Research Article A Novel High Efficiency Fractal Multiview ...

Research ArticleA Novel High Efficiency Fractal Multiview Video Codec

Shiping Zhu Dongyu Zhao and Ling Zhang

Department ofMeasurement Control and Information Technology School of Instrumentation Science andOptoelectronics EngineeringBeihang University Beijing 100191 China

Correspondence should be addressed to Shiping Zhu spzhu163com

Received 17 July 2014 Accepted 15 September 2014

Academic Editor Guido Maione

Copyright copy 2015 Shiping Zhu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Multiview video which is one of the main types of three-dimensional (3D) video signals captured by a set of video cameras fromvarious viewpoints has attracted much interest recently Data compression for multiview video has become a major issue In thispaper a novel high efficiency fractal multiview video codec is proposed Firstly intraframe algorithm based on the H264AVCintraprediction modes and combining fractal and motion compensation (CFMC) algorithm in which range blocks are predictedby domain blocks in the previously decoded frame using translational motion with gray value transformation is proposed forcompressing the anchor viewpoint video Then temporal-spatial prediction structure and fast disparity estimation algorithmexploiting parallax distribution constraints are designed to compress the multiview video data The proposed fractal multiviewvideo codec can exploit temporal and spatial correlations adequately Experimental results show that it can obtain about 036 dBincrease in the decoding quality and 3621 decrease in encoding bitrate compared with JMVC85 and the encoding time is savedby 9571 The rate-distortion comparisons with other multiview video coding methods also demonstrate the superiority of theproposed scheme

1 Introduction

In recent years multiview video (MVV) is attracting consid-erable attentionThis is becauseMVV can provide consumerswith depth sense to the observed scene as if it really existsin front of consumers allow consumers to freely changeviews and interactivelymodify the properties of a sceneThistype of video may be offered in the future home electronicsdevices such as immersive teleconference 3DTV [1] 3Dmobile phone and home video camcorder For example inimmersive teleconference there is an interaction betweenconsumers Participants at different geographical sites meetvirtually and see each other in either free viewpoint or 3DTVstyleThe immersiveness provides amore natural way of com-munications However in such a low bit rate communicationchannel such as thewirelessmobile network owing to the ins-ufficient bit budget MVV compression will cause the heavyloss of visual detail information

MVV contains a large amount of statistical dependenciessince it is a collection of multiple videos simultaneouslycaptured in a scene at different camera locations Therefore

efficient compression techniques are required for the aboveconsumer electronic applications [2]

Fractal compression which has the advantages of highcompression ratio resolution independence and fast decod-ing speed is considered as one of the most promising com-pressionmethodsThe basic idea of fractal image coding is tofind a contractive mapping whose unique attractor approx-imates the original image For the decoding an arbitraryimage with the same size of the original image is input intothe decoder and after several times of iteratively applyingthe recorded contractive mappings to the input image thereconstructed image will be obtained Much effort [3ndash5]has been made to the fractal still image compression afterJacquinrsquos fractal block coding algorithm [6] However a littlework has been reported on the fractal video compression letalone the fractal multiview video compression [7] For fractalvideo compression there are two extensions of still imagecompression which are cube-based compression [8] andframe-based compression [9] In the former method videosequences are partitioned into nonoverlapping 3D rangeblocks and overlapping 3D domain blocks with larger size

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 613714 12 pageshttpdxdoiorg1011552015613714

2 Mathematical Problems in Engineering

than range blocks Then the key issue turns to find the bestmatching domain cuboid and the corresponding contractivemapping for every range cuboid which is very complicatedIn the latter method each frame is encoded using theprevious frame as a domain pool except the first frame whichis encoded using a still image fractal scheme or some othermethods The main advantage of the frame-based algorithmis that decoding a frame consists of just one application ofmapping so that iteration is not required at the decoderHowever the temporal correlation between the frames maynot be effectively exploited since the size of the domain blockis larger than that of the range block [10]

In this paper a novel highly efficient fractal multiviewvideo codec by combined temporalinterview prediction isproposed The anchor viewpoint video is encoded by impro-ved frame-based fractal video compression approach whichcombines the fractal coder with the well-known motioncompensation (MC) technique The other viewpoint videosare not only predicted from temporally neighboring imagesbut also from the corresponding images in adjacent views

This paper is organized as follows The fractal com-pression theory and mathematical background is summa-rized in Section 2 The anchor viewpoint video compressionalgorithm is presented in Section 3 and then the proposedhigh efficiency fractal multiview video codec is presented inSection 4 The experimental results are shown in Section 5Finally the conclusions are outlined in Section 6

2 The Fractal Compression Theory andMathematical Background

21 Mathematical Background The mathematical back-ground of fractal coding technique is the contraction map-ping theorem and the collage theorem [11]

For the complete metric space (119883 119889) where119883 is a set and119889 is a metric on 119883 the mapping 120596 119883 rarr 119883 is said to becontractive if and only if

119889 (120596 (119909) 120596 (119910)) le 120572 sdot 119889 (119909 119910) 0 le 120572 lt 1 forall119909 119910 isin 119883

(1)

where 120572 is called the contractivity factor of the contractivemapping

For a contractive mapping 120596 119883 rarr 119883 on (119883 119889) thenthere exists a unique point 119909119891 isin 119883 such that for any point119909 isin 119883

119909119891 = 120596 (119909119891) = lim119899rarrinfin120596119899(119909) (2)

Such a point 119909119891 is called a fixed point or the attractor ofthe mapping 120596 119883 rarr 119883 where 120596119899(119909) represents the 119899thiteration application of 120596 to 119909 This is the famous Banachrsquosfixed point theorem or contractive mapping theorem [11]

For the fractal image coding if the encoder can find acontractive mapping whose attractor is the original imagethen we only need to store the mapping with less bits insteadof the original pixel values But in the practical implemen-tation it is impossible to find a contractive mapping whoseattractor is exactly the original image Instead the fractal

encoder attempts to find the contractive mapping whose col-lage is close to the original image

The collage theorem is as followsFor the complete metric space (119883 119889) 120572 is the contractiv-

ity factor of contractive mapping 120596 119883 rarr 119883 then the fixedpoint 119909119891 of the contractive mapping 120596 satisfies

