research article integrating a hive triangle pattern with...

Research ArticleIntegrating a Hive Triangle Pattern with Subpixel Analysis forNoncontact Measurement of Structural Dynamic Response byUsing a Novel Image Processing Scheme

Yung-Chi Lu1 Shih-Lin Hung1 and Tzu-Hsuan Lin2

1 Department of Civil Engineering National Chiao-Tung University 1001 University Road Hsinchu 30010 Taiwan2 Sinotech Engineering Consultants Inc 171 Section 5 Nanking East Road Taipei 10569 Taiwan

Correspondence should be addressed to Shih-Lin Hung slhungmailnctuedutw

Received 16 February 2014 Accepted 7 April 2014 Published 11 May 2014

Academic Editor Marija Strojnik

Copyright copy 2014 Yung-Chi Lu 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

This work presents a digital image processing approach with a unique hive triangle pattern by integrating subpixel analysisfor noncontact measurement of structural dynamic response data Feasibility of proposed approach is demonstrated based onnumerical simulation of a photography experiment According to those results the measured time-history displacement ofsimulated image correlates well with the numerical solution A small three-story frame is then mounted on a small shaker tableand a linear variation differential transformation (LVDT) is set on the second floor Experimental results indicate that the relativeerror between data from LVDT and analyzed data from digital image correlation is below 0007 00205 in terms of frequency anddisplacement respectively Additionally the appropriate image block affects the estimation accuracy of the measurement systemImportantly the proposed approach for evaluating pattern center and size is highly promising for use in assigning the adaptiveblock for a digital image correlation method

1 Introduction

Structural health monitoring (SHM) detects a damageand characterization strategy for engineering structuresConventional SHM technology collects structural static ordynamic response data by using wire-based systems How-ever installing these wire-based systems can be expensivein labor cost and time [1] To overcome these obstaclesseveral technologies have emerged to reduce the considerableefforts associated with devising ameasurement systemThesetechnologies include optical laser ultrasound and wirelessAs a mounted wireless module with a sensing device awireless sensing device simplifies the installation process andsignificantly reduces installation costs Although measure-ment data are gained through radio waves packets losses andpower usage must be addressed [2] Given the rapid advancesin optical imaging hardware technology the use of digitalphotography in structural monitoring systems has receivedconsiderable interest among researchers Digital image analy-sis technology is adopted inmanydisciplines especially in the

recent decade [3ndash9] Peters and Ranson [3] proposed digitalimage schemes to measure surface displacement in mechan-ical engineering Laser speckle metrology can be describedin terms of the undeformed and deformed coordinates ofa body Chu et al [4] cited major limitations of speckleschemes stability requirements and the laborious and timeconsuming nature of data processing As a theory used inexperimental mechanics the digital image-correlation (DIC)method is a highly accuratemeans of determining rigid-bodytranslations and rotations Pan andWang [5] proposed usinga camera and a transmission diffraction grating to measurethe surface profile and deformation of small-scale objectsAmodio et al [6] examined the feasibility of constructinga short time real-time speckle correlation device whileconsidering the availability of high resolution cameras andhigh-speed processors at competitive retail prices Theirmethod can be viewed as an extension to digital images ofthe conventional white light speckle photography approachThe modified algorithm can process hundreds of pictures

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 375210 11 pageshttpdxdoiorg1011552014375210

2 The Scientific World Journal

in an acceptable time Chung et al [7] demonstrated theproof-of-concept in which emerging digital image processingtechniques allow for system identification nonintrusivelyand remotely The digital imaging procedure and inverseanalysis algorithms developed for the friction problem canbe extended to identify nonlinear mechanical and struc-tural characteristics Shih et al [8 9] developed the digitalimage correlation (DIC) method for determining the surfacesmoothness of construction materials and to monitor thedynamic responses of buildings under earthquake excitationThe accuracy of the DIC method is sufficiently high forseveral applications

Digital image analysis technology is characterized byan enormous amount of data In a particular time pointusing wireless or wired measurement methods can obtainone data set implying the structural dynamic response ofa sensor However digital image analysis technology mustacquire an image that consists of a specific pattern andleave a sufficient amount of displacement to ensure thatthe specific pattern is displayed in the acquired image atdifferent time point The amount of data of the acquiredimage may be thousands of times or more than that ofwireless or wired measurement methods Data format of thewired measurement method is assumed here to be a single-precision floating point When the sampling rate is 200 thedata storage capacity is 800 bytessThe acquired image size isassumed here to be 1024times 50 and one grayscale pixel is storedwith 8 bits subsequently allowing for the recording of 256different intensities In an identical sampling rate the imagestorage capacity is 10240000 bytes equivalent to 12800 timesthe data storage capacity The acquired image that is the fullimage of a camera has even greater variations Therefore inthis work a region of interest selected from the full imageof camera is saved as the acquired image The region mayconsist of a specific pattern or more patterns in a differentarea of the imagesThe specific pattern is generally painted ona different floor for themeasured structureThe region coversall patterns on each floor of the structure

An image block is a subset of an acquired image Anacquired image which is undisturbed by an external load isassigned as the source image As a subset of the source imagea source image block consists of a specific pattern with a sig-nificant contrast Additionally an acquired image disturbedby an external load is assigned as the target image In a targetimage several target image blocks can be assigned in manypositions Dynamic displacement of the specific position canbe estimated using an adaptive target image block to comparewith a source image block in order to calculate its cross-correlation The size and location of an image block affectthe accuracy and precision of a digital image correlationalgorithm Other influential factors include inherent imagenoise and subpixel interpolation approximation [10] Digitalimage correlation refers to a class of nondestructive methodsthat acquire images of an object store images in digital formand perform image analysis to extract a full-field shape anddeformation andor motion measurements [11]

A higher accuracy and precision generally require a largerimage block size While an adaptive pattern is painted onthe surface of a structure the displacement of a higher

accuracy and precision can be estimated by digital imageanalysis technology and the image block just filled witha specified pattern The specified pattern can provide asignificant contrast in the acquired images to enhance theeffect of digital image correlation coefficient on the acquiredimages When the acquired region of image is enlargeddigital image analysis technology can estimate the dynamicresponse over a wider range Owing to the enormous amountof data from the acquired image the transmission rate mustbe sufficiently large Otherwise the acquired images may losesome frame in the image capture process and the imagemissing rate becomes more severe with a higher samplingrate To reduce the image missing rate the acquired range ofan image is reduced to the region of interest Additionally theproposed measurement system records the missing numberof acquired images to compensate the missing image with aninterpolation method in postprocessing

