Research Article Resolution Enhancement Method Used for …downloads.hindawi.com/journals/js/2015/647427.pdf · 2019-07-31 · Research Article Resolution Enhancement Method Used

Research ArticleResolution Enhancement Method Used forForce Sensing Resistor Array

Karen Flores De Jesus1 Marvin H Cheng1 Lei Jiang1 and Ezzat G Bakhoum2

1Department of Mechanical and Aerospace Engineering West Virginia University Morgantown WV 26505 USA2Department of Electrical and Computer Engineering University of West Florida Pensacola FL 32514 USA

Correspondence should be addressed to Marvin H Cheng marvinchengmailwvuedu

Received 8 October 2014 Accepted 18 December 2014

Academic Editor Aldo Minardo

Copyright copy 2015 Karen Flores De Jesus et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Tactile sensors are one of themajor devices that enable robotic systems to interact with the surrounding environmentThis researchaims to propose a mathematical model to describe the behavior of a tactile sensor based on experimental and statistical analysesandmoreover to develop a versatile algorithm that can be applied to different tactile sensor arrays to enhance the limited resolutionWith the proposed algorithm the resolution can be increased up to twenty times if multiple measurements are available To verifyif the proposed algorithm can be used for tactile sensor arrays that are used in robotic system a 16 times 10 force sensing array (FSR)is adopted The acquired two-dimensional measurements were processed by a resolution enhancement method (REM) to enhancethe resolution which can be used to improve the resolution for single image or multiple measurements As a result the resolutionof the sensor is increased and it can be used as synthetic skin to identify accurate shapes of objects and applied forces

1 Introduction

Recent studies have proposed various approaches to integrat-ingmultiple tactile sensors into a robotic systemThe interac-tion between robotic systems and external environment hasbeen facilitated by the implementation of various sensorswhich can provide important data such as force positionand shape This work aims to present a tactile system thatemulates a synthetic skin which can detect applied force andthe geometric shape of the targeted objects This system isbased on the implementation of force sensing resistor (FSR)array because of its simple work principle and low cost Asingle FSR is a resistor that varies its resistance dependingon applied force The measurements of the tactile sensor arefirst acquired by a supporting circuit and then connected toa data acquisition station The major drawback of an FSRarray is that its resolution and repeatability are both notsatisfactory The measurement of a particular force cannotalways guarantee consistent resistance readout With theinconsistentmeasurement identification of geometric shapescannot be accurate As a result in order to improve theresolution of such a tactile sensor array an image processing

method is necessary In this study a resolution enhancementmethod (REM) that can accurately improve measurementquality of a low resolution image is proposed

The resolution enhancement is an interpolation processof calculating the values of intermediate pixels between theknown pixels of certain low resolution measurement [1]Such kind of methods is commonly divided into differentcategories such as bilinear interpolation nearest neighborinterpolation bicubic interpolation [2] and adaptive cubicspline [3]These techniques are highly used in image process-ing to enhance the image resolutionMany studies using thesetechniques to develop new algorithms have been reportedFor instance the existing Bicubic Convolution algorithm canconvey low resolution images into sharper edges imagesHowever it also produces certain undesirable results whensome textures details need to be preserved In order to com-pensate for this shortcoming Dengwen [4] proposed a newalgorithm based on Bicubic Convolution (BC) Interpolationwhich can produce sharp edges as well as texture detailsOther than these methods super-resolution algorithm [5ndash7] has been widely investigated in image processing field aswell One of the major advantages is that this method can

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 647427 12 pageshttpdxdoiorg1011552015647427

2 Journal of Sensors

greatly improve limited resolution images acquired by lowcost imaging devices It can generate high-quality images byintegratingmultiple low resolution andblurred imageswithinthe same targeted area This technique has been applied tospecific fields such as satellite data surveillance images andmedical imaging

To obtain better image quality Chu et al [8] proposedan improved super-resolution algorithm using a gradient-based adaptive interpolation This approach not only takesinto account the distance between pixels but considers thelocal gradient of the low resolution image The importanceof the pixels is determined by the value of the gradient Toimprove the quality for single low resolution image Yang etal in [9] proposed a method applied to a single image usingsparse representation

From their results super-resolution algorithm hasdemonstrated an excellent performance compared withthe conventional techniques for image processing Someresearchers also demonstrate that this method can be appliedto enhance the resolution of two-dimensional data acquiredby various instrumentation [10 11] Thus this methodcan be a means to improve the measured quality of dataacquisition devices with low resolution In this researcha resolution enhancement method modified from super-resolution algorithm that applies to low cost tactile systemto acquire force position weight and shape of a targetedobject is proposed With the adopted FSR array three majorobjectives need to be fulfilled They are (1) identification ofa statistical model of the tactile sensors (2) development ofsupporting hardware and software interface that can be easilyoperated by users and (3) implementation of a resolutionenhancement method to improve the image quality acquiredby the FSR

The organization of the paper is as follows In thesecond section we will discuss the statistical model andthe corresponding validation of an FSR sensor array Thethird section discusses the theoretical background of theproposed resolution enhanced algorithm (REM) based onsuper-resolution method and the implementation proce-dures Experimental results of both single measurement andmultiple datasets are demonstrated in the fourth sectionSummary and conclusions are given in the last section

