Underwater Acoustic Image Encoding Based on Interest ...downloads.hindawi.com/journals/complexity/2018/5647519.pdf · Underwater Acoustic Image Encoding Based on Interest Region and

Research ArticleUnderwater Acoustic Image Encoding Based on Interest Regionand Correlation Coefficient

Liu Lixin 1 Guo Feng12 and Wu Jinqiu 3

1 Institute of Deep-Sea Science and Engineering Chinese Academy of Sciences Hainan 572000 China2University of Chinese Academy of Sciences Beijing 100049 China3Beijing Institute of Control And Electronic Technology Beijing 100038 China

Correspondence should be addressed to Liu Lixin liulxidsseaccn

Received 19 July 2018 Revised 17 September 2018 Accepted 8 October 2018 Published 21 October 2018

Academic Editor Danilo Comminiello

Copyright copy 2018 Liu Lixin et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

It is difficult for the conventional image compression method to achieve good compression effect in the underwater acousticimage (UWAI) because the UWAI has large amount of noise and low correlation between pixel points In this paper fractalcoding is introduced into UWAI compression and a fractal coding algorithm based on interest region is proposed according tothe importance of different regions in the image The application problems of traditional quadtree segmentation in UWAIs wassolved by the range block segmentation method in the coding process which segmented the interest region into small size andthe noninterest region into large size and balanced the compression ratio and the decoded image quality This paper applies theclassification reduction codebook and correlation coefficient matching strategy to narrow the search range of the range blockin order to solve the problem of the long encoding time and the calculation amount of encoding process is greatly reduced Theexperimental results show that the proposed algorithm improves the compression ratio and encoding speed while ensuring theimage quality of important regions in the UWAI

1 Introduction

The UWAI refers to an image generated by imaging sonaraccording to the characteristics of the underwater targetecho signal by means of acoustic wave detection Due to thelimitation of the underwater acoustic (UWA) channel andthe storage capacity of the device [1 2] the UWAI mustbe compressed to meet the actual application requirementsCompared to ordinary optical images the UWAI is affectedby uncertain factors such as underwater environment vari-ous types of noise ocean reverberation ocean internal het-erogeneity and seabed terrain irregularity which is seriouslypolluted by kinds of noises Generally the signal to noise ratiois low and there are many outliers that differ greatly from thegray values of surrounding pixels The image target area hasless gray level however the background area has rich graylevel The whole image is rough and the complex and fineedges are missing [3 4]

Due to the particularity of UWAIs many methods usedfor optical image compression cannot always achieve good

results The traditional image compression method is basedon removing the correlation redundancy in the image Dueto the existence of noise the correlation between the pixelsof the UWAI is very poor At the same time limited bythe entropy the compression ratio of traditional imagecompression method is generally not high in the UWAIcompression Therefore this paper applies the fractal codingbased on the fractal theory and iterative function system toUWAI compression to improve the image compression per-formance Fractal coding algorithm breaks the limitations ofthe information theory which is based on the widely existingself-similarity in images The basic idea is to achieve highcompression ratio by removing the structural redundancythrough a set of compression transformations Since Barnsleyfirst applied fractal theory to image compression in 1988[5] fractal coding has attracted wide attention by its largecompression potential fast decoding speed and resolution ofdecoded image resolution

In 1992 inspirited by Barnsleyrsquos research Jcaquin pro-posed fractal coding based on the local iterative function

HindawiComplexityVolume 2018 Article ID 5647519 13 pageshttpsdoiorg10115520185647519

2 Complexity

system [6] which made the fractal coding into practice andpromoted the rapid development of fractal coding researchHowever there are still some problems in the fractal coding(1) The coding process is complicated and the amount ofcalculation is large which costs long time for the codingprocedure (2)The compression ratio and the decoded imagequality cannot be balanced In order to solve the long fractalcoding time scholars have proposed several methods suchas classification matching [7ndash10] optimized search rangeand nonsearch coding [11ndash15] scholars propose a variety ofdifferent range block partitioning schemes such as quadtreepartitioning [16ndash18] HV segmentation [19] triangulationand irregular segmentation [20 21] to balance the problemof compression ratio and decoded image quality The latterthree methods require more information to describe theposition and shape of each subblock compared with quadtreepartitioning and the search matching processes are morecomplicated In image processing the K-Means algorithmwhich belongs to the machine learning algorithm is a clus-tering algorithm based on distance similarity [22 23] Bycomparing the similarity between samples the samples ofthe form are divided into the same category However theusage of AI algorithms requires a large number of data setssuch as different signal-to-noise ratios different texturesdifferent types different sources of UWAIs and then thealgorithm can find the most suitable codebook based onvarious feature information of the images which means alarge number of underwater acoustic experiments is requiredand which is unrealizable currently because the acquisitionof UWAIs is difficult Therefore this paper utilizes the widelyused quadtree partitioning algorithm in the segmentationof UWAIs However because of the widespread noise inUWAI most of the segmented images have little or no largesize image blocks which causes difficult in the applicationof the quadtree partitioning algorithm Focusing on this wepropose the improved quadtree partitioning algorithm whichis based on the region of interest In addition by classifyingthe range blocks the search range of the range blocks isoptimized which can significantly improve the encodingspeed At the same time the codebook capacity is reducedand the correlation coefficient is matched which can not onlybalance the compression ratio and the decoded image qualitybut also gain a higher encoding speed

The structure of this paper is as follows the secondsection briefly introduces the principle of basic fractal codingthe third section focuses on the fractal coding algorithmbased on region of interest and the correlation coefficientfractal coding algorithm is proposed the simulation andexperiment results are given in the fourth section the fifthsection comes the conclusion

2 Basic Fractal Coding

The basis fractal coding (BFC) is to find a set of compressiontransformations whose fixed points are similar with theoriginal imageThese sets of compression transformation arecalled the Iterated Function System (IFS) Jacquin proposedthe Partial Iterative Function System (PIFS) and the basic

A1 A2 B1 B2

A3 A4 B3 B4

C1 C2 D1 D2

C3 C4 D3 D4

A B

C D

Figure 1 Four neighborhood pixel average

fractal coding inspired by IFS The implementation of BFCalgorithm is as follows

When encoding the image is first divided into a RangeBlock (R block) and a Domain Block (D Block)The R blocksdo not overlap with each other and the entire R blocks canform the original image The D blocks can be generated bysliding a certain size window in the original image accordingto a preset step size which are allowed to have overlappingareas To ensure the convergence of PIFS the block size of Dshould be larger than that of R (usually the D block size istwice larger than the R block)

