Girod: EE398B: Image Communication II DPCM no. 7
Recall from EE398A: High-rate performance of scalar quantizersHigh-rate distortion-rate function
Scaling factor ε
( ) 2 2 22 RXd R ε σ −≅
2
2
Shannon LowBd Lloyd-Max Entropy-coded
6Uniform 0.703 1 1e
9Laplacian 0.865 4.5 1.2322 6
3Gaussian 1 2.721 1.4232 6
e e
e
π
ππ π
≅
≅ = ≅
≅ ≅
Bernd Girod: EE398B: Image Communication II DPCM no. 8
Predictive coding gain
Distortion-rate function with DPCM
Prediction gain
Smallest achievable prediction error variance for N-dimensional signal determined by spectral flatness
( ) 2 2 22 RDPCM e ed R ε σ −≅
Variance of prediction error
2 2
2 2s s
DPCMe e
G ε σε σ
=
( )( )( )2 1exp ln
2e xxN dσ
π Ω
= Φ Ω Ω
∫
Bernd Girod: EE398B: Image Communication II DPCM no. 9
Predictive coding gain (cont.)
Consider 1-D Gaussian Markov-1 process with correlation coefficient ρAutocorrelation function
Prediction gain2
11DPCMG
ρ=
−
[ ] 2 kn n k sE S S σ ρ− =
Bernd Girod: EE398B: Image Communication II DPCM no. 10
R-D curves for Gauss-Markov-1 source
D
2
1010log
[dB] SNRσ
=
0 1 2 3 4 5 6 70
5
10
15
20
25
30
35
Panter & Dite App Entropy-Constrained Opt.
R(D*), ρ=0.9 DPCM & ECSQ
• Linear predictor order N=1, a=0.9
• Entropy-Constrained Scalar Quantizer with Huffman VLC
• Iterative design algorithm applied
R [bits]
Bernd Girod: EE398B: Image Communication II DPCM no. 11
Prediction example: test pattern
0
0 0.95 0
original
0.95
0 0 0
0.5
0 0.5 0
Bernd Girod: EE398B: Image Communication II DPCM no. 12
Prediction example: Cameraman
original
0.95
0 0 0
0
0 0.95 0
0.5
0 0.5 0
Bernd Girod: EE398B: Image Communication II DPCM no. 13
Histograms: Cameraman
1000
1500
2000
2500
3000
Image signal Prediction error
0
0.5
1
1.5
2x 104
0.5
0 0.5 0
500
00 50 100 150 200 250 -50 0 50
Bernd Girod: EE398B: Image Communication II DPCM no. 14
DPCM with entropy-constrained quantization
K=511, H=4.79 bpp K=15, H=1.98 bpp K=3, H=0.88 bppK...number of reconstruction levels, H...entropy
[J. R. Ohm]
Bernd Girod: EE398B: Image Communication II DPCM no. 15
Transmission errors in a DPCM system
• For a linear DPCM decoder, the transmission error response is superimposed to the reconstructed signal S'
• For a stable DPCM decoder, the transmission error response decays
• For variable length coding, loss of synchronization can lead to errors in many prediction error samples after a single bit-error
Bernd Girod: EE398B: Image Communication II DPCM no. 16
Transmission errors in a DPCM system (cont.)
Example: Lena, 3 bpp (fixed code word length)Error rate: p=10-3
0.5
0 0.5 0
0.95
0 0 0
0
0 0.95 0
[J. R. Ohm]
Bernd Girod: EE398B: Image Communication II DPCM no. 17
Interframe coding of video signals
Interframe coding exploits similarity of temporally successive picturesImportant interframe coding methods:
Adaptive intra-interframe codingConditional replenishmentMotion-compensated prediction
Bernd Girod: EE398B: Image Communication II DPCM no. 18
“It has been customary in the past to transmit successive complete images of the transmitted picture.” [...]“In accordance with this invention, this difficulty is avoided by transmitting only the difference between successive images of the object.”