2 Modeling and ExperimentalSetup of FSR Array

AForce Sensing Resistor (FSR) is a resistive sensor that can beused as a tactile sensor in engineering applications This typeof sensor changes its internal resistance corresponding to theapplied forceThe relationship between applied force and out-put resistance is inversely proportional which signifies thatthe resistance gradient decreases as applied force increasesTypically an FSRdevice ismainly composed of two substratesof resistive polyester which represent the top and the bottomcircuit and a spacer sandwiched between these two surfacesPhysically material and geometrical specifications of thespacer and the layers determine the force necessary to makecontact between the two substrates and hence to start varyingthe resistance

Figure 1 Layout of a Thru Mode FSR array and the configurationof the corresponding circuit

+5V

Radd

Vout

RFSR

Figure 2 Circuit of a voltage divider used to measure FSR output

FSR can be manufactured as a single sensor to measureapplied force and also an integration of multiple FSR canbe synthesized as an array of a fixed number of sensors tomeasure force distribution For instance Sensitronics [12] aprovider of tactile devices supplies two types of FSR arraysThru Mode and Shunt Mode A Shunt Mode sensor arrayintegrates 60 sensors accommodated in 10 rows by 6 columnsA Thru Mode sensor array includes 160 sensors arranged as16 rows by 10 columns In this paper a Thru Mode arrayis adopted due to its greater number of sensors The layoutand circuit configuration of a Thru Mode array are shown inFigure 1

21 Voltage Divider of FSR In order to read the varyingvoltage generated by an FSR an additional resistor (119877add)needs to be added to the voltage divider circuit Figure 2illustrates the basic configuration of the circuit The outputvoltage of the circuit is

119881out =119877FSR119877FSR + 119877add

sdot 119881in (1)

With this equation the variation of 119877FSR can be obtainedby measuring the output voltage 119881out To guarantee that

Journal of Sensors 3

DAQ

CD74HC4067E

CD74HC4067E

E

Z

E

Z

Digital output

Digital output

+5V

middot middot middot




10kΩ

S3S2S1S0

S3S2S1S0

Y3Y2Y1Y0

Y3Y2Y1Y0

Y15

Y15

Figure 3 Configuration of supporting circuit that scans all 160 FSR sensors

the data acquisition device can always read the voltagevariation according to the resistive change an optimal valueof 119877add needs to be determined Based on the experimentaldata the range of resistance of a single FSR varies from57 kΩ to 036 kΩ corresponding to an applied force between2 and 90N However aThruMode FSR array shifts the rangebetween 308 kΩ and 033 kΩ for the same force interval Byconsidering these values and (1) the resistance of individualFSR sensors can be determined Extremely large or small119877addcan yield a small readable range of resistance

22 Configuration of Experimental Setup In order to effi-ciently acquire readings of individual sensors of the ThruMode FSR array a supporting circuit that converts forceto voltage was fabricated Figure 3 shows a diagram of thecircuit which is capable of reading all 160 sensors of theThruMode FSR arrayThe circuit integrates twomultiplexers74HC4067E which can control up to 18 channels separatelyOne multiplexer is in charge of selecting the row and theother one is in charge of selecting the column The statesof the multiplexers are controlled by four digital inputs Thepurpose of the use of these devices is to simplify the 160individual voltage divider circuits The voltage outputs aredesignated by a data acquisition (DAQ) device An add-onresistor of 10 kΩ is part of voltage divider and the activation

voltage is set to be 5V The output voltage can be acquiredby an analog input channel of the DAQ device The analogoutputs and digital inputs are processed by aMATLAB script

The data acquisition device used is a NI-PCI-6221 DAQcard manufactured by National Instrument which is con-trolled by the MATLAB script The script is then in chargeof converting acquired voltages to corresponding forcesand displaying the image of the geometric shape of thedistributed force on the surface of FSR array The graphic-user-interface (GUI) of the script includes three main partsa three-dimensional block display of force distribution ofevery sensor a 16 times 10 table that demonstrates the numericalreadings of applied forces and a two-dimensional image thatshows the shape of the object placed on the array Due tothe switching mechanism the steady-state of each readingfrom individual sensor is sim01 sec Thus the required timeto complete 160 readings of all sensors is approximately18 seconds The GUI and the displayed distribution of themeasurement are shown in Figure 4

23 Statistical Models in Different Regions Themajor advan-tages of an FSR array include the following (1) the supportingcircuit is easy to implement and (2) the cost of an FSR arrayis low compared with other types of sensors However theaccuracy of such kind of sensors is typically an issue For


Figure 4 GUI interface of the data acquisition system used for the FSR array

instance identical force with samemagnitudemay not alwaysyield the same resistance Such a phenomenon is extremelysevere for a force between 0 and 20N Thus precision ofFSR sensors within this specific range needs to be improvedhardware-wise

To identify the relationship between applied force andmeasured output of an FSR sensor in a Thru Mode array 17forces with different magnitudes between 0 and 90N wereapplied to a single sensor to establish the possible statisticalmodel An identical force was tested twelve times for thepurpose of consistence However since the array has 160sensors it is not realistic to identify all the 160 relationshipsInstead 22 sensors in 6 different areas were tested Figure 5illustrates the diagram of the sensor array and the locationsof the selected sensors Depending on the location thesensors behave differently The difference of measurementsat different location can be caused by the existing stress andpossible deformation while being fabricated In particularif the FSR array is wrapped on a curvilinear surface theresistance of sensors under zero loads in different regionsneeds to be identified to compensate for preexisting stressAfter analyzing the experimental data all the tested pointswere classified into six different groups Groups A B C andD are the sensors located along the borderline of the sensorarray and Groups E and F are the sensors located in thecentral area