Supposing the size of the original image is M times M theblock size of R should be B times B and the block size of D blockwill be 2B times 2B The sliding step is represents by 120575 and thenthe whole image is divided into11987221198612 R blocks and ((119872 minus2119861)120575 + 1)2 D blocks

In order to match the D and R blocks the D block needsto do the spatial contraction and its size is scaled from 2Btimes 2B to B times B Usually the four-neighbor pixel averagingmethod is used for spatial contraction (as shown in Figure 1)and S represents the spatial contraction operation D1015840 is thecontracted D block and then the value of each pixel in D1015840 canbe written as

1198891015840119896119897 = 1198892119896minus12119897minus1 + 1198892119896minus12119897 + 11988921198962119897minus1 + 119889211989621198974 (1)

where119889119896119897 and1198891015840119896119897 are the gray values of119863119895 and1198631015840119895 at the point(119896 119897) respectivelyFor each R blocks it is necessary to find the closest

block in the contracted D blocks to obtain the fractal codeAccording to PIFS between the R block and the D blockthere is an affine similarity which means that the R blockis similar to the D block after the equidistant transformation(rotation flipping etc) Jacquin simplified and summarizedthe isometric transformations which is shown in Table 1

In the table 119863119894119895 represents the pixel value of point (119894 119895)and 119905119896 119896 = 1 2 sdot sdot sdot 8 represents the isometric transforma-tion

After the entire D block is contracted and isometrictransformed the codebook Ω (also called the definitiondomain pool) required for block matching is formed Forconvenience the block in the codebook Ω is represented byD

After the above process for any 119877119894 the D block in thecodebook Ω is selected for match searching that is to finda best matching block119863119898(119894) so that119863119898(119894) is the closest one to119877119894 after proper affine transformation which is

119877119894 asymp 119904 sdot 119905119896 (119863119898(119894)) + 119900 (2)

Complexity 3

Table 1 8 kinds of isometric transformations

Index Transformation name Transformed pixel1 Identity transformation (1199051119863)119894119895 = 1198631198941198952 Axisymmetric reflection on the vertical axis (1199052119863)119894119895 = 119863119894119861minus1minus1198953 Axisymmetric reflections on the horizontal (1199053119863)119894119895 = 119863119861minus1minus1198941198954 Symmetric reflection on the main diagonal (1199054119863)119894119895 = 1198631198951198945 Symmetric reflection on the sub-diagonal (1199055119863)119894119895 = 119863119861minus1minus119895119861minus1minus1198946 90∘ counterclockwise about the center (1199056119863)119894119895 = 119863119895119861minus1minus1198947 180∘ counterclockwise about the center (1199057119863)119894119895 = 119863119861minus1minus119894119861minus1minus1198958 270∘ counterclockwise about the center (1199058119863)119894119895 = 119863119861minus1minus119895119894

The original image

Domain block

Range block

Spatial contraction

Isometric transforma

tionCodebook

Fractal code

Match searching

Figure 2The procedure of the BFC

The matching error between D block and R block is119864(119877119863) which is calculated by the following [24 25]

119864 (119877119863) = 10038171003817100381710038171003817119877 minus 119877100381710038171003817100381710038172 minus 1199042 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172119904 = ⟨119877 minus 119877119863 minus 119863⟩10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172119900 = 119877 minus 119904 sdot 119863

(3)

When searching in different D blocks the one withthe smallest matching error 119864(119877119894 119863) is selected as the bestmatching block The procedure can be expressed as

119864 (119877119894 119863119898(119894)) = min119863isinΩ

119864 (119877119894 119863)= min119863isinΩ

1003817100381710038171003817119877119894 minus (119904 sdot 119863 + 119900)10038171003817100381710038172 (4)

in which ⟨sdot sdot⟩ represents the inner productR andD represent119877i and119863119895 respectively 119877 and119863 represent the constant blockformed by themean value ofR andD sdot represents the vector2 norm Such tetrad 119898(119894) 119896 119904 119900 is the fractal code of blockR

The procedure of the BFC is shown in Figure 2The fractal decoding process is relatively simple By

compression transformation the decoded image can beapplied to any image of the same size as the original image119908 corresponds to the fractal code after 5sim8 iterations (8

iterations are selected in this paper)The R block of the image119868(119896) = 119908119868(119896minus1) generated by the kth iteration is determined by

119877119894(119896) = 119904 sdot 119905119896 (119878 (119863(119896minus1)119898(119894) )) + 119900119863(0)119898(119894) = 119863119898(119894) (5)

3 The Proposed Algorithm

31 Quadtree Partitioning Based on Region of Interest Ascan be seen from Section 2 the fractal coding methodonly encodes each R block after image segmentation notthe entire image Therefore the block size of R directlyaffects the compression ratio and the image quality Thelarger the block size of R is the less the block number ofR will be Accordingly the less ldquoentryrdquo in fractal code thehigher compression ratio which causes the increasing of thematching error On the contrary the smaller the block sizeof R is the better the decoded image quality will be but thecompression ratio becomes lower In order to balance thecompression ratio and the decoded image quality this paperimproved the fractal coding based on quadtree partitioning

Quadtree partitioning is similar to the tree structure indata structureThe original image can be regarded as the rootof the tree and the four fork points (corresponding to thefour quadrant regions of the image respectively) are separatedfrom the root node Each of the fork points can select whetherto further divide the four new subnodes according to certainrules (corresponding to four sub-regions of the image areacorresponding to the intersection respectively) The newsubnode continues to split according to this rule and whenthe segmented node reaches the maximum segmentation

4 Complexity

(a) (b)

Figure 3 Ordinary gray image quadtree segmentation (a) original image Lena and (b) effect of quadtree segmentation

(a) (b)

Figure 4 UWAI quadtree segmentation (a) original image ship and (b) effect of quadtree segmentation

depth the segmentation will stop Then the entire image isdivided into several subblocks with different sizes

In practice the gray-scale uniform criterion is generallyused for the quadtree partitioning When the block size ofone image is larger than the minimum segment size whichmeans the difference between the maximum gray value andtheminimumgray value is greater than a preset threshold theblock is further divided Otherwise the block does not needto be split

For different size image blocks generated after segmenta-tion the fractal code can be obtained by match searching inthe corresponding codebooks using the basic fractal codingmethod Therefore the quality of the decoded image can beincreased by dividing the portion of the image with a smallerdifference in the pixel value by a larger size thereby increasing

the compression ratio and dividing the portion with a largerdifference in the pixel value by a smaller size thereby ensuringthe decoding image quality