119889 (119909 119909119891) le1

1 minus 120572119889 (119909 119908 (119909)) (3)

This means that the decoded attractor 119909119891 is close to theoriginal image 119909 if the collage 119908(119909) is close to the originalimage 119909 Therefore it converts to the minimization problemof the collage error

22 Fractal Image Coding In the practical implementationof the fractal image encoding process the original image isfirstly partitioned into nonoverlapping range blocks coveringthe whole image and overlapping domain blocks usuallytwice the size of the range blocks in both width and heightFor each range block the goal is to find a domain block and acontractive mapping that jointly minimize a dissimilarity(distortion) criterion Usually the RMS (root mean square)metric is used The contractive mapping applied to the dom-ain block classically consists of the following parts [12]

(i) geometrical contraction (usually by downsamplingthe domain block to the same size of the range block)

(ii) affine transformation (modeled by the 8 isometric tra-nsformations which contain the identity rotation by90∘ 180∘ and 270∘ and reflection about the midhori-zontal axis themidvertical axis the first diagonal andthe second diagonal)

(iii) gray value transformation (a least square optimiza-tion is performed in order to compute the best valuesfor the parameters 119904 and 119900which are scaling factor andoffset factor resp)

Here 119904 and 119900 can be computed by minimizing the follow-ing equation

119864 (119904 119900) =

119899

sum119894=1

119898

sum119895=1

(119904 sdot 119889119894119895 + 119900 minus 119903119894119895)2 (4)

where 119889119894119895 (119894 = 1 2 119899 119895 = 1 2 119898) is the pixel valueof the domain block after geometrical contraction and affinetransformation and 119903119894119895 (119894 = 1 2 119899 119895 = 1 2 119898) isthe pixel value of the range block

Then 119904 and 119900 can be obtained by making 120597119864(119904 119900)120597119904 and120597119864(119904 119900)120597119904 equal to zero So that

119904 =119899119898sum119899119894=1sum119898119895=1 119889119894119895119903119894119895 minus sum

119899119894=1sum119898119895=1 119889119894119895sum

119899119894=1sum119898119895=1 119903119894119895

119899119898sum119899119894=1sum119898119895=1 1198892119894119895 minus (sum

119899119894=1sum119898119895=1 119889119894119895)

2

119900 =sum119899119894=1sum119898119895=1 119903119894119895 minus 119904 sdot sum

119899119894=1sum119898119895=1 119889119894119895

119899119898

(5)

The fractal encoding process can be finished by storing allthe data necessary for each range block including the location

Mathematical Problems in Engineering 3

of the corresponding domain block the index of the appliedisometric transformation and the values 119904 and 119900 The decod-ing process is to iteratively apply the stored transformationsto an arbitrary initial image

3 The Anchor Viewpoint Video Compression

The most well-known fractal video codec is a hybrid fractalcoder of circular prediction mapping (CPM) and noncon-tractive interframe mapping (NCIM) [13] in which the firstfour frames are encoded by CPM and the remaining framesare encoded by NCIM In both the CPM and the NCIM eachrange block is motion compensated by a domain block in theadjacent frame which is of the same size as the range blockThe main difference between the CPM and the NCIM is thatthe CPM should be contractive and the decoding processneeds iteration while the NCIM need not be contractiveThesimulation results show better performance for the NCIM-coded frames than that for the CPM-coded frames

Different from the abovementioned approach in ourproposed scheme we first partition the video sequences intogroups of frames (GOFs) to avoid error propagation Everyfirst frame in each GOF is encoded by intraframe predictionwithout depending on the previous frames and the remain-ing frames in each GOF are encoded by combining fractalwith themotion compensation (CFMC) as shown in Figure 1In CFMC each range block is motion compensated by adomain block in the adjacent previously predicted framerather than the previous source frame which is of the samesize as the range block

31 Intraframe Prediction The intraframe prediction in ourscheme uses for reference the intraprediction modes ofinternational video coding standard H264AVC [14] Wemake somemodifications tomake it appropriate to the overallfractal video compression scheme Firstly we partition eachframe into range blocks of maximum size 16 times 16 andminimum size 4 times 4 using the quadtree structure [15] whileH264 only has two kinds of sizes of blocks which are 4times4 and16times16 respectively and does not use the quadtree structureSecondly H264 specifies 9 intraprediction modes for 4 times 4luma blocks and 4 intraprediction modes for 16 times 16 lumablocks as shown in Figures 2 and 3 respectively while we usethe 9modes in Figure 2 for range blocks in the bottom level ofthe quadtree and the 4 modes in Figure 3 for range blocks inother levels of the quadtree Thirdly H264 chooses the bestmode using Lagrangian rate distortion optimization (RDO)technique [16] by traversing all the possible block sizes andprediction modes which is very time consuming while forsimplification in our scheme subdivision of the range blockis performed only when the prediction error is still above aprescribed threshold and the minimum allowable partition isnot reached

A prediction frame is generated and subtracted from theoriginal frame to form an error-frame which is further trans-formed quantized and entropy encoded In parallel the qua-ntized data are rescaled and inverse transformed and addedto the prediction frame to reconstruct a coded version of

F0 F1 F2 Fmminus1 Fm Fm+1 Fm+2 Fm+3

GOF0 GOF1

Domain-range mappingFrame-to-frame mapping

Figure 1 The structure of anchor viewpoint video coding

the framewhich is stored for later predictions In the decoderthe bitstreams are entropy decoded rescaled and inversetransformed to form a decoded error-frame The decodergenerates the same prediction that is created at the encoderand adds this to the decoded error-frame to produce areconstructed frame

32 Combining Fractal with Motion Compensation Tradi-tional motion compensation technique making use of blockmatching is based on the assumptions of locally translationalmotion and conservation of image intensity whereas we mayrelax these assumptions when applying motion compensa-tion technique used in our fractal video compression Theassumption of translation is replaced by an affine motion andthe assumption of conservation of image intensity is replacedby the concept of linearly changing image intensity

We investigate and compare the following four schemes

S0 traditional (translational motion and conservation ofimage intensity) block matching

S1 translational motion with gray value transformation

S2 affine block matching using 8 isometric transforma-tions

S3 affine block matching using 8 isometric transforma-tions with gray value transformation