Figure 6 illustrates distributions of statistical data ofgroups in different regions In this figure the solid linesare the mean value of the measurements and the dashlines are the bands that cover 99 of the measurement (ormean value plusmn 3 times standard deviation) It is clear that therelationships between the resistance and the applied forceare consistent if the applied force is greater than 20N Basedon the experimental results the statistical models of all sixregions are 119877A = 49936 119865

minus1105 119877B = 47183 119865minus1086 119877C =

80022 119865minus1259 119877D = 63284 119865

minus1210 119877E = 48280 119865minus1148

and 119877F = 34936 119865minus1052 where 119865 is the applied force and

119877119894

is the generated resistance of the FSR sensors in differentregions From the statistical result Groups A and B havesimilar properties which can be further grouped in the samecategory Due to the preexisting stress of manufacturingGroups C and D can only have similar properties when

Group AGroup BGroup C

Group DGroup EGroup F

1 15 7 16 2

11 1217 18

5 9 10 6

19 13 14 20

3 21 8 22 4

Figure 5 Locations of the tested sensors and the regions of 6different groups

the applied force is greater than a certain value though theyare both on the short sides of the border The functions ofdifferent groups are used to calibrate the measurement

24 Model Validation To validate the statistical modelsanother set of experiments on another Thru Mode FSRarray was performed In the experiment a single sensor wasselected from each group and a theoretical value of resistancewas predicted using the correspondingmodelsThe predictedvalues were then compared with the output of the selectedsensors in the corresponding areas A range of forces from20 to 90N was applied by a force gauge and the resistancewas measured Table 1 lists the difference between modeledresistance and the physical measurement

As shown in the table the maximum error is 4 and theaverage error of all groups is only sim08 The negative errormeans that the physical measurement is smaller than themodeled resistance As a conclusion themathematicalmodel


Group A Group B

Group C Group D

Group E Group F

102

100

Mean + 3stdMean minus 3std

MeanMean + 3stdMean minus 3std

Mean

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

102

100

102

100

102

100

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Figure 6 Locations of the measured sensors


Table 1 Signature profiles of 119877A119877B at different rotating speeds

Force (N) Group A Group BModeled (kΩ) Meas (kΩ) Error () Modeled (kΩ) Meas (kΩ) Error ()

20 182 183 039 182 185 14430 116 119 213 117 115 minus20840 085 088 369 086 083 minus34850 066 069 402 067 069 23160 054 056 331 055 056 12570 046 047 284 047 048 25580 039 041 390 040 039 minus37490 035 036 391 036 035 minus172

Force (N) Group C Group DModeled (kΩ) Meas (kΩ) Error () Modeled (kΩ) Meas (kΩ) Error ()

20 184 187 151 169 166 minus16130 111 110 minus049 103 107 34940 077 080 381 073 075 27850 058 059 152 056 057 23560 046 048 378 045 046 29670 038 039 246 037 036 minus29080 032 033 257 032 032 00090 028 027 minus267 027 028 239

Force (N) Group E Group FModeled (kΩ) Meas (kΩ) Error () Modeled (kΩ) Meas (kΩ) Error ()

20 155 158 193 149 149 minus03230 097 095 minus240 098 095 minus27140 070 068 minus282 072 071 minus15450 054 056 336 057 058 17160 044 044 000 047 049 39670 037 037 000 040 039 minus26080 032 032 000 035 035 00090 028 028 000 031 030 minus240

can accurately predict the value of the resistance caused by theapplied force

3 Resolution Enhancement Method

31 Modified Super-Resolution Method The basic idea of theproposed resolution enhancement method (REM) is that itreconstructs a high resolution image by processing severallower resolution measurements from the same object withslightly different viewpoints In order to reconstruct a highresolution output from low resolution data two constraintsneed to be modeled to solve this ill-posed problem [9]Assume that the sampled data is A which is the blurred anddownsampled measurement of the original object and B isthe original object Thus the relationship betweenA and B is

A = S sdotH sdot B (2)

where H is the blurring filter corresponding to a possi-ble perturbation and S is the downsampling operator Toapply the inverting procedure a linear interpolation amongsamples is adopted for a fast transformation The proposedmethod includes the following phases registration fusion

and deblurring In order to convert the two-dimensionalacquired data from lower resolution to a higher resolutionoutput an estimation algorithm is developed Among differ-entmethods themaximum likelihood approach presented byBresler andMacovski [13] is one of the most intuitive ways todefine the optimal reconstructed signal B which satisfies

B = argB

min [S sdotH sdot B]119879 sdotWminus1 sdot [S sdotH sdot B] (3)

whereW is a weightedmatrix that decreases the impact of theinput noise To obtain the maximum likelihood status of theestimated information a gradient interpolation is used Theinterpolation among four adjacent samples is processed as ablock Each block is transformed from a 2 times 2 matrix to an119871 times 119871matrix Hence if the low resolution data is an image of119873times119873 elements or pixels the high resolution output becomesan image of dimension 119871119873 times 119871119873 The diagram in Figure 7illustrates the gradient interpolation applied to a 2 times 2 block