Figures 3 and 4 show the effect after the quadtree segmen-tation of the ordinary grayscale image Lena and the UWAIShip (the maximum segmentation size is 16 times 16 and theminimum segmentation size is 4 times 4) respectively As can beseen from Figure 3 the Lena image has a good segmentationeffect all blocks of 16times16 8times8 and 4times4 account for a certainpercentage Due to the noise in UWAI the effect of quadtreepartitioning is not obvious All 16 times 16 blocks in the imageare not smaller than the gray threshold and therefore furthersubdivision is needed For the 8 times 8 blocks subdivid only afew blocks satisfy the requirement with no need for furthersegmentationmost of blocks are divided into 4times4 blocks It is

Complexity 5

(a) (b) (c)

(d) (e) (f)

Figure 5 Denoising effect of different methods (a) original image (b) average filtering (c) median filtering (d) Butterworth low-passfiltering (e) Gaussian low-pass filtering (f) Wiener filtering

conceivable that when image noise pollution is more seriousthe effect of quadtree segmentation will be exactly the sameas 4lowast4 segmentation Therefore new quadtree segmentationmethods that suitable for the UWAIs are needed

Considering that the main information of the UWAIis concentrated in the area where the target is located thenoisy background area does not need much attention Forthis reason different size segmentation is used for differentimportant areas in the UWAIs in this paper The importantarea in the image (hereinafter referred to as the regionof interest) is divided by a small size and a large sizesegmentation is adopted for the noninterest region Thespecific segmentation process is as follows

(1) Image Denoising UWAI usually has noise interference sothe image needs to be denoised first to reduce the impactof these interferences on the region of interest in the imageSince this step is to prepare for the extraction of the regionof interest in the next step in order to reduce the nonedgeline interference the image is smoothed while maintainingthe contour of the region of interest while denoising In thissection the average filtering median filtering Butterworthlow-pass filtering Gaussian low-pass filtering Wiener filter-ing and othermethods are used for denoising Figure 5 showsthe denoising effect of theUWAI Ship by differentmethods It

can be seen that the fivemethods produce different degrees ofsmoothing effects on the imageThe average filtering medianfiltering andButterworth low-pass filtering blur the boundarybetween the target and the background while denoisingwhich is not conducive to the extraction of the region ofinterest The Gaussian low-pass filtering does not have theproblem of boundary blurring but the smoothing effect isnot good while wiener filtering has good denoising effect andmaintains the contour of the target area which is the reasonfor selecting it in this paper

(2) Extraction of Interest Region In this section the interestregion in the UWAI is extracted by means of edge detectionand morphological operations Both the target area and theshadow area formed by UWAI contain important informa-tion The principle of extracting the area of interest is toinclude some background areas which will result in thefinal area of interest being larger than the range extractedby traditional target segmentation The specific steps forextracting the interest region are as follows (for the sakeof convenience the target and the shadow are collectivelyreferred to as the target)

A Use the canny operator for edge extraction on thedenoised image

6 Complexity

(a) (b)

Figure 6 Extract results of interest region (a) ship and (b) plane

(a) (b)

Figure 7 Segmentation effect of UWAI (a) ship and (b) plane

B Morphological expansion is used to connect discon-tinuous target edge lines into closed lines

CThe nontarget contour lines caused by interference areremoved by morphological operation

D Fill the target contour areaE Morphological expansion is applied to expand the

target area and the expanded area is the required interestregion for coding

Figure 6 shows the results of the extraction of the regionsof interest for the two UWAIs

(3) Image Segmentation On the basis of Section 2 small-size segmentation is performed for the region of interestand large-scale segmentation is adopted for the non-interest

region Figure 7 shows the segmentation effect of UWAIs bythe small size 4 times 4 and the large size 8 times 8

32 Reducing the Search Area of R Blocks After the UWAIis segmented R blocks of different sizes are generated Foreach R block it is necessary to search for the best matchingblock in its corresponding codebook to obtain a fractal codeAccording to the basic fractal coding proposed by Jacquinthe R block searches in all codebooks which will cost a longtime on encoding Therefore the search area of R block isreasonably reduced and the matching process between Rblock and D block is optimized to reduce the calculationamount of encoding process and improve the encodingspeed

Complexity 7

From formula (3)

119864 (119877119863) = 1198612 (var (119877) minus 1199042 sdot var (119863))119904 = ⟨119877 minus 119877119863 minus 119863⟩1198612 sdot var (119863)119900 = 119877 minus 119904 sdot 119863

(6)

in which 1198612 is the total number of R block pixels 119883 is themean value of 119883 ⟨sdot sdot⟩ represents the vector inner productand var(119883) is the variance of 119883

As can be seen from (6) the following holds for any 119863 isinΩ119864 (119877119863) le 1198612 sdot var (119877) (7)

When the variance of the R block is small the matchingerror is accordingly small Therefore the R block is dividedinto two categories according to the variance the R blockwhose variance is less than the preset threshold 1205782 is regardedas a smooth block otherwise it is regarded as a nonsmoothblock For a smooth block the pixel value of each pointis replaced by its pixel mean value so there is no need tosearch again For nonsmooth blocks in the next section thefollowing methods are adopted

Equation (5) also shows that the D block with smallervariance is unlikely to be the best matching block of the Rblock with larger variance (if these two are the best matchingpairs it is likely that 119904 is greater than 1 and then the PIFSwill no longer converges) Therefore D blocks with smallervariance can be eliminated from the codebook in advanceThe reduction codebook is defined as

Ω120575 = 119863 isin Ω var (119863) ge 1205752 (8)

in which 120575 is the preset threshold For nonsmooth R blockswhose variance is greater than the threshold 1205782 it is onlynecessary to find the best matching D block in the reducedcodebook

33 Match Searching Based on the Correlation CoefficientWhen searching for the best matching block of the R blockit is necessary to calculate the parameters according to (5)and then calculate the matching error 119864(119877119863) between the Rblock and each D blocks Although Section 32 has narroweddown the searching area the computation of this process isstill large If the D blocks that may not be the best matchingblock of the R block can be removed in advance a largenumber of complicated calculations can be avoided and theencoding speed can be improved In this paper according tothe correlation coefficient between R block and D block Dblocks with little correlation is excluded thus the encodingprocess can be speed up

For R block and D block the correlation coefficient isrepresented by

119903 (119877119863) = ⟨119877 minus 119877119863 minus 119863⟩10038171003817100381710038171003817119877 minus 11987710038171003817100381710038171003817 sdot 10038171003817100381710038171003817119863 minus 11986310038171003817100381710038171003817 (9)

in which 119883 represents the mean of 119883 ⟨sdot sdot⟩ represents theproduct of the vector and sdot represents the norm of vector2

This is available in formula (3)

119864 (119877119863) = 10038171003817100381710038171003817119877 minus 119877100381710038171003817100381710038172 minus 1199042 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172= 10038171003817100381710038171003817119877 minus 119877100381710038171003817100381710038172minus (⟨119877 minus 119877119863 minus 119863⟩10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172 )