Exhaustive search in a search window which is formed byextending the collocated domain block by plusmn7 pixels in fourdirections is used for a range block as shown in Figure 4where 119865119898 represents the current frame to be encoded and1198651015840119898minus1 represents the adjacent coded version

Figure 5(a) compares the PSNR performance of the diff-erent schemes on the ldquoBallroomrdquo video Clearly the gray valuetransformation leads to significant PSNR gain whereas thegain for affine transformation is only moderate Figure 5(b)compares the encoding time of the different schemes Obvi-ously the schemes without affine transformation (S0 andS1) are much faster compared to schemes using the affinemotion model (S2 and S3) while gray value transformationis compu-tationally not very expensive Test results on othervideo sequences such as ldquoRacerdquo and ldquoFlamencordquo show thesame trends

Considering the tradeoff between computational com-plexity and quality gain we finally adopt S1 in our CFMC


M A B C D E F G H

I

J

K

L

0 (vertical)

M A B C D E F G H

I

J

K

L

1 (horizontal)

M A B C D E F G H

I

J

K

L

8 (horizontal-up)

M A B C D E F G H

I

J

K

L

7 (vertical-left)

M A B C D E F G H

I

J

K

L

0 (horizontal-down)

M A B C D E F G H

I

J

K

L

5 (vertical-right)

M A B C D E F G H

I

J

K

L

2 (DC)

M A B C D E F G H

I

J

K

L

4 (diagonal down-right)

M A B C D E F G H

I

J

K

L

3 (diagonal down-left)

Mean(AsimD IsimL)

Figure 2 Nine intraprediction modes

algorithm Namely range blocks in the current frame are pre-dicted by domain blocks of the reference-frame using trans-lational motion with gray value transformation

To achieve better quality the prediction frame is sub-tracted from the original frame to form an error-frame whichis transformed quantized and entropy encoded In parallelthe quantized data are rescaled and inverse transformedand added to the prediction frame to reconstruct a codedversion of the frame which is stored for later predictionsand the CFMC data including the positions of correspondingdomain blocks scale factors and offset factors are entropyencoded In the decoder the bitstreams of error-frame areentropy decoded rescaled and inverse transformed to forma decoded error-frame The bitstreams of CFMC data areentropy decoded and generate the prediction frame by apply-ing corresponding translationalmotionwith gray value trans-formation only once without iteration Then a reconstructedframe is produced by adding the prediction frame to thedecoded error-frame This contrasts to 2D fractal video cod-ing schemes which do not consider the coding of error-frames at all

4 Fractal Multiview VideoCompression Scheme

Thecoding structure between different views needs to be con-sidered when extending single view fractal video coding to

multiview video codingTherefore we propose the temporal-spatial prediction structure and fast disparity estimation algo-rithm

41 Temporal-Spatial Prediction Structure Multiview videosequences are captured by several cameras at the same timeand there exists a high degree of correlation between inter-views and intraviews So we propose a temporal-spatial pre-diction structure based on view center and view distanceWhen processing the multiview video signal disparity com-pensation and CFMC are combined to reduce the number ofintraframe coded frames and improve the view compensationefficiency

The proposed new prediction structure is shown inFigure 6 which contains 3 views The center viewpoint videois the anchor video coded with the intraframe prediction andCFMC algorithm in Section 3 and the other viewpoint videosare coded based on disparity compensation and CFMC

Figure 7 is the geometric schematic diagram of temporal-spatial prediction Disparity estimation and CFMC are usedfor prediction to reduce data redundancy adequately

42 Fast Disparity Estimation Algorithm Geometric constra-ints between neighboring frames in multiview video seque-nces can be used to eliminate spatial redundancies Parallaxdistribution constraints which contain epipolar constraintdirectional constraint and spatial-time domain correlationare used in the proposed fast disparity estimation algorithm


H

V

H

V

H

V

H

V

3 (plane)

0 (vertical) 1 (horizontal)

2 (DC)

middot middot middot

Mean (H + V)

Figure 3 Four intraprediction modes

Search window

Best matching

Range block

Domain blocks

FmF998400

mminus1

Figure 4 Search window for range block

Epipolar constraint the epipolar geometry is the intrinsicprojective geometry between two views Epipolar line can be

found in the right image for a point of left image onwhich thecorresponding point can be searched For parallel systemsonly the search of 119909 direction is needed just along the scanline In other words traditional two-dimensional search canbe simplified to one-dimensional search along the scan line

Directional constraint in parallel systems the verticalcomponent of disparity vector is always equal to zeroThe horizontal component is determined by the followingformula

119889119909 (119909 119910 119911) =119865119861

119911 (6)

where 119889119909(119909 119910 119911) represents the horizontal component ofdisparity vector corresponding to the point (119909 119910 119911) 119865 repre-sents the camerarsquos focal length119861 represents the baseline dista-nce between the two cameras We can see from formula (6)that the horizontal component of disparity vector is alwayspositive that is for the same scene the left perspective pro-jection image always moves slightly left relative to the rightimage Therefore searching only in one direction instead oftwo directions is enough

The spatial-time domain correlation the disparity vectorin the same frame has a strong correlation For two adjacentframes only a few pixels move and the positions of most


PSN

R (d

B)

366

368

370

372

374

376

S0 S1 S2 S3

(a) PSNR comparisons

Tim

e (s)

0

500

1000

1500

2000

2500

3000

3500

S0 S1 S2 S3

(b) Encoding time comparisons

Figure 5 Performance comparisons of the four schemes

Time

View

F00 F01 F02 F03 F04

F10 F11 F12 F13 F14

F20 F21 F22 F23 F24

View 0

View 1

View 2

T0 T1 T2 T3 T4

Figure 6 The proposed temporal-spatial prediction structure

mv

View

Time

Adjacent view

mv

mv

CFMC

Disparity estimation

Nminus 1

N

Figure 7 Disparity estimation and CFMC

pixels have not changed The disparities of these pixelswhose positions have not changed keep basically unchangedTherefore corresponding disparity vectors of the neighbor-ing range blocks can be considered as the starting point for asmall area search to find the actual disparity vector quickly

From the three constraints above we can summarize ourfast disparity estimation algorithm as follows Firstly searchbetween the disparity vectors of the previously encoded nei-ghboring range blocks to find one with the minimum RMSerror as the starting search point Then search in the hori-zontal to the right direction within several pixels distance tofind the final disparity vector with the minimum RMS error

