fractal video compression 碎形視訊壓縮方法 chia-yuan chang 張嘉元 department of applied...

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

Topics

• Introduction

• Our approach

• Simulation

• Conclusions

INTRODUCTION

• Standardization of algorithm -- MPEG

• Quad-tree structure

• Slicing floorplan tree

• Fractal dimension

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

– display order

I B B B B B B B B BP P P

group of pictures

time

– coding order

I P B B P B B P B BB B B

group of pictures

time

– motion compensationtime

Forward predictionreference picture

Current pictureBackward prediction

reference picture

– disadvantages

• buffer and time control

• encoding: the fixed block size

• DCT: filter high frequency (like edge)

Quad-tree structure

• basic definition

– top-down : segment

– bottom-up : merge

• application

– Vector Quantization (VQ)

• disadvantage

– efficiency

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.

• disadvantage

– each two-frames has own mask

– noise effect

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

• 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 ,,

Our approach

• Fractal Dimension Estimation

• Slicing Floorplan Segmentation

• Compression

• Decompression

Mask processing

m+ 1sucessive

images

mdifference

images

m imagesamples

featuremap

F(i, j)

Gray-levelscale

Masksegmentation

compute fractal dimension

• 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 ,,

– 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),,(

¡´ (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 .

• 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

Motion estimation

referenceimage

predicted image usingreference image

xi

yi

Compression

referenceimage Fr

Mask

motionestimation

motionvector of

each blockin mask

image Fi

Decompression

referenceimage Fr

Mask

motion vector ofeach block in the

mask

image Fi

Simulation

• test image sequence

– Claire

– football

– Noisy Claire (25db Gaussian noises)

– Noisy football (20db Gaussian noises)

• comparison

– MPEG

(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).

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)

Fig. 4 (a) – (d) The slicing floorplan segmentation maskcorresponding to the image sequences in Fig. 2 (a) – (d), respectively.

(a) (b)

(c) (d)

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.

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

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