2 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172

= 10038171003817100381710038171003817119877 minus 119877100381710038171003817100381710038172(1 minus10038161003816100381610038161003816100381610038161003816100381610038161003816⟨119877 minus 119877119863 minus 119863⟩10038171003817100381710038171003817119877 minus 11987710038171003817100381710038171003817 sdot 10038171003817100381710038171003817119863 minus 11986310038171003817100381710038171003817

100381610038161003816100381610038161003816100381610038161003816100381610038162)

= 1198612var (119877) (1 minus |119903 (119877119863)|2)

(10)

Equation (10) shows that with the increase of absolutevalue of the correlation coefficient between the R block andthe D block the possibility of the two blocks becomingmatching pairs increases For the R block of the variancevar(119877) gt 1205782 (in which 120578 is a preset threshold) it is knownfrom (10)

119864 (119877119863) gt 11986121205782 (1 minus |119903 (119877119863)|2) (11)

This means that if the R block matches the D block(119864(119877119863) is small) |119903(119877119863)| is larger which means thatenough large |119903(119877 119863)| is the necessary and sufficient condi-tion for the R block matching for the D block

According to the above analysis in the encoding proce-dure for each R blocks the correlation coefficient and thematching error of the first D block in the reduced codebookare calculated respectively as 1198620 and 1198640 And then thecorrelation coefficient 119862 between the other D blocks in thereduced codebook and this R block are calculated If 119862 gt 1198620then the matching error 119864(119877119863) between block D and blockR is further calculated otherwise the D block is ignored andturned to the next D block This can prevent the calculationof the parameter 119904 and the matching error for all D blockswhich greatly reduces the computation complexity of theentire encoding process and saves the encoding time

34 The Encoding Procedure of the Proposed Algorithm Fora UWAI to be compressed firstly extract the interest regionThen divides the interest region and the non-interest regioninto different sizes and generates the codebooks with dif-ferent size simultaneously A reduced codebook is generatedaccording to the threshold 1205752 According to the methodproposed in Section 33 of the reduction codebook the fractalcode is obtained by searching and matching the divided Rblocks of different sizes The detailed encoding process is asfollows

(1) Preset the threshold 120578 of R block codebook threshold120575 etc(2) According to the method proposed in Section 31 the

UWAI is segmented by quadtree partitioning based on regionof interest

8 Complexity

(3)According to theR block partition size two codebooksof different sizes are respectively produced and the reducedcodebook is constructed according to the codebook thresh-old 120575

(4) For smooth blocks (R blocks with variance less than)take the constant block as approximated and the fractal codeis directly output without searching

(5) For nonsmooth blocks (R blocks with variance greaterthan or equal to 1205782) perform match searching in the reducedcodebook The search strategy is as follows select the first Dblock in the reduced codebook and calculate its correlationcoefficient 1198640 and matching error 1198620 with R block Then thecorrelation coefficient 119862 of other D blocks in the reducedcodebook with the selected R block is sequentially calculatedIf 119862 gt 1198620 the matching error 119864(119877119863) of the two blocks isfurther calculated If 119864(119877119863) lt 1198640 let 1198620 = 119862 otherwiseignore this D block and move to the next After traversingall the D blocks in the reduced codebook select the D blockcorresponding to 1198620 as the best matching block and thefractal code is output

(6) Complete the encoding of all R blocks to generate anencoded file

The specific steps of the encoding are shown in Figure 8

35The Decoding Process of the Proposed Algorithm (1) Readinformation such as the information of the quadtree parti-tion the position of the best matching block of the R blockin different size codebooks the equidistant transformationmode the contrast factor and the grayscale offset

(2) Define three images Y1 Y2 andXhaving the same sizewith the original image in which X is used to store the imagegenerated by the iterative process and Y1 and Y2 are used togenerate two codebooks with different sizes

(3) Initialize Y1 and Y2(4) For each R block in X according to its fractal code119898(119894) 119896 119904119894 119900119894 locate its corresponding best matching block119863119898(119894) in the corresponding codebook Y and restore the R

block according to the following formula

119877119894 = 119904119894 sdot (119905119896 (119878 (119863119898(119894)))) + 119900119894 (12)

in which 119878 is a four-neighbor averaging operation Afterall the R blocks are obtained by the above affine transforma-tion the iterative image is formed by tiling the above R blocks

(5) If the number of iterations reaches 8 go to step (6)otherwise copy X to Y1 Y2 and go to step (4)

(6) Output image X

4 Experimental Results and Analysis

In order to verify the effectiveness of the algorithm twoUWAIs ship and plane were used for the simulation exper-iment The test image is shown in Figure 9 The PC con-figuration used in the experiment is as follows CPU IntelCore i5-3470 Memory 8G Operating System Windows10Simulation Software MATLAB2015B The parameters thattest the performance of the algorithm are as follows codingtime PSNR and compression ratio PSNR is the objective

evaluation standard for quality of the decoded image whichis obtained by

119875119878119873119877 = 10 log 2552 sdot 1198722sum119872x=1sum119872119910=1 [119891 (119909 119910) minus 1198911015840 (119909 119910)]2 (13)

In which 119891(119909 119910) is the pixel value of the original image withsize119872times119872 at the point (119909 119910) and 1198911015840(119909 119910) is the pixel valueof the decoded image with size119872times119873 at the point (119909 119910)(1) The Influence of Parameters on Encoding PerformanceThe two parameters 120578 and 120575 in the algorithm directly affectthe encoding time and the quality of the decoded imageThe optimal values for the two parameters are difficultto determine theoretically and therefore they can only beselected experimentally In order to observe the influence ofparameters on the decoded image clearly the Lena image isselected as test image When analyzing the influence of theparameter 120578 on the coding performance it is set as 120575 = 0to eliminate the interference of other factors Similarly whenanalyzing the parameter 120575 accordingly set 120578 = 0

A Experimental study of the parameter 120578 The larger 120578is the more number of R blocks are considered as smoothblocks Since the smoothing block does not need to performmatch searching the encoding speed is faster However sincemore R blocks are smoothed the quality of decoded imagesis also degraded (such as Figure 10) It can be seen fromFigure 10 that when 120578 gt 4 blocking effect occurs in someparts of the decoded image and the larger 120578 is the moreobvious the blocking effect will be When 120578 le 4 the blockingeffect is almost negligible Figure 11 is the comparison ofdecode image with different parameters Therefore the bestvalue of this parameter is 4

