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Fractal Video Compression碎形視訊壓縮方法
Chia-Yuan Chang
張嘉元Department of Applied Mathematics
National Sun Yat-Sen University
Kaohsiung, Taiwan
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Topics
• Introduction
• Our approach
• Simulation
• Conclusions
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INTRODUCTION
• Standardization of algorithm -- MPEG
• Quad-tree structure
• Slicing floorplan tree
• Fractal dimension
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Standardization of algorithm• MPEG
– video layers
• I-picture: Intraframe, JPEG DCT, lower compression ratio
• P-picture: Predicted frame, motion compensation
• B-picture: Bi-directional frame,higher compression ratio
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– display order
I B B B B B B B B BP P P
group of pictures
time
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– coding order
I P B B P B B P B BB B B
group of pictures
time
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– motion compensationtime
Forward predictionreference picture
Current pictureBackward prediction
reference picture
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– disadvantages
• buffer and time control
• encoding: the fixed block size
• DCT: filter high frequency (like edge)
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Quad-tree structure
• basic definition
– top-down : segment
– bottom-up : merge
• application
– Vector Quantization (VQ)
• disadvantage
– efficiency
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Slicing floorplan tree
• The Recursive Split Algorithm– Start with R containing a single rectangular
patch that covers the entire frame– Repeat n-1 times Step 1), 2), 3)– 1) Search R for the rectangle r with the largest
error er, and remove it from R.
– 2) Split r into two rectangles r1, r2 such that er1 + er2 is minimized.
– 3) Add r1, r2 to R.
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• disadvantage
– each two-frames has own mask
– noise effect
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Fractal dimension
• Introduction– estimate length of coastline
– general formula
– the measurement, analysis, and classification of shape and texture
DFL 1)(
1rDNr or DNr
r
log
log1
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• Box counting approach (3-D space)– image size : M x M– box size : s x s– ratio : r = s / M– box number in ( i, j) grid
– total box number
– FD equation r
rND1log
log
1, kljinr
jinNji
rr ,,
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Our approach
• Fractal Dimension Estimation
• Slicing Floorplan Segmentation
• Compression
• Decompression
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Mask processing
m+ 1sucessive
images
mdifference
images
m imagesamples
featuremap
F(i, j)
Gray-levelscale
Masksegmentation
compute fractal dimension
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• Fractal dimension estimation– Basic definition
• image sequence: I(x, y, t),
• a group image frames: F1, F2, …, Fm+1,
• reference frame : Fr
• frame difference : Diff(x, y, t)• difference volume : V• voxel (x, y, t)• feature map : F(x, y)
Ntyx ,,
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– A modified box-counting approach• window volume size : mxmxm• cubes size : axaxa. • scaling factor s,• the fractal dimension for the voxel (x, y, t)
mas
1,, ijtyxcont
2,,12
),,(mrqpm
rtqypxcontC
s
CFD tyx 1log
log),,(
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¡´ (x ,y ,m /2 )
Diff (x, y ,1)
Diff (x ,y ,m )
Diff (x, y ,m /2)
¡´ (x, y, m )
n
nm
m
aa
Difference volumeV
a
¡´ (x ,y ,1)
¡´ ¡´
¡´
¡´ ¡´
¡´
T h e r e l a t i o n s h i p b e t w e e n t h e f r a m e d i m e n s i o n n , f r a m e d i f f e r e n c e
D i f f ( x , y , t ) , t h e n u m b e r o f f r a m e d i f f e r e n c e in a m a c r o b l o c k m , a n d
t h e d i m e n s i o n o f t h e m e a s u r i n g c u b e a .
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• Slicing floorplan segmentation.– Start with R containing a single rectangular patch
that covers feature map F(i, j).• 1) search R for the rectangle r with the largest
variance Vr if Vr < Vt then go to Step 4 else remove it from R.
• 2) split r into two rectangles r1, r2 such that is maximized
• 3) add r1, r2 to R, and go to Step 1
• 4) check the mean value of each block. If Mr > Mt then segment Mr to smaller blocks else exit.
M rrM21
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Motion estimation
referenceimage
predicted image usingreference image
xi
yi
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Compression
referenceimage Fr
Mask
motionestimation
motionvector of
each blockin mask
image Fi
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Decompression
referenceimage Fr
Mask
motion vector ofeach block in the
mask
image Fi
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Simulation
• test image sequence
– Claire
– football
– Noisy Claire (25db Gaussian noises)
– Noisy football (20db Gaussian noises)
• comparison
– MPEG
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(a) (b)
(c) (d)
Fig. 2 (a) The 1st frame in the Claire sequence, (b) The 1st frame in the football sequence, (c) 25 dB Gaussian noises are added to part (a), (d) 20 dB Gaussian noises are added to part (b).
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Fig. 3 (a) – (d) The feature map representing the fractal dimension for the image sequences in Fig. 2 (a) – (d), respectively, after normalizing to 255.
(a) (b)
(c) (d)
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Fig. 4 (a) – (d) The slicing floorplan segmentation maskcorresponding to the image sequences in Fig. 2 (a) – (d), respectively.
(a) (b)
(c) (d)
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Image sequences Total block
numbers
Bit rate
(bit/pixel)
Average PSNR
(dB)
Claire 137
199
325
.044526
.052443
.068533
35.71311
35.88222
36.31750
Noisy Claire 88
142
233
.040900
.046518
.058139
27.94569
28.02084
28.13815
Football 122
335
572
.044816
.072016
.102280
21.82529
23.26751
24.22758
Noisy Football 16
45
98
.062575
.066278
.073046
16.30597
17.11834
17.80838
Table 1. The relationship between the number of blocks, the compression ratio, and
PSNR for the image sequence.
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Image sequences Compression
methodology
Bit rate
(bit/pixel)
Average PSNR
(dB)
Claire MPEG
Our approach
.143985
.044526
35.38568
35.71311
Noisy Claire MPEG
Our approach
.143985
.040900
23.34401
27.94569
Football MPEG
Our approach
.143985
.035877
19.25690
19.26762
Noisy Football MPEG
Our approach
.143985
.062575
16.32646
16.30597
Table 2. Comparison of PSNR and bit rate for our approach and MPEG
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Conclusions
• Our algorithm can get higher compression ratio than MPEG in the same average PSNR for the same image sequence.
• Future research
– compression speed improvement