The optical image facility has advanced annually Theresolution of an acquired image can be enlarged by using atelescope lens and a high frequency response of structurecan be evaluated by a high-speed digital camera Howeverimage exposure time is reduced in the high-speed imagecapture process implying that the acquired imagemay be toodark to identify in addition the processing time of acquiringan image may be too short to retrieve all images in everytime interval Therefore a smaller and adaptive image is ofpriority concern In this work a hive triangle pattern (HTP)is stuck on a small three-story frame and an evaluationmethod of the pattern center and size can register the locationaccurately and estimate the pattern sizeThe pattern increasesthe efficiency of a correlation coefficient Analysis resultsindicate that the relative error is only slight and the evaluateddisplacement time history closely resembles the numericalsolution and LVDT

2 Research Problem and Experimental Setup

This work introduces a digital image displacement measure-ment problem under a source and target image The objectof a source image may appear somewhere in a target imageWhen the object is a rigid body the displacement may alsoinclude the body rotations However the displacement of119910-axis in relation to the 119909-axis is negligible Therefore theexperimental result can be regarded as a linear translationThe simplified form of displacement estimation is expressedas follows

maxCC (1198681199090 1199100

1198681015840

1199091 1199101

) (1)

where 119868 denotes the based block from source image 119878 1198681015840represents the estimated block from target image 119879 thesubscripts denote the coordinate 119909 and 119910 correspondence 119878and 119879 and CC refers to the correlation coefficient functionto evaluate with the two blocks The coordinate (119909

0 1199100)

of a source image is predefined with an appropriate valuedescribed later and the coordinate (119909

1 1199101) of a target image is

selected from a measurement system to obtain the maximalcorrelation coefficient Figure 1 shows these parameters andactual images

The Scientific World Journal 3

Afterdeformationdeformation

Before

Source image Target image

u

(u )

I

x-axis

y-axis

(x0 y0)

(x1 y1)

I998400

(a)

(x0 y0)

(b)

(x1 y1)

(c)

Figure 1 (a) Simplified diagram of source and target image showing displacement variation of image block (b) Source images (c) Targetimage

W

H

HW = sin(60∘)

Figure 2 Generation of hive triangle pattern from circle andSierpinski triangle

For two-image block the value of the correlation coeffi-cient represents the degree of their similarity to each otherTheoretically the object coordinate of source image changesto another location appearing on the target image in whichthe maximal correlation coefficient should be one indicatingtheir identical coordinates However the images shootings atdifferent time points always differ from each other even if theobject of an image remains constant Although the maximalcorrelation coefficient is always less than one the estimationscheme can determine the accuracy displacement betweenimages based on the similarity A specified pattern which ispainted on a structure can provide the necessary contrast tocorrelate images well to enhance the effect of the correlationcoefficient on image similarity In this work the specifiedpattern is a hive triangle pattern which is derived from circleand Sierpinski triangle as shown in Figure 2

Selecting an image block is of priority concern whenusing a correlation coefficient to estimate object displace-ment As location and size are twomajor factors for the image

Hive triangle pattern

Speckle

Figure 3 An image frame that includes the speckle and hive trianglepatterns is used as reference object in numerical simulation

block this work estimates efficiently the appropriate valueof the factor with the proposed evaluation method by usingthe hive triangle pattern The hive triangle pattern has theblack and white characteristics The pattern causes the image


04m

04m

04m

04m

LVDT

Shaker table

(a) (b) (c)

Figure 4 Configuration of small three-story frame and an LVDT on second floor (a) Image frame captured using measurement system withlower (b) and higher resolution (c)

CorrelationcoefficientSource image

x-axis

y-axis

Additional cccc max in(U minus xminus V) (U + x+ V)

I (U V minus yminusyminus

)

(U V + y+)

(U + x+V minus yminus)

(U V)

cc max in xminus cc max in x+

cc max in y+

Ideal hive triangle pattern (P)

Figure 5 Correct location of pattern is estimated from source image and ideal hive triangle pattern with digital image correlation coefficientThree largest circles (green blue and orange) indicate three largest correlation coefficients the highest correlation coefficient is in119909

+direction

pixel values to significantly differ in the evaluated imageDespite the very small displacement of an object the value ofcorrelation coefficient can still clearly show how the imagesdiffer from each other

Numerical simulation of a photography experiment ata short range demonstrates the feasibility of the proposedapproach The speckle and hive triangle patterns are com-bined as a single image frame and a Flash animation programdisplays the frame in different locations with sine variationFigure 3 shows the speckle and hive triangle patterns

In another experiment a small three-story frame ismounted on a small shaker table and an LVDT is set onthe second floor (Figure 4) To compare those results withthose of LVDT the experiment focuses on the second flooras shown in the bottom image of Figure 1

Hardware of the digital image measurement system con-sists of a high-speed digital camera (Basler A504kc samplingrate of 500Hz) camera lens and high level computer withan image acquisition card The digital camera is a colormodel whose image-type is Bayer pattern decoding mustbe performed to obtain acceptable gray images The high

level computer is equipped with an i-RAM expansion cardfor increasing the access speed The expansion card hasthe performance benefits of solid state storage howevera maximum capacity of 4GB limits the number of imageframes Fortunately the image storage capacity of most of theexperiment is less than 4GB However the processing andaccess speed is still too slow and the acquisition data losesome frames in a higher sampling rateTherefore the lost datais interpolated linearly as compensation

3 Methods

The work presents a novel hive triangle pattern to painton the surface of structure The pattern location affectsthe displacement estimation accuracy Figure 5 describes ascheme to estimate the original location (119909

0 1199100) of the hive

triangle pattern Two acquired images are first selected as119878 and 119879 The image 119878 is an undeformed image and theimage 119879 is a slightly deformed image relative to image 119878 Asimple difference method is incorporated in the two imagesas shown in (2) The equation value indicates the maximal


difference (255) and is exactly identical (0) of specified pixelThe pixel value of the same background is close to zero andthe value of pattern position is relatively large