Fast disparity estimation algorithm is helpful to reducethe number of search candidates and further to decrease thedisparity estimation time It can greatly improve the codingefficiency whichmakes full use of the correlation between leftand right views and can find the best matching block morequickly

43 FractalMultiviewVideo Compression Process Theoverallcoding process of the proposed fractal multiview video codecis shown in Figure 8

Step 1 Partition the video sequences into GOFs

Step 2 Encode the first frame of GOF in the anchor viewusing intraframe prediction and process the error-frame

Step 3 Encode the first frame ofGOF in the nonanchor viewsusing fast disparity estimation from collocated frame in theadjacent view and process the error-frame

Step 4 Encode the remaining frames of GOF in the anchorview using CFMC from the previous decoded frame andprocess the error-frames

Step 5 Encode the remaining frames of GOF in the nonan-chor views using CFMC from the previous decoded frameand then encode them using fast disparity estimation fromcollocated frames in the adjacent view Choose the one withthe minimum RMS and process the error-frames

Step 6 Encode the next GOF using Step 2 to Step 5 until allthe frames have been finished


Start

Anchor view

Yes

Intraframeprediction

CFMC from theprevious decodedframe and get the

minimum RMS

The first frame of GOF


Yes

Yes

The last frameNo

End

Fast disparityestimation from thecollocated frame in

adjacent view and getthe minimum RMS

Get the minimumvalue between RMS1

and RMS2

Yes

No No

No

CFMC from theprevious decodedframe and get theminimum RMS1


adjacent view and getthe minimum RMS2

To next frame

Figure 8 The encoding process block diagram of the proposed system

5 Experimental Results

To verify the performance of the proposed fractal multiviewvideo codec three multiview video sequences ldquoBallroomrdquo(250 frames) ldquoRacerdquo (300 frames) and ldquoFlamencordquo (300frames) are tested The quadtree structure we used containsthree levels and the sizes of range blocks are 16 times 16 8 times 8and 4 times 4 respectively Frame filtering is also applied Thesimulations are run on a PC with Intel Core i7 quad 34GHzCPU and 8GB DDR RAM The proposed method is imple-mented and compared with the state-of-the-art multiviewvideo coding (MVC) reference software JMVC85 [20] Theconfiguration settings of the JMVC85 simulation environ-ment are shown in Table 1

Table 2 shows the PSNR bit number and encoding timecomparisons between the proposed codec and JMVC85using the simulation conditions given above The numericalresults are obtained by computing the average value of allthe encoded frames Overall average time savings of about9571 bit number savings of about 3621 and PSNR gainsof 036 dB can be observed Apparently there is a great impro-vement on encoding time bitrate and PSNR compared to theJMVC85

Table 1 Configuration settings of the JMVC85 simulation environ-ment

NumViewsMinusOne 2ViewOrder 0-2-1NumberReferenceFrames 2GOP size 12IntraPeriod 12SearchMode 0 BlockSearchFrames to be encoded all framesQP of all frames 28SearchRange plusmn7 pixelsMotion estimation Full searchSymbolMode CAVLC

Figures 9(a)ndash9(c) show the PSNR comparisons of theldquoBallroomrdquo left center and right view respectively betweenthe proposed fractal multiview video codec and JMVC85Figures 10(a)ndash10(c) show the coding bit number comparisonsof the ldquoBallroomrdquo left center and right view respectively


Frame number

PSN

R (d

B)

355

360

365

370

375

380

385

390

JMVC85Proposed

0 20 40 60 80 100 120 140 160 180 200 220 240 260

(a) Left view

PSN

R (d

B)

JMVC85Proposed

360

365

370

375

380

385

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(b) Center view

JMVC85Proposed

365

370

375

380

385

390

PSN

R (d

B)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(c) Right view

Figure 9 PSNR comparisons of ldquoBallroomrdquo

Table 2 Performance comparisons between the proposed codec with JMVC85

Video sequences PSNR (dB) Bit number (bitsframe) Time (msframe)JMVC85 Proposed JMVC85 Proposed JMVC85 Proposed

BallroomLeft 3722 3744 46275 20924 22976 632

Center 3725 3752 35635 47503 36595 2127Right 3755 3745 41230 25627 23384 632

RaceLeft 3735 3798 91580 22545 21055 661

Center 3763 3812 57711 85537 35543 2226Right 3746 3799 89584 31300 21438 661

FlamencoLeft 3954 4006 59219 21883 20665 606

Center 4031 4025 39659 51859 34552 2048Right 3934 4007 63750 27508 21949 610

Average 3818 3854 58294 37187 26462 1134


Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view

Figure 10 Bit number comparisons of ldquoBallroomrdquo

Figures 11(a)ndash11(c) show the encoding time comparisons ofthe ldquoBallroomrdquo left center and right view

From Figures 9ndash11 we can conclude that the proposedfractal multiview video codec reduces the encoding time andimproves coding efficiency greatly which leads to more real-time applications Figure 12 shows the 18th frame original anddecoded images of ldquoRacerdquo resulted from JMVC85 and theproposed method

To verify the good performance of the proposed methodFigure 13 illustrates the rate-distortion comparisons of ldquoFla-mencordquo among the proposedmethod color correction prepr-ocessing method [17] histogram-matching method [18] illu-mination compensation method [19] no correction method[17] fractal method proposed in [7] and JMVC85 [20] In

order to facilitate the comparison the average performancecomparisons of ldquoFlamencordquo between the proposed codec andthe other schemes computedwith the Bjontegaardmetric [21]are shown in Table 3

From Figure 13 and Table 3 we can see that with thebitrate increasing the proposed fractalmultiview video codecperforms better and the overall encoding performance ofthe proposed codec is superior to that of algorithms in thereferences

6 Conclusion

In this paper a novel high efficiency fractal multiview videocodec is presented to improve the encoding performance


Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view

Figure 11 Encoding time comparisons of ldquoBallroomrdquo

Table 3 Average performance comparisons of ldquoFlamencordquo betweenthe proposed codec and the other schemes computed with theBjontegaard metric

Schemes BDPSNR(dB) BDBR ()