Depending on the availability of datasets the proposedREM method can be applied to a single dataset or multipledatasets for better image quality In case only one lowresolution measurement can be available the procedure that


x

y

x

y y

y

(a) LR image4 times 4 pixel

(b) Enhancedimage by L = 2

3 times 3 pixel

(c) Enhancedimage by L = 3

6 times 6 pixel

a1 1 a1 2

a2 1 a2 2

Figure 7 Schematic illustration of a low resolution block reconstructed to a higher resolution

reconstructs a high resolution image is based on gradientinterpolationThe gradient interpolation of the 119896th block canbe represented as

B119896

= T119879 sdot A119896

sdot T (4)

whereT is the gradient transformationmatrixThe size of thetransformation matrix T is 2 times 119871 which is a linear iterationapproximation matrix The size ofA

119896

is 2 times 2 which includesthe four corners of the targeted areaAfter the transformationthe matrix B

119896

becomes an 119871 times 119871 matrix The value 119871 isdetermined Once all blocks are processed individual blockscan be combined and the synthesized output becomes

B =119873times119873

⋃

119896=1

B119896

(5)

A gradient interpolation method is adopted to approximatethe slopes among points due to its fast calculation speed

32 Translation and Integration of Multiple MeasurementsHowever due to perturbations and limited resolution of theacquisition device a single sample is usually not enough toidentify all the details inmost cases whichmeans some infor-mation can bemissed By takingmultiple measurements oneof the samples is possibly to contain some details that othersamples do not have Thus the missing information can bepossibly collected and revealed if multiple measurements areacquired In other words the quality of the output imagecan be improved by applying the proposed REM method tomultiple sets of measurements

In order to acquire more details multiple measurementswithminor translations and rotations in either the acquisitiondevice or the targeted object can be helpful With the tinymovements small details can be revealed The main idea isthat the acquired data of the targeted object always has aslight difference in every measurement By collecting thesetiny differences from various sampled datasets unclear detailof existing parts will be concentrated Hence it is importantto develop a method to register the position of the individualsampled datasets to a common reference map

To find a common reference many pattern recognitiontechniques [14 15] were tested However with the limitedresolution of acquired measurement it is difficult to identifymultiple objects that can align multiple images correctly onthe same map Thus a contrast map was adopted to identifythe area occupied by the targeted object in individual mea-surement To build a contrastmap allmeasured samples wereconverted into a black-and-white image which is determinedby the difference among adjacent samples If the differencesare larger than a preset threshold the specific locations areregistered Once the contrast information is collected theoriginal image can be divided into clusters All clusters withthe targeted object are identified on each sample data Thusa common reference map can be applied to bring all the areasto the same coordinates With all targeted objects aligned toa common coordinate the proposed REM can be applied toindividualmeasurements [11]The proposed datasets are thencombined to obtain a single image that includes all the detailsfrom every image The simplest combination method is totake the average of every pixel That is

B = 1119872

119872

sum

119894=1

B119894

(6)

where119872 is the number of total measurements and B119894

is the119894th processed dataset Deblurring technique using a Wienerfilter [16] can be adopted to remove the blurred effect causedby the operation of low-pass filter

33 Resolution Enhancement of a Sensor Array The adoptedtactile sensor array is a Thru Mode FSR array provided bySensitronics LLCThis array is composed of 160 sensors thatis a 16 times 10matrix While measuring the object is placed onthe surface of the Thru Mode FSR array The measurementsof individual sensors are then collected by a DAQ stationHowever due to the low resolution of the sensor array thegeometric shape of the object can barely be identified evenafter all the readings are taken Due to the low resolutionand repeatability of tactile devices a resolution enhancement


50

100

150

200

250

300

350

400

450

50

100

150

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250

300

350

400

450

50

100

150

200

250

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350

400

450

50

100

150

200

250

300

350

400

450

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100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400 100 200 300 400

100 200 300 400 100 200 300 400 100 200 300 400

Original sample Patch size = 2 Patch size = 3

Patch size = 4 Patch size = 5 Patch size = 6

480 times 480 pixels 240 times 240 pixels

PSNR = 315dB

160 times 160 pixels

PSNR = 301dB


PSNR = 293dB

96 times 96 pixels

PSNR = 287 dB

80 times 80 pixels

PSNR = 283 dB

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400

Patch size = 8 Patch size = 10

60 times 60 pixels

PSNR = 278dB

48 times 48 pixels

PSNR = 274dB

Figure 8 Comparison of reconstructed results among different patch sizes

method is requiredThe procedure of data collection and dataprocessing follows the steps discussed

It is also required to have ametric that estimates the quan-titative improvement of the proposed technique However itcan be difficult to determine the improvement of the pro-cessed outcomewithout a reference To quantize the quality ofapproximated outcomes PSNR (peak signal-to-noise ratio)

can be used to evaluate the distortion after approximationThe metric of PSNR between original measurement B andprocessed measurement B is defined as

PSNR = 20 sdot log10

Lumiance

(11198732

)sum119872

119894=1

sum119872

119894=1

10038161003816100381610038161003816B (119894 119895) minus B (119894 119895)10038161003816100381610038161003816

2

(7)


38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)

Figure 9 (a) An annulus placed on the adopted FSR array (b) original 16 times 10 pixel measurement and (c) processed outcome with a 2 times 10transformation matrix (119871 = 10)

where 119872 is the size of the measurement The luminance isthe largest possible value of the signal In general the largerPSNR value implies that the reconstructed image is a betterapproximation of the original image To evaluate the outputquality of the proposed iteration method it is recommendedthat the value of PSNR should not be lower than 25 dBmdashifthe two datasets are converted to 8-bit grayscale images Therelative difference between twoPSNRvalues for two differentreconstructed images gives the metrics of the reconstructionor compression quality