119863 = |119878 minus 119879| (2)

Additionally the approximate coordinates of the patternas in (3) are located using a mean-max method The methodcalculates themeans of all columns and rows in the differenceimage The maximum value of the mean averages of thecolumns and rows indicates the 119909-axis and 119910-axis coordinaterespectively

119883119894=

sum119899

119895=1119863(119894 119895)

119899

119884119895=

sum119898

119894=1119863(119894 119895)

119898

119883 = 119880 where 119883119880gt 119883119894for 119894 = 1 sim 119898 and 119894 = 119880

= 119881 where 119883119881gt 119883119895for 119895 = 1 sim 119899 and 119895 = 119881

(3)

Moreover the algorithm creates an ideal hive trianglepattern (119875) for using to calculate the correlation coefficientwith the source image The correlation coefficient has manyformulations This work uses the following equation

119862 =

sumsum [(119891 minus ⟨119891⟩) sdot (119892 minus ⟨119892⟩)]

[sumsum (119891 minus ⟨119891⟩)2

sdot sumsum (119892 minus ⟨119892⟩)2

]

12

(4)

In (4) 119891 and 119892 are image blocks that represent the pixelvalue of the source image and target image respectivelyThe sign ⟨sdot⟩ denotes the mean operator Precision of themeasurement unit is an integer pixel value with originalimagesThe subpixel analysis can improve the precision basedon the subpixel estimation of a target image

Finally a bilateral search can determine the maximal cor-relation coefficient of an individual direction An additionalpoint is determined by the previous maximal correlationcoefficients For instance the maximal correlation coefficientof119883-axis appears to be in a positive direction (right) and themaximal correlation coefficient of 119884-axis appears to be in anegative one (up)The additional point is assigned the uprightlocation (Figure 5) Notably the correlation coefficient ofthe new point may be less than the previous maximalcorrelation coefficient Therefore the three larger correlationcoefficients are evaluated simultaneously to determine theadaptive moving step Figure 5 illustrates the three largercorrelation coefficients in the search mechanism and thecc max of 119909

+direction is the largest correlation coefficient

The initial location (119880 119881) moves to the new location (119880 +

119909+ 119881) in the next iteration In the iterative process of the

proposed approach the final maximal correlation coefficientis determined and the evaluated location of pattern is foundThemethodmay fail to locate the position of the hive trianglepattern due to an inappropriate target image Experimentalresults indicate that the maximum correlation coefficient ishigher than 095 in the correct search and lower than 075 inthe fail search Therefore an appropriate threshold can helpto determine the validity of the search In the fail situationanother target image is selected to evaluate the maximumcorrelation coefficient again

Another simple algorithm based on the pattern location(1199090 1199100) evaluates the pattern size Owing to the triangle

characteristic of the hive triangle pattern its height has afixed ratio (sin 60∘) with thewidthThemaximumcorrelationcoefficient can be evaluated based on the source image blockand ideal pattern with different sizes The pattern width(119882) is determined in terms of integer-pixel accuracy Inthis work the pattern size of subpixel precision is estimatedusing a subpixel technician Figure 6 shows the estimationformulation of the subpixel

After subpixel offsets the estimation block can be cal-culated with the correlation coefficient to compare witha previous maximal correlation coefficient allowing us toevaluate the adaptive size of pattern in terms of subpixelaccuracy Because the gray pixel value ranges from 0 to 255in this work the precision of 01 pixel value is acceptableTheprecisionmay be unreliable for a subpixel value less than 001Figure 7 shows the variation of a correlation in different pixelscales In too small of a scale the correlation is too sensitiveto affirm the reliability of the displacement In the subpixelanalysis of this work the divided factor can determine thesubpixel scale For instance the factor is set to 10 indicatingone pixel divided into ten 01 subpixelsThe 01 pixel is dividedinto ten 001 subpixels

Another important algorithm displacement evaluationalgorithm compares the source image block and targetimage block by using the digital image correlation coeffi-cient to evaluate the displacement of pattern Based on afixed attempt our previous study evaluated displacementusing digital image correlation for different pixel scales [12]Additional computing time is expended in evaluating theiterationTherefore an improved algorithm (Figure 8) showsthe flowchart Based on the location and size of the patternin a source image estimated from a previous algorithm asource image block 119868 is created as a reference block Someimage blocks are selected from a target image to comparewith reference block 119868 Displacement of the target image isdetermined by the maximal correlation coefficient of theseimage blocks with reference block 119868 Parameters 119889

0 gap

movePNand tryIt are initialized as given valueThe1198890value is

the currently estimated displacement the gap is amoving stepwith a pixel unit movePN is the moving direction where 1denotes positive direction andminus1 denotes a negative one tryItis the count of an estimated fail in a particular direction Anestimated fail indicates that the current correlation coefficientis less than the current maximal correlation coefficient Thefirst target image block was selected based on the previousdisplacement A closer target block to the pattern of atarget image generally implies a larger correlation coefficientof the target and reference block The algorithm attemptsbilaterally to obtain the maximal correlation coefficient Inour previous work [12] the measurement system has afixed number of attempts to evaluate the correlation in apositive or negative direction Several computing times werewasted in iterative process The new proposed algorithmcan quickly obtain the maximal correlation coefficient todetermine the evaluated displacement of the target imageA flexible number of attempts (maxTry) can be assigned tothe measurement system by a user or default Analysis results


One pixel

P1 P2

P3 P4

Subpixel

Subpixeldivided Resampling

sX

sY

sP1

(1 minus sX) lowast (1 minus sY) sX lowast (1 minus sY)

(1 minus sX) lowast sY sX lowast sY

sP1 = P1 lowast (1 minus sX) lowast (1 minus sY)+

P2 lowast sX lowast (1 minus sY)+

P3 lowast (1 minus sX) lowast sY+

P4 lowast sX lowast sY

Figure 6 Subpixel and formula (sP1) for estimating its gray level For block that must be resample owing to subpixel displacement gray levelof every pixel must be recalculated using estimation formula