Color correctionpreprocessing [17] 106 minus78

Histogram-matching [18] 129 minus43Illumination compensation[19] 143 minus57

No correction method [17] 164 minus75Fractal [7] 006 minus04JMVC85 235 minus178

The video sequences are firstly partitioned intoGOFs to avoiderror propagation Then we improve the intraframe predic-tion to make it suitable for fractal encoding and propose theCFMC algorithm to get better performance of the anchorview In addition temporal-spatial prediction structure andfast disparity estimation algorithm are applied to further raisethe compression efficiency

Experimental results show that the proposed fractal mul-tiview video codec spends less encoding time and achieveshigher compression ratio with better decoding image qualityAn average encoding time saving of about 9571 a bitratesaving of about 3621 and a PSNR gain of 036 dB canbe achieved compared with JMVC85 In addition it alsoshows superiority compared with color correction prepro-cessing method histogram-matching method illumination


(a) Original image (b) Decoded image with JMVC 85

(c) Decoded image with the proposed method

Figure 12 The decoded image results of 18th frame of ldquoRacerdquo

Bit rate (kbpsview)850 900 950 1000 1050 1100

PSN

R (d

B)

32

34

36

38

40

42

Color correction preprocessing [17]Histogram-matching [18]Illumination compensation [19]No correction [17]

Fractal [7]JMVC85 Proposed

Figure 13 Rate-distortion comparisons of ldquoFlamencordquo

compensation method and no correction method It hasbuilt a good foundation for the further research of multiviewfractal video coding and other related coding methods

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This project is funded by the National Natural Science Foun-dation of China (NSFC) under Grants nos 61375025 61075-011 and 60675018 and also the ScientificResearch Foundationfor the Returned Overseas Chinese Scholars from the StateEducation Ministry of China The authors would also like toexpress their appreciations to the reviewers for their thoroughreview and very helpful comments which help improve thispaper

References

[1] H M Ozaktas and L Onural Three-Dimensional TelevisionCapture Transmission Display Springer New York NY USA2007

[2] P Merkle A Smolic K Muller and T Wiegand ldquoEfficient pre-diction structures for multiview video codingrdquo IEEE Transac-tions on Circuits and Systems for Video Technology vol 17 no 11pp 1461ndash1473 2007

[3] T K Truong C M Kung J H Jeng and M L Hsieh ldquoFastfractal image compression using spatial correlationrdquo ChaosSolitons and Fractals vol 22 no 5 pp 1071ndash1076 2004


[4] C-CWang and C-H Hsieh ldquoAn efficient fractal image-codingmethod using interblock correlation searchrdquo IEEE Transactionson Circuits and Systems for Video Technology vol 11 no 2 pp257ndash261 2001

[5] Y Iano F S da Silva and A L M Cruz ldquoA fast and efficienthybrid fractal-wavelet image coderrdquo IEEE Transactions onImage Processing vol 15 no 1 pp 98ndash105 2006

[6] A E Jacquin ldquoImage coding based on a fractal theory of iteratedcontractive image transformationsrdquo IEEE Transactions of ImageProcessing vol 1 no 1 pp 18ndash30 1992

[7] S Zhu L Li and Z Wang ldquoA novel fractal monocular andstereo video codec with object-based functionalityrdquo EURASIPJournal on Advances in Signal Processing vol 2012 no 1 article227 14 pages 2012

[8] M S Lazar and L T Bruton ldquoFractal block coding of digitalvideordquo IEEE Transactions on Circuits and Systems for VideoTechnology vol 4 no 3 pp 297ndash308 1994

[9] Y Fisher D Rogovin and T P Shen ldquoFractal (self-VQ)encoding of video sequencesrdquo in Visual Communications andImage Processing (VCIP rsquo94) vol 2308 of Proceedings of SPIEpp 1359ndash1370 Chicago Ill USA September 1994

[10] C-S Kim and S-U Lee ldquoFractal coding of video sequence bycircular prediction mappingrdquo Fractals vol 5 no 1 pp 75ndash881997

[11] M Barnsley Fractals Everywhere Academic Press New YorkNY USA 1988

[12] A Pommer C Hufnagl and A Uhl ldquoFractal motion compen-sationrdquo in Proceedings of the Visual Communications and ImageProcessing pp 1050ndash1061 San Jose Calif USA January 1998

[13] C-S Kim R-C Kim and S-U Lee ldquoFractal coding of videosequence using circular prediction mapping and noncontrac-tive interframe mappingrdquo IEEE Transactions on Image Process-ing vol 7 no 4 pp 601ndash605 1998

[14] T Wiegand G J Sullivan G Bjoslashntegaard and A LuthraldquoOverview of the H264AVC video coding standardrdquo IEEETransactions on Circuits and Systems for Video Technology vol13 no 7 pp 560ndash576 2003

[15] Y Fisher Fractal Image Compression-Theory and ApplicationSpringer New York NY USA 1995

[16] G J Sullivan and TWiegand ldquoRate-distortion optimization forvideo compressionrdquo IEEE Signal Processing Magazine vol 15no 6 pp 74ndash90 1998

[17] C Doutre and P Nasiopoulos ldquoColor correction preprocessingfor multiview video codingrdquo IEEE Transactions on Circuits andSystems for Video Technology vol 19 no 9 pp 1400ndash1405 2009

[18] U Fecker M Barkowsky and A Kaup ldquoHistogram-basedprefiltering for luminance and chrominance compensation ofmultiview videordquo IEEE Transactions on Circuits and Systems forVideo Technology vol 18 no 9 pp 1258ndash1267 2008

[19] A Vetro P Pandit H Kimata A Smolic and Y K WangldquoJoint Multiview Video Model (JMVM) 80rdquo ISOIEC JTC1SC29WG11 and ITU-TQ6SG16 Doc JVT-AA207 April 2008

[20] Joint Video Team of ITU-T VCEG and ISOIEC MPEG ldquoWD 1Reference software for MVC (JMVC85)rdquo March 2011

[21] G Bjontegaard ldquoCalculation of average PSNR differences bet-ween RD curvesrdquo in Proceedings of the 13th VCEG-M33MeetingAustin Tex USA April 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


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Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