In this section a measurement of two sets of datameasuring the same sample with different resolutions wasused to evaluate the effectiveness of the proposed techniqueThe measurement of Figure 8 is a roughness analysis dataacquired using NanoScope manufactured by Digital Instru-ments The original scan size is 7593 120583m with a resolutionof 512 times 512 samples To evaluate the proposed method withdifferent sizes of approximation patch the data was croppedto 480 times 480 samples The image was downsampled to differ-ent sizes and then restored to the original size accordinglyThe selected patch sizes are 2 3 4 5 6 8 and 10 Basedon the values of PSNR the quality of restored image can bedetermined From the results shown in Figure 8 the PSNR

drops from 315 dB to 287 dB which is sim3 dB when the patchsize is 5 The quality can still be acceptable if the patch size is10 since the PSNR is still greater than the threshold of 25 dB

4 Experimental Results

41 Processing of a Single Set of Data To verify that REM canbe used in all kind of scenarios several objects with differentshapes and sizes are used In the experiments the object isplaced on the surface of aThruMode FSR array with an 86Nforce appliedThe force was calibrated by a force gauge (FGE-20X manufactured by Shimpo Instruments) The individualreadings of all sensors are then acquired by the DAQ stationand saved as a raw image Based on the adopted FSR arraythe resolution of the image is 16 times 10 pixels This image isthen processed by the proposed REM To further improvethe image qualitymultiple images are used to compensate themissing parts of a single acquired image

The object used is an annulus shown as Figure 9(a)Figure 9(b) demonstrates the raw data of the measurementThe processed results are shown in Figure 9(c) with 119871 = 10It is clear that the geometric shape of the annulus can be


5

10

15

5

10

15

5

10

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5

10

15

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10

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15

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10

15

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10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

Figure 10 Twelve measurements of an ldquoLrdquo shape object located at different locations

outlined even with only a singlemeasurementThe image canbe further enhanced by a deblurring algorithm

42 Processing of Multiple Sets of Data The results afterprocessing and deblurring a single image are usually goodenough to identify the shape of the targeted object Howevera single image can sometimes miss some detail due to twoimportant reasons the low repeatability of the tactile sensorand the physical malformations of the analyzed objects In

this section multiple measurements of the same objects usedin the previous section are processed it is anticipated togenerate a more accurate result

In each case twelve measurements were collected fromindividual objectsTheobjectwas placed at different positionson the surface of the adopted FSR array while the data wascollectedThe patch size used for multiple sets of data is 3 times 3Figure 10 illustrates the twelve measurements of an ldquoLrdquo shapeobject Once the twelve measurements of a specific object


(a) (b) (c)

Outline of shape

Figure 11 (a) Processed result from multiple measurements (b) processed result from a single measurement and (c) the ldquoLrdquo shape objectlocated on the FSR array

were collected all the measured outcomes need to be shiftedto a common reference individually

To simplify the calculation the area enclosing the objectis considered to be within an119873times119873 square matrix Each areahas its unique associated coordinate (119909 119910) at four corners inits original measurement This targeted area can be foundby applying a predetermined threshold value to individualimages and locating the boundary points of the four cornersAs a result the maximum and minimum points in 119909- and119910-axis of individual images can be identified to enclose theobject which determine location of targeted area Once thetargeted areas are identified for individual measurementsREM is applied to the areas for resolution enhancement AfterREM has been applied centroids of the enhanced imagesare calculated It is assumed that the centroids of the sameobject are located at the same positionThus by knowing thelocations of centroids all the targeted areas from individualmeasurements can be brought to a common coordinate

The individual enhanced results are then merged to gen-erate a final result that contains all the information processedAfter translation and averaging the processed and deblurredimages are shown in Figure 11(a) Notice that the translationactually reduces the image size of processed result since allindividual measurements are shifted to a common referencecoordinate Nevertheless compared with the processed resultfrom a singlemeasurement as shown in Figure 11(b) it is clearthat the result from multiple measurements actually revealsmissing detail in the processed result of a singlemeasurementeven if the resolutions are identical The improvement ofquality can be evaluated by the metric of PSNR The originalsensor array is first gridded into a 30 times 48 map with theresolution of the desired patch By overlapping the geometricshape on the map all occupied cells are marked as 255(gray scale) while others are marked as 0 Then the PSNRsof the two outcomes can be evaluated With this method

the processed result from multiple measurements has higherPSNR However the PSNR can only be used to evaluate thesimilarity of geometric shapes It cannot be used to evaluatethe force distribution since the data of force measurementwith high resolution is not available Figures 12(a) and 12(b)demonstrate the processed results from multiple measure-ments and a single measurement of another ldquoTrdquo shape objectIt is also clear that the results from multiple measurementscan show better detail even if the resolution of the twoprocessed data is identical

5 Conclusion

The goal of this research was to propose an integrated tactilesystem that can be used as a synthetic skin which can providedata of force distribution weight location and geometricshape while contacting an object The adopted Thru ModeFSR array has the advantages of low cost and convenientdeployment A mathematical approximation of the sensorarray has also been identified A supporting circuit and DAQsystem were set up as well Though the resolution is limitedthe proposed REM method can greatly enhance the reso-lution In particular processing with multiple measurementcan greatly improve the resolution of the raw data The maincontribution of this study was the implementation of theintegrated system which provides a skin-like platform In thefuture the proposed algorithm will be applied to differentplatforms for other applications such as AFM images andscanning of 3D images