The correlation of source and target image blocks

(20 0) r = 099907121

08

06

04

02

0

2010

0minus10

minus20 010

2030

40

Z-a

xis (

corr

elat

ion)

Y-axis (pixel) X-axis (pixel)

(a)


1

0

Z-a

xis (

corr

elat

ion)


r = 09994999

0995

099

0985

098

0975

097

105

minus05minus1 19

19520

20521

0)

05

20205

(202 0)

(b)


0

Z-a

xis (

corr

elat

ion)

(2019 minus003) r = 0999520609995

09994

09993

09992

09991

01005

minus005minus01 201

2015202

2025203


(c)


Z-a

xis (

corr

elat

ion) (20185 minus0034) r = 09995228

0999525

0999520

0999515

0999510

0999505

0999500

minus002minus0025

minus003minus0035

minus004 201820185

201920195

202


(d)

Figure 7 Variation of correlation coefficient with displacement scales (a) 1 pixel (b) 01 pixel (c) 001 pixel and (d) 0001 pixel


Start Set reference block Ifrom source image

Choose target imageSet = 0 gap = 1

movePN = 1 tryIt = 0

Get the target blockbased on prev target

Calculate correlationcoefficient

Caclulate correlationcoefficient

Yes

Yes

Yes YesNo

No

No

No

tryIt = 0

movePN 1

gap = gapdividerdefault (divider) = 10

Stop

tryIt ge maxTry

movePN = minus

gap ge minGap

is estimateddisplacement

tryIt = tryIt +1

tryIt = tryIt +1

Try to get the newgt

II998400

= tryIt = 0

d0

d0

C998400

CC998400

C998400 CC998400

C998400

CC998400

Target I998400block base on

1lowastmovePN

(d0 + gaplowastmovePN)

d0 = d0+ gaplowastmovePN

Figure 8 Flowchart of displacement evaluation algorithm which has better execution time and accuracy than that in our earlier work

indicate that an attempt can still be made to estimate theaccuracy displacement in a slight variation of source andtarget image The above algorithms are implemented usingMATLAB software

Images are acquired from a high-speed digital cameraby using LabVIEW software However the image acquisitionprogram encounters two problems the total image storagecapacity is too large and too high of a sampling rate causesan insufficient computational time As the first problemthe program cuts the image into a smaller critical blockto save the image The critical block includes the patternand approximate number of maximum pixel displacementsMoreover the program records the number of each imageframe to identify the lost frame in the acquirement procedureof a higher sampling rate Based on the interpolationmethodthe images are reconstructed to increase the accuracy of time-history data

The digital camera which has a Bayer filter sensor typemust decode an image for the Bayer pattern Otherwise theimage displays many grid lines (Figure 9) This problem canbe solved with a library function of LabVIEW

The original length unit of image displacement is integerpixel size The actual length (119871) of the pattern is a knownquantity and the pixel width (119882) of the pattern has beenevaluated by the measurement system The actual struc-tural displacement can be calculated using estimated pixeldisplacement to multiply by a pixel ratio (119877

119901) from (5)

At this point the time-history displacements are estimatedcompletely in the digital image measurement system

119877119901=

119871

119882

(119906 V) = (119889119909 119889119910) lowast 119877119901 (5)

4 Results and Analysis

41 Numerical Simulation Result The work developed anumerical simulated image which included digital randomspeckle and hive triangle patterns as shown in Figure 3 Thesimulated image was generated from the PHP web languageA FLASH animation program was designed to display thesimulated image in different locations with sine variationThe animation was played on a computer monitor and thetime-history displacementwas estimated in themeasurementsystem Figure 10 summarizes those results

The time-history displacement calculated by using theproposed hive triangle pattern was smoother than thatcalculated by using a digital random speckle The exampleconsidered in this work indicated that the result of using hivetriangle pattern was better than the digital random speckleto compare with simulated sin displacement Speckle patterncannot be accurately identified with poor image quality Inaddition this is owing to the fact that the position andsize of an image block affected the computational time andaccuracy of evaluation in to digital image correlationmethodTherefore several evaluations were estimated and comparedwithin different positions and sizes of the image block Table 1summarizes those comparison results The block of case 1is selected in human visual discrimination and case 2 ischose by the measurement system Case 3 is based on case2 with the image block size cropped from 57 times 49 to 49times 42 Simulation results reveal that the execution time isshorter but the root mean square error (RMSE) reveals thatthe accuracy is lower than in case 2 Cases 5 and 6 involvethe random speckle pattern with different block sizes Theblock in case 7 as in case 2 includes one-hive trianglepattern which is detected by the measurement system andcase 8 involves parts of three-hive triangle patterns ldquoTimerdquo


(a) (b)

Figure 9 Bayer decoding (a) Original captured image frame with many grid lines and (b) Bayer-decoded image

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinPrevious Study

(a)

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinSpeckle

(b)

Figure 10 Numerically simulated time history of displacement (a) Hive triangle pattern and (b) random speckle

represents the execution time in any case For a given blockthe execution time herein is shorter than in the previousstudy The faster execution supports applications that arecloser real-time systemsThe RMSE herein is better than thatachieved in the aforementioned previous study Simulationresults reveal that the work herein is better than that in theprevious study in terms of execution time and accuracy

For the random speckle pattern a higher RMSE appearedinwhich an image block is located in the interior region of theentire speckle When the width of a random speckle imageblock is greater than that of the entire speckle a satisfactoryaccuracy can be obtained Outside of the entire speckleis white the boundary is thus significantly different frominside to outside Closely examining the acquired imagesrevealed that the image quality was unacceptable owing toan insufficient exposure time and highly compact densityof the random speckle In displacement estimation thecorrelation coefficient of speckle pattern cannot be correctlyestimated owing to undesirable image quality However inthe ideal simulated images the results closely correspond tothe actual displacement during simulationThe theory of esti-mated displacement with speckle is valid only limited under

certain circumstances Based on our experimental resultswe recommend increasing the speckle size and spacingAdditionally the entire speckle region is set as the referenceimage block is considered another possible solution Theadditional computational time cost must be spent for a largerimage block