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International Journal of


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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


than range blocks Then the key issue turns to find the bestmatching domain cuboid and the corresponding contractivemapping for every range cuboid which is very complicatedIn the latter method each frame is encoded using theprevious frame as a domain pool except the first frame whichis encoded using a still image fractal scheme or some othermethods The main advantage of the frame-based algorithmis that decoding a frame consists of just one application ofmapping so that iteration is not required at the decoderHowever the temporal correlation between the frames maynot be effectively exploited since the size of the domain blockis larger than that of the range block [10]

In this paper a novel highly efficient fractal multiviewvideo codec by combined temporalinterview prediction isproposed The anchor viewpoint video is encoded by impro-ved frame-based fractal video compression approach whichcombines the fractal coder with the well-known motioncompensation (MC) technique The other viewpoint videosare not only predicted from temporally neighboring imagesbut also from the corresponding images in adjacent views

This paper is organized as follows The fractal com-pression theory and mathematical background is summa-rized in Section 2 The anchor viewpoint video compressionalgorithm is presented in Section 3 and then the proposedhigh efficiency fractal multiview video codec is presented inSection 4 The experimental results are shown in Section 5Finally the conclusions are outlined in Section 6

2 The Fractal Compression Theory andMathematical Background

21 Mathematical Background The mathematical back-ground of fractal coding technique is the contraction map-ping theorem and the collage theorem [11]

For the complete metric space (119883 119889) where119883 is a set and119889 is a metric on 119883 the mapping 120596 119883 rarr 119883 is said to becontractive if and only if

119889 (120596 (119909) 120596 (119910)) le 120572 sdot 119889 (119909 119910) 0 le 120572 lt 1 forall119909 119910 isin 119883

(1)

where 120572 is called the contractivity factor of the contractivemapping

For a contractive mapping 120596 119883 rarr 119883 on (119883 119889) thenthere exists a unique point 119909119891 isin 119883 such that for any point119909 isin 119883

119909119891 = 120596 (119909119891) = lim119899rarrinfin120596119899(119909) (2)

Such a point 119909119891 is called a fixed point or the attractor ofthe mapping 120596 119883 rarr 119883 where 120596119899(119909) represents the 119899thiteration application of 120596 to 119909 This is the famous Banachrsquosfixed point theorem or contractive mapping theorem [11]

For the fractal image coding if the encoder can find acontractive mapping whose attractor is the original imagethen we only need to store the mapping with less bits insteadof the original pixel values But in the practical implemen-tation it is impossible to find a contractive mapping whoseattractor is exactly the original image Instead the fractal

encoder attempts to find the contractive mapping whose col-lage is close to the original image

The collage theorem is as followsFor the complete metric space (119883 119889) 120572 is the contractiv-

ity factor of contractive mapping 120596 119883 rarr 119883 then the fixedpoint 119909119891 of the contractive mapping 120596 satisfies

119889 (119909 119909119891) le1

1 minus 120572119889 (119909 119908 (119909)) (3)

This means that the decoded attractor 119909119891 is close to theoriginal image 119909 if the collage 119908(119909) is close to the originalimage 119909 Therefore it converts to the minimization problemof the collage error

22 Fractal Image Coding In the practical implementationof the fractal image encoding process the original image isfirstly partitioned into nonoverlapping range blocks coveringthe whole image and overlapping domain blocks usuallytwice the size of the range blocks in both width and heightFor each range block the goal is to find a domain block and acontractive mapping that jointly minimize a dissimilarity(distortion) criterion Usually the RMS (root mean square)metric is used The contractive mapping applied to the dom-ain block classically consists of the following parts [12]

(i) geometrical contraction (usually by downsamplingthe domain block to the same size of the range block)

(ii) affine transformation (modeled by the 8 isometric tra-nsformations which contain the identity rotation by90∘ 180∘ and 270∘ and reflection about the midhori-zontal axis themidvertical axis the first diagonal andthe second diagonal)

(iii) gray value transformation (a least square optimiza-tion is performed in order to compute the best valuesfor the parameters 119904 and 119900which are scaling factor andoffset factor resp)

Here 119904 and 119900 can be computed by minimizing the follow-ing equation

119864 (119904 119900) =

119899

sum119894=1

119898

sum119895=1

(119904 sdot 119889119894119895 + 119900 minus 119903119894119895)2 (4)

where 119889119894119895 (119894 = 1 2 119899 119895 = 1 2 119898) is the pixel valueof the domain block after geometrical contraction and affinetransformation and 119903119894119895 (119894 = 1 2 119899 119895 = 1 2 119898) isthe pixel value of the range block

Then 119904 and 119900 can be obtained by making 120597119864(119904 119900)120597119904 and120597119864(119904 119900)120597119904 equal to zero So that

119904 =119899119898sum119899119894=1sum119898119895=1 119889119894119895119903119894119895 minus sum

119899119894=1sum119898119895=1 119889119894119895sum

119899119894=1sum119898119895=1 119903119894119895

119899119898sum119899119894=1sum119898119895=1 1198892119894119895 minus (sum

119899119894=1sum119898119895=1 119889119894119895)

2

119900 =sum119899119894=1sum119898119895=1 119903119894119895 minus 119904 sdot sum

119899119894=1sum119898119895=1 119889119894119895

119899119898

(5)

The fractal encoding process can be finished by storing allthe data necessary for each range block including the location









GOF0 GOF1














M A B C D E F G H

I

J

K

L

0 (vertical)

M A B C D E F G H

I

J

K

L

1 (horizontal)

M A B C D E F G H

I

J

K

L

8 (horizontal-up)

M A B C D E F G H

I

J

K

L

7 (vertical-left)

M A B C D E F G H

I

J

K

L

0 (horizontal-down)

M A B C D E F G H

I

J

K

L

5 (vertical-right)

M A B C D E F G H

I

J

K

L

2 (DC)

M A B C D E F G H

I

J

K

L


M A B C D E F G H

I

J

K

L


Mean(AsimD IsimL)












H

V

H

V

H

V

H

V

3 (plane)


2 (DC)


Mean (H + V)


Search window

Best matching

Range block

Domain blocks

FmF998400

mminus1





119889119909 (119909 119910 119911) =119865119861

119911 (6)




PSN

R (d

B)

366

368

370

372

374

376

S0 S1 S2 S3


Tim

e (s)