B Experimental study of the parameter 120575 The value of 120575determines the size of the reduced codebook As can be seenfrom Figure 12 the larger 120575 is the shorter the encoding timewill be When 120575 increases from 0 to 20 the PSNR decreasesslowly and when 120575 increases from 20 to 45 the PSNRdrops rapidly This means when the threshold 120575 is small theencoding time can be significantly reduced at the cost of thedecoded image qualityrsquos slightly lower While the threshold120575 is large the best matching block is likely to be excludedfrom the codebook resulting in degrade in the quality of thedecoded image quality Considering the encoding time andthe decoded image quality this paper chooses 20 as the bestvalue for 120575(2) Comparison of the Proposed Algorithm with Other Algo-rithms The maximum segment size of the algorithm in thispaper is 8times 8 and theminimum split size is 4times 4TheRblocksize of other algorithms used for comparison is also chosenas the above two sizes Table 2 lists the experimental results ofthe proposed algorithm and the basic fractal algorithm (BFC)[6] the variance based fast search algorithm (VBFC) [26] andthe particle swarm optimization algorithm (PSO) [27]

It can be seen from Table 2 that as the partition sizeincreases from 4 times 4 to 8 times 8 the coding time and the PSNRof the BFC algorithm the VBFC algorithm and the PSOalgorithm are gradually reduced and the compression ratio

Complexity 9

Image to be encoded

Two different size codebooks

R block is approximated by a constant

block

Calculate the correlation coefficient C0 and the matchingerror E0 of the first D block and

the R block in the reduced codebook

Calculate the correlation coefficient C of other D blocks

and R blocks in the reduced codebook

Different sizes of R blocks

Generate reduced codebook

according to codebook threshold

Select the corresponding allowable codebook according to the R block

sizeSelect any D block in the codebook as the best matching block

Select one Rblock

block R

Yes

No

Region of interest

Non-interest region

Large size segmentation

Small size segmentation

Output the fractal code

Select the D block corresponding to C0 as the best matching block

Calculate the matching error

between R block and D block E

Over

No

Traversing all D blocks in the reduced codebook

Traverse all R blocks

Yes

Yes

No

No

Yes

No

Yes

Calculate the variance ６２ of

６２lt 2

gt0

lt0

Update 0 0 forC E

Figure 8 Specific steps of encoding based on the interest region algorithm

10 Complexity

Table 2 Experimental results comparison of different algorithms

Algorithm

ImageShip Plane

Encoding Time (s) PSNR Compression ratio Encoding Time (s) PSNR Compression ratio(dB) (dB)

BFC (4 times 4) 3040 15970 512 2919 16012 512BFC (8 times 8) 2658 4041 2048 2502 4054 2048VBFC (4 times 4) 2980 1771 512 2841 1731 512VBFC (8 times 8) 2638 505 2048 2475 512 2048PSO (4 times 4) 2923 1178 512 2804 1138 512PSO (8 times 8) 2569 346 2048 2425 357 2048The proposed algorithm 2877 302 1387 2749 315 1325

(a) (b)

Figure 9 UWAIs (a) ship and (b) plane

33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R

Figure 10 Conversion curve of encoding performance with 120578is gradually increased In the comparison of the encodingtime the proposed algorithm of is only 153 of the 4 times 4BFC algorithm and 113 of the 8 times 8 BFC algorithm whichis mainly own to the optimization of the encoding process

According to the strategy of Section 32 by reducing thecodebook capacity searching for matching based on correla-tion coefficient setting the ending condition ofmatching etcThe calculation amount of the encoding process is effectivelyreduced and the encoding speed is greatly improved

Since most of the images are noninterest regions thispaper adopts a large size 8 times 8 segmentation for these partsAnd for interest region the small size 4 times 4 segmentation isadopted Therefore the compression of the algorithm in thispaper is significantly improved compared with the basic 4 times4 algorithm In the quality of the decoded image it can beseen from Figure 13 that the decoding quality of the interestregion in the image is close to the BFC 4 times 4 algorithm andthe recovery of the noninterest region approaches the BFC 8times 8 algorithm Although the PSNR is not as good as the BFC 4times 4 algorithm the important information in the image is wellrecoveredThe proposed algorithm balances the compressionratio and the decoded image quality well

The VBFC algorithm and the PSO algorithm use themethod of variance approximation matching and particleswarm optimization to improve the encoding speed It canbe seen from the experimental results that the coding time of

Complexity 11

=2 =4 =8=6

Figure 11 Decode image comparison with different 120578

20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R

Figure 12 Conversion curve of encoding performance with differ-ent 120575the VBFC and PSO algorithms decreases with the increaseof the R block partition size but even the PSO (8 times 8)algorithm with the smallest coding time is also longer thanthe encoding time of the proposed algorithm This is mainlybecause the algorithm in this paper comprehensively adoptsmultiple strategies such as reduced codebook and fast searchbased on correlation coefficient while VBFC algorithm andPSO algorithm only improve the match searching modeand the calculation efficiency is not good than the proposedalgorithm

It can be seen from Figure 13 that the quality of thedecoding image in the proposed algorithm is higher than theVBFC and PSO algorithms when the R block partition sizeis 8 times 8 For the interest region in the image in order toreduce thematching error and improve the image quality thispaper adopts a small size 4 times 4 segmentation to preserve theimportant details in the image Results show that the recoveryquality is better than the other two algorithms with the samesegmentation size In addition the compression ratio of thealgorithm proposed in this paper is also significantly higherthan that of the VBFC and PSO algorithms using 4 times 4segmentation (as shown in Table 2)

The proposed algorithm is also compared with thequadtree fractal algorithm The quadtree fractal algorithmwas first proposed by Fisher but Fisherrsquos method needs tocalculate the matching error of four subblocks in each block

and the matching process adopts the full search strategywhich is the same as the BFC algorithm resulting in a largeamount of computation and long encoding time Thereforethis paper chooses an improved quadtree fractal codingalgorithm for comparison The improved algorithm firstlyperforms quadtree decomposition on the image according tothe gray uniformity criterion and then performs matchingsearch on the decomposed R blocks of different sizes inthe reduced codebook The encoding efficiency is greatlyimproved compared with Fisherrsquos method

The maximum segmentation size of the improvedquadtree algorithm and the proposed algorithm are 8times 8 andthe minimum segmentation size is 4 times 4 As can be seen fromTable 3 when the quadtree algorithm is used to decomposethe image the small size image block occupies a largeproportion which leads a significantly lower compressionratio of the quadtree improvement algorithm compared tothe proposed algorithm At the same time due to the largenumber of small sized blocks the quadratic tree improvedalgorithm has a larger computational complexity and becauseof adopting the full search strategy which results in a muchlonger coding time than the proposed algorithm