This work improves the ability of the proposed algorithmused to estimate the displacement in the previous studyTable 1 indicates that the proposed approach is better thanthe previous algorithm within an identical position and sizeof image block including RMSE and frequency peaks Inparticular displacement estimation can obtainmore accurateresults by using the pattern location algorithm to locatethe adaptive reference image block Despite only a slightimprovement the findings still demonstrate the advantagesof the proposed algorithm Therefore the algorithm is afeasible noncontact displacement estimation method withsubsequent experiments undertaken using this method

42 Simulation Results of a Small Earthquake The exper-iment involves two image resolutions Figure 11 shows the


(a) (b)

Figure 11 Patterns with different resolutions (a) High resolution 57 times 49 (b) Low resolution 10 times 9

Table 1 The comparison of numerical simulation result

Simulationcase Blocka Execution time (s) RMSE

Previous study [12]

1 64 times 280 30 times 30 26 05958497232 51 times 271 57 times 49 81 05713940473 55 times 275 49 times 42 64 05904424054 51 times 271 205 times 10 49 0572254826

5 160 times 120 120 times 30 76 07260095346 70 times 50 205 times 10 46 068851133

This work 7 51 times 271 57 times 49 16 05547492248 51 times 271 205 times 10 13 0550491283

aThe datum denotes (Left) times (Top) (Width) times (Height)

0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)

LVDTHTP-DICSquare error

Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001

The time-history displacement of small three-storyframe in higher resolution (57 times 49)

1601 1801

Figure 12 Time history of displacement and square error ofdisplacement of small three-story frame at high resolution (57 times 49)

pattern image within different resolutions First the cameralens focuses on the second floor in a large resolution Figure 2shows the sample of a captured image while Figure 12 showsthe estimated time-history displacement and square errorThe curve of LVDT is very similar to the estimation of a


minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror

The time-history displacement of small three-storyframe in lower resolution (10 times 9)

05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667

Figure 13 Time history of displacement and square error ofdisplacement of small three-story frame at low resolution (10 times 9)

measurement system The peak value of frequency calcu-lated in FFT is 01258944579 and 01259031566 respectivelyThe relative error of a frequency is minus690952E-05 and theroot mean square error is 0020523298 Second the camerarecords the entire three-story frame building Figure 4 showsthe sample of a captured image The El Centro earthquake


is generated from the small shaker table and the time-history displacement is estimated from the digital imagemeasurement system Figure 13 summarizes those resultsindicating that the curves are similar to each other Thepeak value of frequency calculated in FFT is 1835178054 and1835320253 respectively The relative error of a frequency isminus774851E-05 Two peak values of frequency are similar toidentical The root mean square error is 0084863876 Owingto lower image resolution in the displacement estimationthe results cannot be estimated accurately In sum the curveof time-history displacement resembles that of the results ofLVDT

43 Data Analysis This work extends the results of ourprevious study [12] In the evaluated iteration a fixed numberof attempts which attempt to derive the maximal correlationcoefficient are transformed into flexible maximal attemptsThe computational time in thiswork is significantly decreasedover that that in our previous study Table 1 shows theexecution time in different experiments The position andsize of the image block directly affect the computationaltime of the estimation and the accuracy of the results Thepattern location algorithm of the measurement system canprecisely identify the position and size of the pattern forthe reference image block By using the reference imageblock calculating the correlation coefficient can increase theaccuracy of estimated displacement However this patternlocation algorithm also has certain limitations When theresolution of an acquired image is insufficiently high theposition and size of the pattern cannot be located correctlyFor instance the width of a pattern is only 10 pixels in anacquired image in addition the position and size of patternare still difficult to find The width of a pattern is 57 pixels inthe first experiment of Section 42 while the position and sizeof pattern can be obtained with this algorithm

The reference image block is set based on a visualobservation to determine the position and size of patternin our previous work The estimated displacement is similarto the measurement of LVDT In contrast in this work thereference image block set accurately can achievemore preciseresults Actually the acquired image has some referenceobjects which can be used as a reference image blocks toestimate the structural displacement However the resultsmay not be satisfactorily accurate

5 Conclusion

This work presents a novel digital image measurement sys-tem which is a feasible option for noncontact measurementThe time-history displacement estimated by the digital imagesystem is very similar to LVDT in some experiments Thecurves shown in Figure 12 nearly overlap each other in allperiods The curves shown in Figure 13 have a similar trendyet are inaccurate Additionally the actual length of onepixel is presented in the pixel ratio 119877

119901 If 119877

119901is large the

image is rough if 119877119901is small the image is meticulous By

using subpixel analysis the measurement system increasesthe accuracy to a pixel value of 01 or even 001 Therefore if

119877119901is less than 01mm the accuracy easily achieves 001mm

Based on our results we conclude the following

(i) in a higher resolution the time-history displacementshows highly similar results In a lower resolution thedisplacement trend is approximate yet the error ofdisplacement is too large The digital image measure-ment system is applicable in estimating the displace-ment of structural test in a higher resolution

(ii) the higher sampling rate decreases the exposure timeof the camera to affect the images quality in whichthe image acquisition program does not fully accessall images

(iii) the setup of the image measurement system is rela-tively easy as well as a very serviceable scheme and

(iv) the size of hive triangle pattern might cause an errorin the measurement procedure and therefore severalpatterns are measured to diminish the error

Highlights

(i) The setup of the image measurement system is rela-tively easy

(ii) High-speed digital camera is suitable in experimentalmeasurement

(iii) A specific hive triangle pattern is proposed(iv) An evaluation of peak of frequency is accurate with

digital image correlation(v) Numerical and experimental studies reveal the feasi-

bility of proposed measurement system

Conflict of Interests

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

Acknowledgments

The authors would like to thank the National Chiao TungUniversity and National Science Council of the Republic ofChina Taiwan for financially supporting this research underContract no NSC 98-2221-E-0009-097

References

[1] M Celebi ldquoSeismic instrumentation of buildings (with empha-sis on Federal buildings)rdquo Tech Rep 0-7460-68170 UnitedStates Geological Survey Menlo Park Calif USA 2002

[2] T H Lin S L Hung C S Huang and T K Lin ldquoDetection ofdamage location using a novel substructure- based frequencyresponse function approach with a wireless sensing systemrdquoInternational Journal of Structural Stability and Dynamics vol12 no 4 Article ID 125002 2012