Bernd Girod: EE398B: Image Communication II DPCM no. 19
Principle of adaptive intra-interframe DPCM
Predictor is switched between two states:A: Intraframe prediction for
moving or changed areas.B: Interframe prediction (previous frame
prediction) for still areas of the picture.
S22 S23 S24
S21 S20 S25
FRAME N - 1
S2 S3 S4
S1 S0
FRAME N
40 ms
ˆ S inter = S20
frameinterval τ
S22 S23 S24
S21 S20 S25
FRAME N - 1
S2 S3 S4
S1 S0
FRAME N
ˆ S intra = a1S1 + a2S2 + a3S3 + a4 S4
Bernd Girod: EE398B: Image Communication II DPCM no. 20
Intra-interframe DPCM: feedback adaptation
Quantizer
Interframe predictor
es +
-s
sinter
e'
Predictor adaptation
Intraframe predictor
sintra
Interframe predictor
Entropy decoder
s
sinter
Entropycoder
Intraframe predictor
sintraPredictor
adaptation
s'e'
s'
Coder Decoder
Bernd Girod: EE398B: Image Communication II DPCM no. 21
Intra-interframe DPCM: feedforward adaptation
Interframe predictor
Intraframe predictor
Entropy decoderEntropy coderQuantizer
Interframe predictor
Intraframe predictor
Predictor adaptation
es +
-s
sinter
sintra
e'
s
sinter
sintra
s'e'
s'
intra-/interframeswitching information
Coder Decoder
Bernd Girod: EE398B: Image Communication II DPCM no. 22
Conditional replenishment
SIGNAL INPUT
SEGMENTER (MOVEMENT DETECTOR)
CODING, ADDRESSING, BUFFERING
BUFFERING, DECODING, ADDRESSING
FRAME DELAY
TRANSMISSION CHANNEL
SIGNAL OUTPUT
Changedetector
Frame store Frame store
DECODERCODER
Still areas: repeat from frame storeMoving areas: encode and transmit address and waveform
Bernd Girod: EE398B: Image Communication II DPCM no. 23
Change detection
Example of a pixel-wise change detector
Example of a block-wise change detector
ABSAverage of 3x3 window
Eliminate isolated points or pairs of points
+
-
Current frame
Previous frame
Decision changed/ unchanged
Threshold
ABSAccumulate over NxN blocks
+
-
Current frame
Previous frame
Decision changed/ unchanged
Threshold
Bernd Girod: EE398B: Image Communication II DPCM no. 24
Rate-distortion optimized mode selection
How to choose the decision threshold, if distortion D shall be minimized for a given rate R?Assumptions
Blockwise mode selection, block index iAdditive overall distortion and rate
Lagrangian cost function
Strategy: minimize Ji for each block i separately, using a common Lagrange multiplier λ
ii
D D= ∑ ii
R R= ∑
i i ii i
J D R D R Jλ λ= + = + =∑ ∑
Bernd Girod: EE398B: Image Communication II DPCM no. 25
Rate-distortion optimized mode selection (cont.)
DD1(R1)
D2(R2)
Consider 2 blocks with D(R) = D1(R1) +D2(R2)
R
Bernd Girod: EE398B: Image Communication II DPCM no. 26
The “Dirty Window” effect
Conditional replenishment scheme with change detection threshold set too high leads to the subjective impression of looking through a dirty window.
BackgroundMoving area picked up by change detector
Moving areasmissed bychange detector
Bernd Girod: EE398B: Image Communication II DPCM no. 27
Crawford noise reduction filter
+-
++
δ f(δ)NL
frame store clean video
signal
noisy video signal
δ
f(δ)
Non-linearity
Bernd Girod: EE398B: Image Communication II DPCM no. 28
DPCM - Summary
DPCM: Prediction from previously coded/transmitted samples (known at transmitter and receiver)Typical signal distortions for intraframe DPCM: granular noise, edge busyness, slope overloadPrediction gain depends on spectral flatnessAdaptive Intra-Interframe-DPCM: forward adaptation vs. backward adaptationConditional replenishment: only transmit frame-to-frame changesTemporal noise reduction by nonlinear, recursive frame differencing