5 Conclusion

In view of the particularity of UWAIs this paper uses fractalcoding based on partial similarity to compress the UAWIIn order to improve the encoding speed and compressionratio this paper proposes a fractal coding algorithm basedon interest region and correlation coefficient The algorithmdivides the interest region in the image into small sizeand divides the noninterest region into large size whicheffectively increases the compression ratio and recovers theinformation of important regions well At the encodingstage the R block searching range is reduced by reducingthe codebook and classification and the inappropriate Dblock is pre-excluded according to the correlation coeffi-cient between the R block and the D block which greatlyreduces the calculation amount of the encoding process Thesimulation results verify that the proposed algorithm notonly improves the UWAI compression ratio but also signif-icantly reduces the encoding time while at the same timeensuring the restoration quality of the interest region in theimage

12 Complexity

Table 3 Comparison of improved quadtree algorithm with the proposed algorithm

The number of 4 times 4blocks

The number of 8 times 8blocks Encoding time PSNR Compression ratio

Improved quadtreealgorithm 3996 25 18635 3018 553

Proposed algorithm 1128 742 302 2877 1387

(a) The original image (b) BFC (4 times 4) (c) BFC (8 times 8)

(d) VBFC (4 times 4) (e) VBFC (8 times 8) (f) PSO (4 times 4)

(g) PSO (8 times 8) (h) The proposed algorithm

Figure 13 Decoding image of BFC VBFC PSO and the proposed algorithm

Complexity 13

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors acknowledge the project of the National NaturalScience Foundation of China (Grant no 61701487) theInnovation Foundation of Chinese Academy of Sciences(Grant no CXJJ-17-M126) the Natural Science Foundation ofHainan Province (Grant no 417211) the Young Talentsrsquo Sci-ence and Technology Innovation Project of Hainan Associa-tion for Science and Technology (Grant no QCXM201812)the National Key Research and Development Program ofChina (Grant no 2016YFC1400100) the Strategic PriorityResearch Program of Chinese Academy of Sciences (Grantno XDA13030000) and the Fundamental Research Fundsin Heilongjiang Provincial Department of Education (no135209239) The authors also thank the Technical Bureau ofQiqihar GYGG-201622

References

[1] L Liu H Bian S-I Yagi and X Yang ldquoA prior-knowledge-based threshold segmentation method of forward-lookingsonar images for underwater linear object detectionrdquo JapaneseJournal of Applied Physics vol 55 no 7 2016

[2] W Jinqiu et al ldquoInfluence of pulse shaping filters on PAPRperformance of underwater 5G communication system tech-niquerdquo Wireless Communications and Mobile Computing vol2017 Article ID 4361589 4 pages 2017

[3] SHongResearch onKey Technologies of Sonar Image ProcessingHarbin Engineering University 2011

[4] S Zhengyan Research on Sonar Image Denoising and Segmen-tation Technology Harbin Engineering University 2010

[5] M Barnsley and A Sloan ldquoA better way to compress imagesrdquoByte vol 1 pp 215ndash222 1988

[6] A E Jacquin ldquoImage coding based on a fractal theory ofiterated contractive image transformationsrdquo IEEE Transactionson Image Processing vol 1 no 1 pp 18ndash30 1992

[7] Y Deng and Y Ke ldquoFast fractal image coding schemerdquo inProceedings of the 1996 3rd International Conference on SignalProcessing ICSPrsquo96 Part 1 (of 2) pp 1047ndash1050 October 1996

[8] E W Jacobs Y Fisher and R D Boss ldquoImage compression astudy of the iterated transform methodrdquo Signal Processing vol29 no 3 pp 251ndash263 1992

[9] X-Y Wang and D-D Zhang ldquoDiscrete wavelet transform-based simple range classification strategies for fractal imagecodingrdquo Nonlinear Dynamics vol 75 no 3 pp 439ndash448 2014

[10] L Weisheng and L Gaoping ldquoImproved fractal image codingalgorithm for fractional box dimensionrdquo Journal of SouthwestUniversity for Nationalities vol 1 pp 141ndash145 2012

[11] H Chuanjiang and H Xiwei ldquoFast fractal image codingalgorithm based on image block crossingrdquo Chinese Journal ofComputers vol 10 pp 1753ndash1761 2005

[12] C K Lee andW K Lee ldquoFast fractal image block coding basedon local variancesrdquo IEEE Transactions on Image Processing vol7 no 6 pp 888ndash891 1998

[13] Z Aihua S Fei Y Pei et al ldquoFast fractal coding algorithmbasedon similarity ratiordquoComputer Technology andDevelopment vol11 pp 176ndash178 2012

[14] W Lina L Xiaodong H Xinghua et al ldquoFast fractal imagecoding algorithm based on subdomain diagonal sumrdquo Micro-electronics and Computer vol 05 pp 82ndash86 2011

[15] S Furao and O Hasegawa ldquoA fast no search fractal imagecoding methodrdquo Signal Processing Image Communication vol19 no 5 pp 393ndash404 2004

[16] Q Chunqiang and W Jicheng ldquoApplication of quadtree theoryin fractal image codingrdquo Computer Engineering and Applica-tions vol 23 pp 61ndash63 2007

[17] Z Yunping and C Chuanbo ldquoA fast fractal image compressionalgorithmbased on newquadtreerdquo Small Computer Systems vol8 pp 1465ndash1469 2007

[18] B D Choi and S J Ko ldquoSplit-and-merge based block parti-tioning for high efficiency image codingrdquo IEEE Transactions onCircuits and Systems for Video Technology vol 99 p 1 2018

[19] AAit-Kheddache and S A Rajala ldquoTexture classification basedon higher-order fractalsrdquo in Proceedings of the Internationalconference on acoustics speech and signal processing pp 1112ndash1115 1988

[20] Z Zhiliang Z Yuli and Y Hai ldquoFast fractal image compressionalgorithm based on pixel distribution and triangle segmenta-tionrdquo Journal of ComputerApplications vol 2 pp 337ndash340 2010

[21] Q-M Zheng M Zhao F-H Wang and J-Z Zhao ldquoFractalcompression algorithm based on irregular region segmentationand gray sorting classificationrdquo Journal of China University ofPetroleum vol 3 pp 169ndash173 2014

[22] J G Conejeros ldquoA distributed K-means Segmentation Algo-rithm applied to Lobesia botrana Recognitionrdquo Complexity vol2017 Article ID 5137317 14 pages 2017

[23] Y C Hum K W Lai and M I Mohamad Salim ldquoMultiob-jectives bihistogram equalization for image contrast enhance-mentrdquo Complexity vol 20 no 2 pp 22ndash36 2014

[24] H Chuanjiang Algorithm Research of Fractal Image CodingTechnology Chongqing University 2004