[3] W H Peters and W F Ranson ldquoDigital imaging techniques inexperimental stress analysisrdquo Optical Engineering vol 21 no 3pp 427ndash431 1982


[4] T C Chu W F Ranson and M A Sutton ldquoApplications ofdigital-image-correlation techniques to experimental mechan-icsrdquo Experimental Mechanics vol 25 no 3 pp 232ndash244 1985

[5] B Pan and Q Wang ldquoSingle-camera microscopic stereo digitalimage correlation using a diffraction gratingrdquo Optics Expressvol 21 pp 25056ndash22506 2013

[6] D Amodio G B Broggiato F Campana and G M NewazldquoDigital speckle correlation for strain measurement by imageanalysisrdquo Experimental Mechanics vol 43 no 4 pp 396ndash4022003

[7] H-C Chung J Liang S Kushiyama and M ShinozukaldquoDigital image processing for non-linear system identificationrdquoInternational Journal of Non-LinearMechanics vol 39 no 5 pp691ndash707 2004

[8] M-H Shih W-P Sung S-H Tung D Bacinskas and GKaklauskas ldquoDeveloping three-dimensional digital image cor-relation techniques to detect the surface smoothness of con-struction materialsrdquo International Journal of Materials andProduct Technology vol 42 no 3-4 pp 234ndash246 2011

[9] M H Shih W P Sung and S C Chen ldquoApplication of digitalimage correlation technique to monitor dynamic responseof building under earthquake excitationrdquo Advanced ScienceLetters vol 5 pp 963ndash966 2012

[10] H W Schreier J R Braasch and M A Sutton ldquoSystematicerrors in digital image correlation caused by intensity interpo-lationrdquo Optical Engineering vol 39 no 11 pp 2915ndash2921 2000

[11] M A Sutton J J Orteu and H W Schreier Image Correlationfor Shape Motion and Deformation Measurements SpringerBerlin Germany 2009

[12] S L Hung and Y C Lu ldquoThe study of combining hive-gridtarget with sub-pixel analysis for measurement of structuralexperimentrdquo in Proceedings of the International ConferenceComputing in Civil and Building Engineering W Tizani Ed p79 Nottingham University Press Nottingham UK June-July2010 paper no 40

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



in an acceptable time Chung et al [7] demonstrated theproof-of-concept in which emerging digital image processingtechniques allow for system identification nonintrusivelyand remotely The digital imaging procedure and inverseanalysis algorithms developed for the friction problem canbe extended to identify nonlinear mechanical and struc-tural characteristics Shih et al [8 9] developed the digitalimage correlation (DIC) method for determining the surfacesmoothness of construction materials and to monitor thedynamic responses of buildings under earthquake excitationThe accuracy of the DIC method is sufficiently high forseveral applications

Digital image analysis technology is characterized byan enormous amount of data In a particular time pointusing wireless or wired measurement methods can obtainone data set implying the structural dynamic response ofa sensor However digital image analysis technology mustacquire an image that consists of a specific pattern andleave a sufficient amount of displacement to ensure thatthe specific pattern is displayed in the acquired image atdifferent time point The amount of data of the acquiredimage may be thousands of times or more than that ofwireless or wired measurement methods Data format of thewired measurement method is assumed here to be a single-precision floating point When the sampling rate is 200 thedata storage capacity is 800 bytessThe acquired image size isassumed here to be 1024times 50 and one grayscale pixel is storedwith 8 bits subsequently allowing for the recording of 256different intensities In an identical sampling rate the imagestorage capacity is 10240000 bytes equivalent to 12800 timesthe data storage capacity The acquired image that is the fullimage of a camera has even greater variations Therefore inthis work a region of interest selected from the full imageof camera is saved as the acquired image The region mayconsist of a specific pattern or more patterns in a differentarea of the imagesThe specific pattern is generally painted ona different floor for themeasured structureThe region coversall patterns on each floor of the structure

An image block is a subset of an acquired image Anacquired image which is undisturbed by an external load isassigned as the source image As a subset of the source imagea source image block consists of a specific pattern with a sig-nificant contrast Additionally an acquired image disturbedby an external load is assigned as the target image In a targetimage several target image blocks can be assigned in manypositions Dynamic displacement of the specific position canbe estimated using an adaptive target image block to comparewith a source image block in order to calculate its cross-correlation The size and location of an image block affectthe accuracy and precision of a digital image correlationalgorithm Other influential factors include inherent imagenoise and subpixel interpolation approximation [10] Digitalimage correlation refers to a class of nondestructive methodsthat acquire images of an object store images in digital formand perform image analysis to extract a full-field shape anddeformation andor motion measurements [11]

A higher accuracy and precision generally require a largerimage block size While an adaptive pattern is painted onthe surface of a structure the displacement of a higher

accuracy and precision can be estimated by digital imageanalysis technology and the image block just filled witha specified pattern The specified pattern can provide asignificant contrast in the acquired images to enhance theeffect of digital image correlation coefficient on the acquiredimages When the acquired region of image is enlargeddigital image analysis technology can estimate the dynamicresponse over a wider range Owing to the enormous amountof data from the acquired image the transmission rate mustbe sufficiently large Otherwise the acquired images may losesome frame in the image capture process and the imagemissing rate becomes more severe with a higher samplingrate To reduce the image missing rate the acquired range ofan image is reduced to the region of interest Additionally theproposed measurement system records the missing numberof acquired images to compensate the missing image with aninterpolation method in postprocessing

The optical image facility has advanced annually Theresolution of an acquired image can be enlarged by using atelescope lens and a high frequency response of structurecan be evaluated by a high-speed digital camera Howeverimage exposure time is reduced in the high-speed imagecapture process implying that the acquired imagemay be toodark to identify in addition the processing time of acquiringan image may be too short to retrieve all images in everytime interval Therefore a smaller and adaptive image is ofpriority concern In this work a hive triangle pattern (HTP)is stuck on a small three-story frame and an evaluationmethod of the pattern center and size can register the locationaccurately and estimate the pattern sizeThe pattern increasesthe efficiency of a correlation coefficient Analysis resultsindicate that the relative error is only slight and the evaluateddisplacement time history closely resembles the numericalsolution and LVDT