Conflict of Interests

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


Outline of shape

(a) (b) (c)

Figure 12 (a) Processed result from multiple measurements (b) processed result from a single measurement and (c) the ldquoTrdquo shape objectlocated on the FSR array

Acknowledgment

The authors gratefully acknowledge NASA West VirginiaSpace Grant Consortium for the financial support of thisproject

References

[1] S E El-Khamy M M Hadhoud M I Dessouky B M Salamand F E-S Abd El-Samie ldquoNew techniques to conquer theimage resolution enhancement problemrdquo Progress in Electro-magnetics Research B vol 7 pp 13ndash51 2008

[2] D Shepard ldquoA two-dimensional interpolation function forirregularly-spaced datardquo in Proceedings of the 1968 23rd ACMNational Conference pp 517ndash524 1968

[3] J H Friedman ldquoMultivariate adaptive regression splinesrdquo TheAnnals of Statistics vol 19 no 1 pp 1ndash67 1991

[4] Z Dengwen ldquoAn edge-directed bicubic interpolation algo-rithmrdquo in Proceedings of the 3rd International Congress on Imageand Signal Processing (CISP rsquo10) vol 3 pp 1186ndash1189 YantaiChina October 2010

[5] W T Freeman T R Jones and E C Pasztor ldquoExample-basedsuper-resolutionrdquo IEEE Computer Graphics and Applicationsvol 22 no 2 pp 56ndash65 2002

[6] S C ParkM K Park andMG Kang ldquoSuper-resolution imagereconstruction a technical overviewrdquo IEEE Signal ProcessingMagazine vol 20 no 3 pp 21ndash36 2003

[7] T Kasetkasem M K Arora and P K Varshney ldquoSuper-resolution land cover mapping using a Markov random fieldbased approachrdquo Remote Sensing of Environment vol 96 no3-4 pp 302ndash314 2005

[8] J Chu J Liu J Qiao X Wang and Y Li ldquoGradient-basedadaptive interpolation in super-resolution image restorationrdquoin Proceedings of the 9th International Conference on SignalProcessing (ICSP rsquo08) pp 1027ndash1030 Beijing China October2008

[9] J Yang J Wright T S Huang and Y Ma ldquoImage super-reso-lution via sparse representationrdquo IEEE Transactions on ImageProcessing vol 19 no 11 pp 2861ndash2873 2010

[10] D J van den Heever K Schreve and C Scheffer ldquoTactilesensing using force sensing resistors and a super-resolutionalgorithmrdquo IEEE Sensors Journal vol 9 no 1 pp 29ndash35 2009

[11] M H Cheng S D Cronin K A Sierros and E A BakhoumldquoA versatile spatial resolution enhancement method for dataacquisitionrdquoMeasurement Science and Technology In press

[12] ldquoFSR 101mdashthe basicsrdquo 2013 httpsensitronicscomfsr101htm[13] Y Bresler andAMacovski ldquoExactmaximum likelihood param-

eter estimation of superimposed exponential signals in noiserdquoIEEE Transactions on Acoustics Speech and Signal Processingvol 34 no 5 pp 1081ndash1089 1986

[14] S Baker and T Kanade ldquoLimits on super-resolution and howto break themrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 24 no 9 pp 1167ndash1183 2002

[15] A K Jain R P W Duin and J Mao ldquoStatistical patternrecognition a reviewrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 22 no 1 pp 4ndash37 2000

[16] J Biemond R L Lagendijk and R M Mersereau ldquoIterativemethods for image deblurringrdquo Proceedings of the IEEE vol 78no 5 pp 856ndash883 1990

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



greatly improve limited resolution images acquired by lowcost imaging devices It can generate high-quality images byintegratingmultiple low resolution andblurred imageswithinthe same targeted area This technique has been applied tospecific fields such as satellite data surveillance images andmedical imaging

To obtain better image quality Chu et al [8] proposedan improved super-resolution algorithm using a gradient-based adaptive interpolation This approach not only takesinto account the distance between pixels but considers thelocal gradient of the low resolution image The importanceof the pixels is determined by the value of the gradient Toimprove the quality for single low resolution image Yang etal in [9] proposed a method applied to a single image usingsparse representation

From their results super-resolution algorithm hasdemonstrated an excellent performance compared withthe conventional techniques for image processing Someresearchers also demonstrate that this method can be appliedto enhance the resolution of two-dimensional data acquiredby various instrumentation [10 11] Thus this methodcan be a means to improve the measured quality of dataacquisition devices with low resolution In this researcha resolution enhancement method modified from super-resolution algorithm that applies to low cost tactile systemto acquire force position weight and shape of a targetedobject is proposed With the adopted FSR array three majorobjectives need to be fulfilled They are (1) identification ofa statistical model of the tactile sensors (2) development ofsupporting hardware and software interface that can be easilyoperated by users and (3) implementation of a resolutionenhancement method to improve the image quality acquiredby the FSR

The organization of the paper is as follows In thesecond section we will discuss the statistical model andthe corresponding validation of an FSR sensor array Thethird section discusses the theoretical background of theproposed resolution enhanced algorithm (REM) based onsuper-resolution method and the implementation proce-dures Experimental results of both single measurement andmultiple datasets are demonstrated in the fourth sectionSummary and conclusions are given in the last section