[25] G Li Fractal Image Compression Coding vol 347 SouthwestJiaotong University Press 2010

[26] A N Backiam and R Kousalyadevi ldquoFast fractal image com-pression based on Fisherrsquos classification schemerdquo in Proceedingsof the 2014 International Conference on Electronics and Commu-nication Systems ICECS 2014 India February 2014

[27] AMA Banu ldquoAdaptive fractal image compression using PSOrdquoProcedia Computer Science pp 338ndash344 2010

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2 Complexity

system [6] which made the fractal coding into practice andpromoted the rapid development of fractal coding researchHowever there are still some problems in the fractal coding(1) The coding process is complicated and the amount ofcalculation is large which costs long time for the codingprocedure (2)The compression ratio and the decoded imagequality cannot be balanced In order to solve the long fractalcoding time scholars have proposed several methods suchas classification matching [7ndash10] optimized search rangeand nonsearch coding [11ndash15] scholars propose a variety ofdifferent range block partitioning schemes such as quadtreepartitioning [16ndash18] HV segmentation [19] triangulationand irregular segmentation [20 21] to balance the problemof compression ratio and decoded image quality The latterthree methods require more information to describe theposition and shape of each subblock compared with quadtreepartitioning and the search matching processes are morecomplicated In image processing the K-Means algorithmwhich belongs to the machine learning algorithm is a clus-tering algorithm based on distance similarity [22 23] Bycomparing the similarity between samples the samples ofthe form are divided into the same category However theusage of AI algorithms requires a large number of data setssuch as different signal-to-noise ratios different texturesdifferent types different sources of UWAIs and then thealgorithm can find the most suitable codebook based onvarious feature information of the images which means alarge number of underwater acoustic experiments is requiredand which is unrealizable currently because the acquisitionof UWAIs is difficult Therefore this paper utilizes the widelyused quadtree partitioning algorithm in the segmentationof UWAIs However because of the widespread noise inUWAI most of the segmented images have little or no largesize image blocks which causes difficult in the applicationof the quadtree partitioning algorithm Focusing on this wepropose the improved quadtree partitioning algorithm whichis based on the region of interest In addition by classifyingthe range blocks the search range of the range blocks isoptimized which can significantly improve the encodingspeed At the same time the codebook capacity is reducedand the correlation coefficient is matched which can not onlybalance the compression ratio and the decoded image qualitybut also gain a higher encoding speed

The structure of this paper is as follows the secondsection briefly introduces the principle of basic fractal codingthe third section focuses on the fractal coding algorithmbased on region of interest and the correlation coefficientfractal coding algorithm is proposed the simulation andexperiment results are given in the fourth section the fifthsection comes the conclusion

2 Basic Fractal Coding

The basis fractal coding (BFC) is to find a set of compressiontransformations whose fixed points are similar with theoriginal imageThese sets of compression transformation arecalled the Iterated Function System (IFS) Jacquin proposedthe Partial Iterative Function System (PIFS) and the basic

A1 A2 B1 B2

A3 A4 B3 B4

C1 C2 D1 D2

C3 C4 D3 D4

A B

C D

Figure 1 Four neighborhood pixel average

fractal coding inspired by IFS The implementation of BFCalgorithm is as follows

When encoding the image is first divided into a RangeBlock (R block) and a Domain Block (D Block)The R blocksdo not overlap with each other and the entire R blocks canform the original image The D blocks can be generated bysliding a certain size window in the original image accordingto a preset step size which are allowed to have overlappingareas To ensure the convergence of PIFS the block size of Dshould be larger than that of R (usually the D block size istwice larger than the R block)

Supposing the size of the original image is M times M theblock size of R should be B times B and the block size of D blockwill be 2B times 2B The sliding step is represents by 120575 and thenthe whole image is divided into11987221198612 R blocks and ((119872 minus2119861)120575 + 1)2 D blocks

In order to match the D and R blocks the D block needsto do the spatial contraction and its size is scaled from 2Btimes 2B to B times B Usually the four-neighbor pixel averagingmethod is used for spatial contraction (as shown in Figure 1)and S represents the spatial contraction operation D1015840 is thecontracted D block and then the value of each pixel in D1015840 canbe written as

1198891015840119896119897 = 1198892119896minus12119897minus1 + 1198892119896minus12119897 + 11988921198962119897minus1 + 119889211989621198974 (1)

where119889119896119897 and1198891015840119896119897 are the gray values of119863119895 and1198631015840119895 at the point(119896 119897) respectivelyFor each R blocks it is necessary to find the closest

block in the contracted D blocks to obtain the fractal codeAccording to PIFS between the R block and the D blockthere is an affine similarity which means that the R blockis similar to the D block after the equidistant transformation(rotation flipping etc) Jacquin simplified and summarizedthe isometric transformations which is shown in Table 1

In the table 119863119894119895 represents the pixel value of point (119894 119895)and 119905119896 119896 = 1 2 sdot sdot sdot 8 represents the isometric transforma-tion

After the entire D block is contracted and isometrictransformed the codebook Ω (also called the definitiondomain pool) required for block matching is formed Forconvenience the block in the codebook Ω is represented byD

After the above process for any 119877119894 the D block in thecodebook Ω is selected for match searching that is to finda best matching block119863119898(119894) so that119863119898(119894) is the closest one to119877119894 after proper affine transformation which is

119877119894 asymp 119904 sdot 119905119896 (119863119898(119894)) + 119900 (2)

Complexity 3



The original image

Domain block

Range block

Spatial contraction


tionCodebook

Fractal code

Match searching




(3)


119864 (119877119894 119863119898(119894)) = min119863isinΩ

119864 (119877119894 119863)= min119863isinΩ

1003817100381710038171003817119877119894 minus (119904 sdot 119863 + 119900)10038171003817100381710038172 (4)





119877119894(119896) = 119904 sdot 119905119896 (119878 (119863(119896minus1)119898(119894) )) + 119900119863(0)119898(119894) = 119863119898(119894) (5)




4 Complexity

(a) (b)


(a) (b)







Complexity 5

(a) (b) (c)

(d) (e) (f)








6 Complexity

(a) (b)


(a) (b)










Complexity 7

From formula (3)


(6)





Ω120575 = 119863 isin Ω var (119863) ge 1205752 (8)








2 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172


100381610038161003816100381610038161003816100381610038161003816100381610038162)

= 1198612var (119877) (1 minus |119903 (119877119863)|2)

(10)


119864 (119877119863) gt 11986121205782 (1 minus |119903 (119877119863)|2) (11)






8 Complexity










119877119894 = 119904119894 sdot (119905119896 (119878 (119863119898(119894)))) + 119900119894 (12)