2 Research Problem and Experimental Setup

This work introduces a digital image displacement measure-ment problem under a source and target image The objectof a source image may appear somewhere in a target imageWhen the object is a rigid body the displacement may alsoinclude the body rotations However the displacement of119910-axis in relation to the 119909-axis is negligible Therefore theexperimental result can be regarded as a linear translationThe simplified form of displacement estimation is expressedas follows

maxCC (1198681199090 1199100

1198681015840

1199091 1199101

) (1)

where 119868 denotes the based block from source image 119878 1198681015840represents the estimated block from target image 119879 thesubscripts denote the coordinate 119909 and 119910 correspondence 119878and 119879 and CC refers to the correlation coefficient functionto evaluate with the two blocks The coordinate (119909

0 1199100)

of a source image is predefined with an appropriate valuedescribed later and the coordinate (119909

1 1199101) of a target image is

selected from a measurement system to obtain the maximalcorrelation coefficient Figure 1 shows these parameters andactual images



Before


u

(u )

I

x-axis

y-axis

(x0 y0)

(x1 y1)

I998400

(a)

(x0 y0)

(b)

(x1 y1)

(c)


W

H

HW = sin(60∘)





Speckle




04m

04m

04m

04m

LVDT

Shaker table

(a) (b) (c)



x-axis

y-axis



)

(U V + y+)


(U V)


cc max in y+



+direction






3 Methods






119863 = |119878 minus 119879| (2)


119883119894=

sum119899

119895=1119863(119894 119895)

119899

119884119895=

sum119898

119894=1119863(119894 119895)

119898



(3)


119862 =


[sumsum (119891 minus ⟨119891⟩)2


]

12

(4)











0 gap




One pixel

P1 P2

P3 P4

Subpixel


sX

sY

sP1









(20 0) r = 099907121

08

06

04

02

0

2010

0minus10

minus20 010

2030

40

Z-a

xis (

corr

elat

ion)


(a)


1

0

Z-a

xis (

corr

elat

ion)


r = 09994999

0995

099

0985

098

0975

097

105

minus05minus1 19

19520

20521

0)

05

20205

(202 0)

(b)


0

Z-a

xis (

corr

elat

ion)

(2019 minus003) r = 0999520609995

09994

09993

09992

09991

01005

minus005minus01 201

2015202

2025203


(c)


Z-a

xis (

corr

elat

ion) (20185 minus0034) r = 09995228

0999525

0999520

0999515

0999510

0999505

0999500

minus002minus0025

minus003minus0035

minus004 201820185

201920195

202


(d)









Yes

Yes

Yes YesNo

No

No

No

tryIt = 0

movePN 1


Stop

tryIt ge maxTry

movePN = minus

gap ge minGap


tryIt = tryIt +1

tryIt = tryIt +1


II998400

= tryIt = 0

d0

d0

C998400

CC998400

C998400 CC998400

C998400

CC998400


1lowastmovePN








119901) from (5)


119877119901=

119871

119882

(119906 V) = (119889119909 119889119910) lowast 119877119901 (5)





(a) (b)


minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinPrevious Study

(a)

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinSpeckle

(b)








(a) (b)




Previous study [12]





0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)


Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001


1601 1801




minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror


05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667







5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Before


u

(u )

I

x-axis

y-axis

(x0 y0)

(x1 y1)

I998400

(a)

(x0 y0)

(b)

(x1 y1)

(c)


W

H

HW = sin(60∘)





Speckle




04m

04m

04m

04m

LVDT

Shaker table

(a) (b) (c)



x-axis

y-axis



)

(U V + y+)


(U V)


cc max in y+



+direction






3 Methods






119863 = |119878 minus 119879| (2)


119883119894=

sum119899

119895=1119863(119894 119895)

119899

119884119895=

sum119898

119894=1119863(119894 119895)

119898



(3)


119862 =


[sumsum (119891 minus ⟨119891⟩)2


]

12

(4)











0 gap




One pixel

P1 P2

P3 P4

Subpixel


sX

sY

sP1









(20 0) r = 099907121

08

06

04

02

0

2010

0minus10

minus20 010

2030

40

Z-a

xis (

corr

elat

ion)


(a)


1

0

Z-a

xis (

corr

elat

ion)


r = 09994999

0995

099

0985

098

0975

097

105

minus05minus1 19

19520

20521

0)

05

20205

(202 0)

(b)


0

Z-a

xis (

corr

elat

ion)

(2019 minus003) r = 0999520609995

09994

09993

09992

09991

01005

minus005minus01 201

2015202

2025203


(c)


Z-a

xis (

corr

elat

ion) (20185 minus0034) r = 09995228

0999525

0999520

0999515

0999510

0999505

0999500

minus002minus0025

minus003minus0035

minus004 201820185

201920195

202


(d)









Yes

Yes

Yes YesNo

No

No

No

tryIt = 0

movePN 1


Stop

tryIt ge maxTry

movePN = minus

gap ge minGap


tryIt = tryIt +1

tryIt = tryIt +1


II998400

= tryIt = 0

d0

d0

C998400

CC998400

C998400 CC998400

C998400

CC998400


1lowastmovePN








119901) from (5)


119877119901=

119871

119882

(119906 V) = (119889119909 119889119910) lowast 119877119901 (5)





(a) (b)


minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinPrevious Study

(a)

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinSpeckle

(b)








(a) (b)




Previous study [12]





0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)


Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001


1601 1801




minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror


05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667







5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










04m

04m

04m

04m

LVDT

Shaker table

(a) (b) (c)



x-axis

y-axis



)

(U V + y+)


(U V)


cc max in y+



+direction






3 Methods






119863 = |119878 minus 119879| (2)


119883119894=

sum119899

119895=1119863(119894 119895)

119899

119884119895=

sum119898

119894=1119863(119894 119895)

119898



(3)


119862 =


[sumsum (119891 minus ⟨119891⟩)2


]

12

(4)











0 gap




One pixel

P1 P2

P3 P4

Subpixel


sX

sY

sP1









(20 0) r = 099907121

08

06

04

02

0

2010

0minus10

minus20 010

2030

40

Z-a

xis (

corr

elat

ion)


(a)