2 Modeling and ExperimentalSetup of FSR Array

AForce Sensing Resistor (FSR) is a resistive sensor that can beused as a tactile sensor in engineering applications This typeof sensor changes its internal resistance corresponding to theapplied forceThe relationship between applied force and out-put resistance is inversely proportional which signifies thatthe resistance gradient decreases as applied force increasesTypically an FSRdevice ismainly composed of two substratesof resistive polyester which represent the top and the bottomcircuit and a spacer sandwiched between these two surfacesPhysically material and geometrical specifications of thespacer and the layers determine the force necessary to makecontact between the two substrates and hence to start varyingthe resistance

Figure 1 Layout of a Thru Mode FSR array and the configurationof the corresponding circuit

+5V

Radd

Vout

RFSR

Figure 2 Circuit of a voltage divider used to measure FSR output

FSR can be manufactured as a single sensor to measureapplied force and also an integration of multiple FSR canbe synthesized as an array of a fixed number of sensors tomeasure force distribution For instance Sensitronics [12] aprovider of tactile devices supplies two types of FSR arraysThru Mode and Shunt Mode A Shunt Mode sensor arrayintegrates 60 sensors accommodated in 10 rows by 6 columnsA Thru Mode sensor array includes 160 sensors arranged as16 rows by 10 columns In this paper a Thru Mode arrayis adopted due to its greater number of sensors The layoutand circuit configuration of a Thru Mode array are shown inFigure 1

21 Voltage Divider of FSR In order to read the varyingvoltage generated by an FSR an additional resistor (119877add)needs to be added to the voltage divider circuit Figure 2illustrates the basic configuration of the circuit The outputvoltage of the circuit is

119881out =119877FSR119877FSR + 119877add

sdot 119881in (1)

With this equation the variation of 119877FSR can be obtainedby measuring the output voltage 119881out To guarantee that


DAQ

CD74HC4067E

CD74HC4067E

E

Z

E

Z

Digital output

Digital output

+5V





10kΩ

S3S2S1S0

S3S2S1S0

Y3Y2Y1Y0

Y3Y2Y1Y0

Y15

Y15












minus1105 119877B = 47183 119865minus1086 119877C =

80022 119865minus1259 119877D = 63284 119865

minus1210 119877E = 48280 119865minus1148


119877119894




1 15 7 16 2

11 1217 18

5 9 10 6

19 13 14 20

3 21 8 22 4






Group A Group B

Group C Group D

Group E Group F

102

100



Mean

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

102

100

102

100

102

100

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)
















B = argB





x

y

x

y y

y



3 times 3 pixel


6 times 6 pixel

a1 1 a1 2

a2 1 a2 2



B119896

= T119879 sdot A119896

sdot T (4)


119896


119896


B =119873times119873

⋃

119896=1

B119896

(5)





B = 1119872

119872

sum

119894=1

B119894

(6)





50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400 100 200 300 400

100 200 300 400 100 200 300 400 100 200 300 400




PSNR = 315dB


PSNR = 301dB


PSNR = 293dB

96 times 96 pixels

PSNR = 287 dB

80 times 80 pixels

PSNR = 283 dB

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400


60 times 60 pixels

PSNR = 278dB

48 times 48 pixels

PSNR = 274dB






Lumiance

(11198732

)sum119872

119894=1

sum119872

119894=1

10038161003816100381610038161003816B (119894 119895) minus B (119894 119895)10038161003816100381610038161003816

2

(7)


38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)









5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










DAQ

CD74HC4067E

CD74HC4067E

E

Z

E

Z

Digital output

Digital output

+5V





10kΩ

S3S2S1S0

S3S2S1S0

Y3Y2Y1Y0

Y3Y2Y1Y0

Y15

Y15












minus1105 119877B = 47183 119865minus1086 119877C =

80022 119865minus1259 119877D = 63284 119865

minus1210 119877E = 48280 119865minus1148


119877119894




1 15 7 16 2

11 1217 18

5 9 10 6

19 13 14 20

3 21 8 22 4






Group A Group B

Group C Group D

Group E Group F

102

100



Mean

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

102

100

102

100

102

100

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)
















B = argB





x

y

x

y y

y



3 times 3 pixel


6 times 6 pixel

a1 1 a1 2

a2 1 a2 2



B119896

= T119879 sdot A119896

sdot T (4)


119896


119896


B =119873times119873

⋃

119896=1

B119896

(5)





B = 1119872

119872

sum

119894=1

B119894

(6)





50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400 100 200 300 400

100 200 300 400 100 200 300 400 100 200 300 400




PSNR = 315dB


PSNR = 301dB


PSNR = 293dB

96 times 96 pixels

PSNR = 287 dB

80 times 80 pixels

PSNR = 283 dB

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400


60 times 60 pixels

PSNR = 278dB

48 times 48 pixels

PSNR = 274dB






Lumiance

(11198732

)sum119872

119894=1

sum119872

119894=1

10038161003816100381610038161003816B (119894 119895) minus B (119894 119895)10038161003816100381610038161003816

2

(7)


38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)









5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














minus1105 119877B = 47183 119865minus1086 119877C =

80022 119865minus1259 119877D = 63284 119865

minus1210 119877E = 48280 119865minus1148


119877119894




1 15 7 16 2

11 1217 18

5 9 10 6

19 13 14 20

3 21 8 22 4






Group A Group B

Group C Group D

Group E Group F

102

100



Mean

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

102

100

102

100

102

100

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)
