(6) Output image X









Complexity 9

Image to be encoded



block










Select one Rblock

block R

Yes

No

Region of interest

Non-interest region







Over

No



Yes

Yes

No

No

Yes

No

Yes


６２lt 2

gt0

lt0

Update 0 0 forC E


10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








Complexity 3



The original image

Domain block

Range block

Spatial contraction


tionCodebook

Fractal code

Match searching




(3)


119864 (119877119894 119863119898(119894)) = min119863isinΩ

119864 (119877119894 119863)= min119863isinΩ

1003817100381710038171003817119877119894 minus (119904 sdot 119863 + 119900)10038171003817100381710038172 (4)





119877119894(119896) = 119904 sdot 119905119896 (119878 (119863(119896minus1)119898(119894) )) + 119900119863(0)119898(119894) = 119863119898(119894) (5)




4 Complexity

(a) (b)


(a) (b)







Complexity 5

(a) (b) (c)

(d) (e) (f)








6 Complexity

(a) (b)


(a) (b)










Complexity 7

From formula (3)


(6)





Ω120575 = 119863 isin Ω var (119863) ge 1205752 (8)








2 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172


100381610038161003816100381610038161003816100381610038161003816100381610038162)

= 1198612var (119877) (1 minus |119903 (119877119863)|2)

(10)


119864 (119877119863) gt 11986121205782 (1 minus |119903 (119877119863)|2) (11)






8 Complexity










119877119894 = 119904119894 sdot (119905119896 (119878 (119863119898(119894)))) + 119900119894 (12)



(6) Output image X









Complexity 9

Image to be encoded



block










Select one Rblock

block R

Yes

No

Region of interest

Non-interest region







Over

No



Yes

Yes

No

No

Yes

No

Yes


６２lt 2

gt0

lt0

Update 0 0 forC E


10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








4 Complexity

(a) (b)


(a) (b)







Complexity 5

(a) (b) (c)

(d) (e) (f)








6 Complexity

(a) (b)


(a) (b)










Complexity 7

From formula (3)


(6)





Ω120575 = 119863 isin Ω var (119863) ge 1205752 (8)








2 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172


100381610038161003816100381610038161003816100381610038161003816100381610038162)

= 1198612var (119877) (1 minus |119903 (119877119863)|2)

(10)


119864 (119877119863) gt 11986121205782 (1 minus |119903 (119877119863)|2) (11)






8 Complexity










119877119894 = 119904119894 sdot (119905119896 (119878 (119863119898(119894)))) + 119900119894 (12)



(6) Output image X









Complexity 9

Image to be encoded



block










Select one Rblock

block R

Yes

No

Region of interest

Non-interest region







Over

No



Yes

Yes

No

No

Yes

No

Yes


６２lt 2

gt0

lt0

Update 0 0 forC E


10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








Complexity 5

(a) (b) (c)

(d) (e) (f)








6 Complexity

(a) (b)


(a) (b)










Complexity 7

From formula (3)


(6)





Ω120575 = 119863 isin Ω var (119863) ge 1205752 (8)








2 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172


100381610038161003816100381610038161003816100381610038161003816100381610038162)

= 1198612var (119877) (1 minus |119903 (119877119863)|2)

(10)


119864 (119877119863) gt 11986121205782 (1 minus |119903 (119877119863)|2) (11)






8 Complexity










119877119894 = 119904119894 sdot (119905119896 (119878 (119863119898(119894)))) + 119900119894 (12)



(6) Output image X









Complexity 9

Image to be encoded



block










Select one Rblock

block R

Yes

No

Region of interest

Non-interest region







Over

No



Yes

Yes

No

No

Yes

No

Yes


６２lt 2

gt0

lt0

Update 0 0 forC E


10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








6 Complexity

(a) (b)


(a) (b)










Complexity 7

From formula (3)


(6)





Ω120575 = 119863 isin Ω var (119863) ge 1205752 (8)








2 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172


100381610038161003816100381610038161003816100381610038161003816100381610038162)

= 1198612var (119877) (1 minus |119903 (119877119863)|2)

(10)


119864 (119877119863) gt 11986121205782 (1 minus |119903 (119877119863)|2) (11)






8 Complexity










119877119894 = 119904119894 sdot (119905119896 (119878 (119863119898(119894)))) + 119900119894 (12)



(6) Output image X









Complexity 9

Image to be encoded



block










Select one Rblock

block R

Yes

No

Region of interest

Non-interest region







Over

No



Yes

Yes

No

No

Yes

No

Yes


６２lt 2

gt0

lt0

Update 0 0 forC E


10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








Complexity 7

From formula (3)


(6)





Ω120575 = 119863 isin Ω var (119863) ge 1205752 (8)








2 10038171003817100381710038171003817119863 minus 119863100381710038171003817100381710038172


100381610038161003816100381610038161003816100381610038161003816100381610038162)

= 1198612var (119877) (1 minus |119903 (119877119863)|2)

(10)


119864 (119877119863) gt 11986121205782 (1 minus |119903 (119877119863)|2) (11)






8 Complexity










119877119894 = 119904119894 sdot (119905119896 (119878 (119863119898(119894)))) + 119900119894 (12)



(6) Output image X









Complexity 9

Image to be encoded



block










Select one Rblock

block R

Yes

No

Region of interest

Non-interest region







Over

No



Yes

Yes

No

No

Yes

No

Yes


６２lt 2

gt0

lt0

Update 0 0 forC E


10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








8 Complexity










119877119894 = 119904119894 sdot (119905119896 (119878 (119863119898(119894)))) + 119900119894 (12)



(6) Output image X









Complexity 9

Image to be encoded



block










Select one Rblock

block R

Yes

No

Region of interest

Non-interest region







Over

No



Yes

Yes

No

No

Yes

No

Yes


６２lt 2

gt0

lt0

Update 0 0 forC E


10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








Complexity 9

Image to be encoded



block










Select one Rblock

block R

Yes

No

Region of interest

Non-interest region







Over

No



Yes

Yes

No

No

Yes

No

Yes


６２lt 2

gt0

lt0

Update 0 0 forC E


10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








10 Complexity


Algorithm

ImageShip Plane



(a) (b)


33

325

32

315

31130 110 90 70 50

Time

=6

=4

=2

=8

=10

PSN

R





Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








Complexity 11

=2 =4 =8=6


20 0406080100

=45

=40

=35=30

=25=20=15=10=5

33

325

32

315

31

Time

PSN

R






5 Conclusion


12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








12 Complexity










Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018








Complexity 13

Data Availability




Acknowledgments


References



































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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Underwater Acoustic Image Encoding Based on Interest ...downloads.hindawi.com/journals/complexity/2018/5647519.pdf · Underwater Acoustic Image Encoding Based on Interest Region and