0

500

1000

1500

2000

2500

3000

3500

S0 S1 S2 S3



Time

View

F00 F01 F02 F03 F04

F10 F11 F12 F13 F14

F20 F21 F22 F23 F24

View 0

View 1

View 2

T0 T1 T2 T3 T4


mv

View

Time

Adjacent view

mv

mv

CFMC


Nminus 1

N













Start

Anchor view

Yes



minimum RMS



Yes

Yes

The last frameNo

End




and RMS2

Yes

No No

No




To next frame









Frame number

PSN

R (d

B)

355

360

365

370

375

380

385

390

JMVC85Proposed

0 20 40 60 80 100 120 140 160 180 200 220 240 260

(a) Left view

PSN

R (d

B)

JMVC85Proposed

360

365

370

375

380

385

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(b) Center view

JMVC85Proposed

365

370

375

380

385

390

PSN

R (d

B)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(c) Right view




BallroomLeft 3722 3744 46275 20924 22976 632

Center 3725 3752 35635 47503 36595 2127Right 3755 3745 41230 25627 23384 632

RaceLeft 3735 3798 91580 22545 21055 661

Center 3763 3812 57711 85537 35543 2226Right 3746 3799 89584 31300 21438 661

FlamencoLeft 3954 4006 59219 21883 20665 606

Center 4031 4025 39659 51859 34552 2048Right 3934 4007 63750 27508 21949 610

Average 3818 3854 58294 37187 26462 1134


Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view







6 Conclusion



Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















GOF0 GOF1














M A B C D E F G H

I

J

K

L

0 (vertical)

M A B C D E F G H

I

J

K

L

1 (horizontal)

M A B C D E F G H

I

J

K

L

8 (horizontal-up)

M A B C D E F G H

I

J

K

L

7 (vertical-left)

M A B C D E F G H

I

J

K

L

0 (horizontal-down)

M A B C D E F G H

I

J

K

L

5 (vertical-right)

M A B C D E F G H

I

J

K

L

2 (DC)

M A B C D E F G H

I

J

K

L


M A B C D E F G H

I

J

K

L


Mean(AsimD IsimL)












H

V

H

V

H

V

H

V

3 (plane)


2 (DC)


Mean (H + V)


Search window

Best matching

Range block

Domain blocks

FmF998400

mminus1





119889119909 (119909 119910 119911) =119865119861

119911 (6)




PSN

R (d

B)

366

368

370

372

374

376

S0 S1 S2 S3


Tim

e (s)

0

500

1000

1500

2000

2500

3000

3500

S0 S1 S2 S3



Time

View

F00 F01 F02 F03 F04

F10 F11 F12 F13 F14

F20 F21 F22 F23 F24

View 0

View 1

View 2

T0 T1 T2 T3 T4


mv

View

Time

Adjacent view

mv

mv

CFMC


Nminus 1

N













Start

Anchor view

Yes



minimum RMS



Yes

Yes

The last frameNo

End




and RMS2

Yes

No No

No




To next frame









Frame number

PSN

R (d

B)

355

360

365

370

375

380

385

390

JMVC85Proposed

0 20 40 60 80 100 120 140 160 180 200 220 240 260

(a) Left view

PSN

R (d

B)

JMVC85Proposed

360

365

370

375

380

385

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(b) Center view

JMVC85Proposed

365

370

375

380

385

390

PSN

R (d

B)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(c) Right view




BallroomLeft 3722 3744 46275 20924 22976 632

Center 3725 3752 35635 47503 36595 2127Right 3755 3745 41230 25627 23384 632

RaceLeft 3735 3798 91580 22545 21055 661

Center 3763 3812 57711 85537 35543 2226Right 3746 3799 89584 31300 21438 661

FlamencoLeft 3954 4006 59219 21883 20665 606

Center 4031 4025 39659 51859 34552 2048Right 3934 4007 63750 27508 21949 610

Average 3818 3854 58294 37187 26462 1134


Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view







6 Conclusion



Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










M A B C D E F G H

I

J

K

L

0 (vertical)

M A B C D E F G H

I

J

K

L

1 (horizontal)

M A B C D E F G H

I

J

K

L

8 (horizontal-up)

M A B C D E F G H

I

J

K

L

7 (vertical-left)

M A B C D E F G H

I

J

K

L

0 (horizontal-down)

M A B C D E F G H

I

J

K

L

5 (vertical-right)

M A B C D E F G H

I

J

K

L

2 (DC)

M A B C D E F G H

I

J

K

L


M A B C D E F G H

I

J

K

L


Mean(AsimD IsimL)












H

V

H

V

H

V

H

V

3 (plane)


2 (DC)


Mean (H + V)


Search window

Best matching

Range block

Domain blocks

FmF998400

mminus1





119889119909 (119909 119910 119911) =119865119861

119911 (6)




PSN

R (d

B)

366

368

370

372

374

376

S0 S1 S2 S3


Tim

e (s)

0

500

1000

1500

2000

2500

3000

3500

S0 S1 S2 S3



Time

View

F00 F01 F02 F03 F04

F10 F11 F12 F13 F14

F20 F21 F22 F23 F24

View 0

View 1

View 2

T0 T1 T2 T3 T4


mv

View

Time

Adjacent view

mv

mv

CFMC


Nminus 1

N













Start

Anchor view

Yes



minimum RMS



Yes

Yes

The last frameNo

End




and RMS2

Yes

No No

No




To next frame









Frame number

PSN

R (d

B)

355

360

365

370

375

380

385

390

JMVC85Proposed

0 20 40 60 80 100 120 140 160 180 200 220 240 260

(a) Left view

PSN

R (d

B)

JMVC85Proposed

360

365

370

375

380

385

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(b) Center view

JMVC85Proposed

365

370

375

380

385

390

PSN

R (d

B)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(c) Right view




BallroomLeft 3722 3744 46275 20924 22976 632

Center 3725 3752 35635 47503 36595 2127Right 3755 3745 41230 25627 23384 632

RaceLeft 3735 3798 91580 22545 21055 661

Center 3763 3812 57711 85537 35543 2226Right 3746 3799 89584 31300 21438 661

FlamencoLeft 3954 4006 59219 21883 20665 606

Center 4031 4025 39659 51859 34552 2048Right 3934 4007 63750 27508 21949 610

Average 3818 3854 58294 37187 26462 1134


Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view







6 Conclusion



Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










H

V

H

V

H

V

H

V

3 (plane)