B = argB





x

y

x

y y

y



3 times 3 pixel


6 times 6 pixel

a1 1 a1 2

a2 1 a2 2



B119896

= T119879 sdot A119896

sdot T (4)


119896


119896


B =119873times119873

⋃

119896=1

B119896

(5)





B = 1119872

119872

sum

119894=1

B119894

(6)





50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400 100 200 300 400

100 200 300 400 100 200 300 400 100 200 300 400




PSNR = 315dB


PSNR = 301dB


PSNR = 293dB

96 times 96 pixels

PSNR = 287 dB

80 times 80 pixels

PSNR = 283 dB

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400


60 times 60 pixels

PSNR = 278dB

48 times 48 pixels

PSNR = 274dB






Lumiance

(11198732

)sum119872

119894=1

sum119872

119894=1

10038161003816100381610038161003816B (119894 119895) minus B (119894 119895)10038161003816100381610038161003816

2

(7)


38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)









5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Group A Group B

Group C Group D

Group E Group F

102

100



Mean

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

0 20 40 60 80Force (N)

102

100

102

100

102

100

102

100

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)

Resis

tanc

e (kO

hm)
















B = argB





x

y

x

y y

y



3 times 3 pixel


6 times 6 pixel

a1 1 a1 2

a2 1 a2 2



B119896

= T119879 sdot A119896

sdot T (4)


119896


119896


B =119873times119873

⋃

119896=1

B119896

(5)





B = 1119872

119872

sum

119894=1

B119894

(6)





50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400 100 200 300 400

100 200 300 400 100 200 300 400 100 200 300 400




PSNR = 315dB


PSNR = 301dB


PSNR = 293dB

96 times 96 pixels

PSNR = 287 dB

80 times 80 pixels

PSNR = 283 dB

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400


60 times 60 pixels

PSNR = 278dB

48 times 48 pixels

PSNR = 274dB






Lumiance

(11198732

)sum119872

119894=1

sum119872

119894=1

10038161003816100381610038161003816B (119894 119895) minus B (119894 119895)10038161003816100381610038161003816

2

(7)


38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)









5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























B = argB





x

y

x

y y

y



3 times 3 pixel


6 times 6 pixel

a1 1 a1 2

a2 1 a2 2



B119896

= T119879 sdot A119896

sdot T (4)


119896


119896


B =119873times119873

⋃

119896=1

B119896

(5)





B = 1119872

119872

sum

119894=1

B119894

(6)





50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400 100 200 300 400

100 200 300 400 100 200 300 400 100 200 300 400




PSNR = 315dB


PSNR = 301dB


PSNR = 293dB

96 times 96 pixels

PSNR = 287 dB

80 times 80 pixels

PSNR = 283 dB

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400


60 times 60 pixels

PSNR = 278dB

48 times 48 pixels

PSNR = 274dB






Lumiance

(11198732

)sum119872

119894=1

sum119872

119894=1

10038161003816100381610038161003816B (119894 119895) minus B (119894 119895)10038161003816100381610038161003816

2

(7)


38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)









5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










x

y

x

y y

y



3 times 3 pixel


6 times 6 pixel

a1 1 a1 2

a2 1 a2 2



B119896

= T119879 sdot A119896

sdot T (4)


119896


119896


B =119873times119873

⋃

119896=1

B119896

(5)





B = 1119872

119872

sum

119894=1

B119894

(6)





50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400 100 200 300 400

100 200 300 400 100 200 300 400 100 200 300 400




PSNR = 315dB


PSNR = 301dB


PSNR = 293dB

96 times 96 pixels

PSNR = 287 dB

80 times 80 pixels

PSNR = 283 dB

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400


60 times 60 pixels

PSNR = 278dB

48 times 48 pixels

PSNR = 274dB






Lumiance

(11198732

)sum119872

119894=1

sum119872

119894=1

10038161003816100381610038161003816B (119894 119895) minus B (119894 119895)10038161003816100381610038161003816

2

(7)


38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)









5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400 100 200 300 400

100 200 300 400 100 200 300 400 100 200 300 400




PSNR = 315dB


PSNR = 301dB


PSNR = 293dB

96 times 96 pixels

PSNR = 287 dB

80 times 80 pixels

PSNR = 283 dB

50

100

150

200

250

300

350

400

450

50

100

150

200

250

300

350

400

450

100 200 300 400 100 200 300 400


60 times 60 pixels

PSNR = 278dB

48 times 48 pixels

PSNR = 274dB






Lumiance

(11198732

)sum119872

119894=1

sum119872

119894=1

10038161003816100381610038161003816B (119894 119895) minus B (119894 119895)10038161003816100381610038161003816

2

(7)


38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)









5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










38 cm

(a)

2

4

6

8

10

2 4 6 8 10

12

14

16

(b)

20

40

60

80

100

20 40 60 80 100

120

140

160

(c)









5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10

2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10







(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)

Outline of shape






5 Conclusion





Outline of shape

(a) (b) (c)


Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Outline of shape

(a) (b) (c)


Acknowledgment


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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Research Article Resolution Enhancement Method Used for …downloads.hindawi.com/journals/js/2015/647427.pdf · 2019-07-31 · Research Article Resolution Enhancement Method Used