1

0

Z-a

xis (

corr

elat

ion)


r = 09994999

0995

099

0985

098

0975

097

105

minus05minus1 19

19520

20521

0)

05

20205

(202 0)

(b)


0

Z-a

xis (

corr

elat

ion)

(2019 minus003) r = 0999520609995

09994

09993

09992

09991

01005

minus005minus01 201

2015202

2025203


(c)


Z-a

xis (

corr

elat

ion) (20185 minus0034) r = 09995228

0999525

0999520

0999515

0999510

0999505

0999500

minus002minus0025

minus003minus0035

minus004 201820185

201920195

202


(d)









Yes

Yes

Yes YesNo

No

No

No

tryIt = 0

movePN 1


Stop

tryIt ge maxTry

movePN = minus

gap ge minGap


tryIt = tryIt +1

tryIt = tryIt +1


II998400

= tryIt = 0

d0

d0

C998400

CC998400

C998400 CC998400

C998400

CC998400


1lowastmovePN








119901) from (5)


119877119901=

119871

119882

(119906 V) = (119889119909 119889119910) lowast 119877119901 (5)





(a) (b)


minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinPrevious Study

(a)

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinSpeckle

(b)








(a) (b)




Previous study [12]





0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)


Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001


1601 1801




minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror


05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667







5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119863 = |119878 minus 119879| (2)


119883119894=

sum119899

119895=1119863(119894 119895)

119899

119884119895=

sum119898

119894=1119863(119894 119895)

119898



(3)


119862 =


[sumsum (119891 minus ⟨119891⟩)2


]

12

(4)











0 gap




One pixel

P1 P2

P3 P4

Subpixel


sX

sY

sP1









(20 0) r = 099907121

08

06

04

02

0

2010

0minus10

minus20 010

2030

40

Z-a

xis (

corr

elat

ion)


(a)


1

0

Z-a

xis (

corr

elat

ion)


r = 09994999

0995

099

0985

098

0975

097

105

minus05minus1 19

19520

20521

0)

05

20205

(202 0)

(b)


0

Z-a

xis (

corr

elat

ion)

(2019 minus003) r = 0999520609995

09994

09993

09992

09991

01005

minus005minus01 201

2015202

2025203


(c)


Z-a

xis (

corr

elat

ion) (20185 minus0034) r = 09995228

0999525

0999520

0999515

0999510

0999505

0999500

minus002minus0025

minus003minus0035

minus004 201820185

201920195

202


(d)









Yes

Yes

Yes YesNo

No

No

No

tryIt = 0

movePN 1


Stop

tryIt ge maxTry

movePN = minus

gap ge minGap


tryIt = tryIt +1

tryIt = tryIt +1


II998400

= tryIt = 0

d0

d0

C998400

CC998400

C998400 CC998400

C998400

CC998400


1lowastmovePN








119901) from (5)


119877119901=

119871

119882

(119906 V) = (119889119909 119889119910) lowast 119877119901 (5)





(a) (b)


minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinPrevious Study

(a)

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinSpeckle

(b)








(a) (b)




Previous study [12]





0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)


Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001


1601 1801




minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror


05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667







5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










One pixel

P1 P2

P3 P4

Subpixel


sX

sY

sP1









(20 0) r = 099907121

08

06

04

02

0

2010

0minus10

minus20 010

2030

40

Z-a

xis (

corr

elat

ion)


(a)


1

0

Z-a

xis (

corr

elat

ion)


r = 09994999

0995

099

0985

098

0975

097

105

minus05minus1 19

19520

20521

0)

05

20205

(202 0)

(b)


0

Z-a

xis (

corr

elat

ion)

(2019 minus003) r = 0999520609995

09994

09993

09992

09991

01005

minus005minus01 201

2015202

2025203


(c)


Z-a

xis (

corr

elat

ion) (20185 minus0034) r = 09995228

0999525

0999520

0999515

0999510

0999505

0999500

minus002minus0025

minus003minus0035

minus004 201820185

201920195

202


(d)









Yes

Yes

Yes YesNo

No

No

No

tryIt = 0

movePN 1


Stop

tryIt ge maxTry

movePN = minus

gap ge minGap


tryIt = tryIt +1

tryIt = tryIt +1


II998400

= tryIt = 0

d0

d0

C998400

CC998400

C998400 CC998400

C998400

CC998400


1lowastmovePN








119901) from (5)


119877119901=

119871

119882

(119906 V) = (119889119909 119889119910) lowast 119877119901 (5)





(a) (b)


minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinPrevious Study

(a)

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinSpeckle

(b)








(a) (b)




Previous study [12]





0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)


Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001


1601 1801




minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror


05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667







5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















Yes

Yes

Yes YesNo

No

No

No

tryIt = 0

movePN 1


Stop

tryIt ge maxTry

movePN = minus

gap ge minGap


tryIt = tryIt +1

tryIt = tryIt +1


II998400

= tryIt = 0

d0

d0

C998400

CC998400

C998400 CC998400

C998400

CC998400


1lowastmovePN








119901) from (5)


119877119901=

119871

119882

(119906 V) = (119889119909 119889119910) lowast 119877119901 (5)





(a) (b)


minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinPrevious Study

(a)

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinSpeckle

(b)








(a) (b)




Previous study [12]





0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)


Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001


1601 1801




minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror


05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667







5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)


minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinPrevious Study

(a)

minus40

minus30

minus20

minus10

0

10

20

30

40

1 101 201 301 401 501

SinSpeckle

(b)








(a) (b)




Previous study [12]





0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)


Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001


1601 1801




minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror


05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667







5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)




Previous study [12]





0

001

002

003

004

005

minus3

minus2

minus1

0

1

1

2

3

Disp

lace

men

t (cm

)


Squa

re er

ror

201 401 601 801 1001 12 01 1401 2001


1601 1801




minus3

minus4

minus2

minus1

0

1

2

3

4

Disp

lace

men

t (cm

)

Squa

re er

ror


05045040350302502015010050

1 87 173

259

345

431

517603689775

861

947

1033

1119

1205

1291

1377

1463

1549

1635

1721

1807

1893

1979

2065

2151

2237

2323

2409

2495

2581

2667







5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













5 Conclusion


119901 If 119877

119901is large the









Highlights








Acknowledgments


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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