2 (DC)


Mean (H + V)


Search window

Best matching

Range block

Domain blocks

FmF998400

mminus1





119889119909 (119909 119910 119911) =119865119861

119911 (6)




PSN

R (d

B)

366

368

370

372

374

376

S0 S1 S2 S3


Tim

e (s)

0

500

1000

1500

2000

2500

3000

3500

S0 S1 S2 S3



Time

View

F00 F01 F02 F03 F04

F10 F11 F12 F13 F14

F20 F21 F22 F23 F24

View 0

View 1

View 2

T0 T1 T2 T3 T4


mv

View

Time

Adjacent view

mv

mv

CFMC


Nminus 1

N













Start

Anchor view

Yes



minimum RMS



Yes

Yes

The last frameNo

End




and RMS2

Yes

No No

No




To next frame









Frame number

PSN

R (d

B)

355

360

365

370

375

380

385

390

JMVC85Proposed

0 20 40 60 80 100 120 140 160 180 200 220 240 260

(a) Left view

PSN

R (d

B)

JMVC85Proposed

360

365

370

375

380

385

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(b) Center view

JMVC85Proposed

365

370

375

380

385

390

PSN

R (d

B)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(c) Right view




BallroomLeft 3722 3744 46275 20924 22976 632

Center 3725 3752 35635 47503 36595 2127Right 3755 3745 41230 25627 23384 632

RaceLeft 3735 3798 91580 22545 21055 661

Center 3763 3812 57711 85537 35543 2226Right 3746 3799 89584 31300 21438 661

FlamencoLeft 3954 4006 59219 21883 20665 606

Center 4031 4025 39659 51859 34552 2048Right 3934 4007 63750 27508 21949 610

Average 3818 3854 58294 37187 26462 1134


Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view







6 Conclusion



Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










PSN

R (d

B)

366

368

370

372

374

376

S0 S1 S2 S3


Tim

e (s)

0

500

1000

1500

2000

2500

3000

3500

S0 S1 S2 S3



Time

View

F00 F01 F02 F03 F04

F10 F11 F12 F13 F14

F20 F21 F22 F23 F24

View 0

View 1

View 2

T0 T1 T2 T3 T4


mv

View

Time

Adjacent view

mv

mv

CFMC


Nminus 1

N













Start

Anchor view

Yes



minimum RMS



Yes

Yes

The last frameNo

End




and RMS2

Yes

No No

No




To next frame









Frame number

PSN

R (d

B)

355

360

365

370

375

380

385

390

JMVC85Proposed

0 20 40 60 80 100 120 140 160 180 200 220 240 260

(a) Left view

PSN

R (d

B)

JMVC85Proposed

360

365

370

375

380

385

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(b) Center view

JMVC85Proposed

365

370

375

380

385

390

PSN

R (d

B)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(c) Right view




BallroomLeft 3722 3744 46275 20924 22976 632

Center 3725 3752 35635 47503 36595 2127Right 3755 3745 41230 25627 23384 632

RaceLeft 3735 3798 91580 22545 21055 661

Center 3763 3812 57711 85537 35543 2226Right 3746 3799 89584 31300 21438 661

FlamencoLeft 3954 4006 59219 21883 20665 606

Center 4031 4025 39659 51859 34552 2048Right 3934 4007 63750 27508 21949 610

Average 3818 3854 58294 37187 26462 1134


Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view







6 Conclusion



Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Start

Anchor view

Yes



minimum RMS



Yes

Yes

The last frameNo

End




and RMS2

Yes

No No

No




To next frame









Frame number

PSN

R (d

B)

355

360

365

370

375

380

385

390

JMVC85Proposed

0 20 40 60 80 100 120 140 160 180 200 220 240 260

(a) Left view

PSN

R (d

B)

JMVC85Proposed

360

365

370

375

380

385

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(b) Center view

JMVC85Proposed

365

370

375

380

385

390

PSN

R (d

B)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(c) Right view




BallroomLeft 3722 3744 46275 20924 22976 632

Center 3725 3752 35635 47503 36595 2127Right 3755 3745 41230 25627 23384 632

RaceLeft 3735 3798 91580 22545 21055 661

Center 3763 3812 57711 85537 35543 2226Right 3746 3799 89584 31300 21438 661

FlamencoLeft 3954 4006 59219 21883 20665 606

Center 4031 4025 39659 51859 34552 2048Right 3934 4007 63750 27508 21949 610

Average 3818 3854 58294 37187 26462 1134


Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view







6 Conclusion



Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Frame number

PSN

R (d

B)

355

360

365

370

375

380

385

390

JMVC85Proposed

0 20 40 60 80 100 120 140 160 180 200 220 240 260

(a) Left view

PSN

R (d

B)

JMVC85Proposed

360

365

370

375

380

385

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(b) Center view

JMVC85Proposed

365

370

375

380

385

390

PSN

R (d

B)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

(c) Right view




BallroomLeft 3722 3744 46275 20924 22976 632

Center 3725 3752 35635 47503 36595 2127Right 3755 3745 41230 25627 23384 632

RaceLeft 3735 3798 91580 22545 21055 661

Center 3763 3812 57711 85537 35543 2226Right 3746 3799 89584 31300 21438 661

FlamencoLeft 3954 4006 59219 21883 20665 606

Center 4031 4025 39659 51859 34552 2048Right 3934 4007 63750 27508 21949 610

Average 3818 3854 58294 37187 26462 1134


Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view







6 Conclusion



Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Bit n

umbe

r (kb

its)

0

50

100

150

200

250

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

50

100

150

200

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

Bit n

umbe

r (kb

its)

JMVC85Proposed

(c) Right view







6 Conclusion



Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Tim

e (s)

0

10

20

30

40

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(a) Left view

Tim

e (s)

0

10

20

30

40

50

60

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(b) Center view

0

10

20

30

40

Tim

e (s)

Frame number0 20 40 60 80 100 120 140 160 180 200 220 240 260

JMVC85Proposed

(c) Right view














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














PSN

R (d

B)

32

34

36

38

40

42







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article A Novel High Efficiency Fractal Multiview ...

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