Research Article Analysis and Implementation of Kidney ...downloads.hindawi.com/archive/2015/581961.pdf · kidney image with stone portion Counter (2^14) (14-bit counter) Image preprocessing

Research ArticleAnalysis and Implementation of Kidney StoneDetection by Reaction Diffusion Level Set SegmentationUsing Xilinx System Generator on FPGA

Kalannagari Viswanath1 and Ramalingam Gunasundari2

1Pondicherry Engineering College Puducherry 605 014 India2Department of ECE Pondicherry Engineering College Puducherry 605 014 India

Correspondence should be addressed to Kalannagari Viswanath viswa kvpecedu

Received 20 October 2014 Revised 15 April 2015 Accepted 20 April 2015

Academic Editor Mohamed Masmoudi

Copyright copy 2015 K Viswanath and R Gunasundari This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Ultrasound imaging is one of the available imaging techniques used for diagnosis of kidney abnormalities whichmay be like changein shape and position and swelling of limb there are also other Kidney abnormalities such as formation of stones cysts blockageof urine congenital anomalies and cancerous cells During surgical processes it is vital to recognize the true and precise location ofkidney stone The detection of kidney stones using ultrasound imaging is a highly challenging task as they are of low contrast andcontain speckle noiseThis challenge is overcome by employing suitable image processing techniquesThe ultrasound image is firstpreprocessed to get rid of speckle noise using the image restoration process The restored image is smoothened using Gabor filterand the subsequent image is enhanced by histogram equalization The preprocessed image is achieved with level set segmentationto detect the stone region Segmentation process is employed twice for getting better results first to segment kidney portion andthen to segment the stone portion respectively In this work the level set segmentation uses two terms namely momentum andresilient propagation (Rprop) to detect the stone portion After segmentation the extracted region of the kidney stone is given toSymlets Biorthogonal (bio37 bio39 and bio44) and Daubechies lifting scheme wavelet subbands to extract energy levels Theseenergy levels provide evidence about presence of stone by comparing them with that of the normal energy levels They are trainedby multilayer perceptron (MLP) and back propagation (BP) ANN to classify and its type of stone with an accuracy of 988 Theprosed work is designed and real time is implemented on both Filed Programmable Gate Array Vertex-2Pro FPGA using XilinxSystem Generator (XSG) Verilog and Matlab 2012a

1 Introduction

Kidney stone disease is one of the major life threatening ail-ments persistingworldwideThe stone diseases remain unno-ticed in the initial stage which in turn damages the kidney asthey develop Amajority of people are affected by kidney fail-ure due to diabetes mellitus hypertension glomerulonephri-tis and so forth Since kidney malfunctioning can be menac-ing diagnosis of the problem in the initial stages is advisableUltrasound (US) image is one of the currently availablemethods with noninvasive low cost and widely used imagingtechniques for analyzing kidney diseases [1] Shock wavelithotripsy (SWL) percutaneous nephrolithotomy (PCNL)

and relative super saturation (RSS) are the available prac-tices to test urine The Robertson Risk Factor Algorithms(RRFA) are open and are used for laparoscopic surgery thesealgorithms are assigned for exceptional [2] special casesHyaluronan is a large (gt106Da) linear glycosaminoglycancomposed of repeating units of glucuronic acid (GlcUA) andN-acetyl glucosamine (GlcNAc) disaccharides [3] It has asignificant role in a number of processes that can eventuallylead to renal stone disease including urine concentrationuric acid salt form crystal crystallization inhibition crystalretention magnesium ammonium phosphate and aminoacid

Hindawi Publishing CorporationVLSI DesignVolume 2015 Article ID 581961 10 pageshttpdxdoiorg1011552015581961

2 VLSI Design

Rahman andUddin have proposed diminution of specklenoise and segmentation from US image It not only detectsproblem in the kidney region but also provides image qualityenhancement [1] Hafizah proposed kidney US images anddivides them into four dissimilar categories normal bacte-rial infection cystic disease and kidney stones using graylevel cooccurrencematrix (GLCM)This categorization helpsdoctors to identify the abnormalities in kidney [4] Rathi andPalani have proposed a Hierarchical Self-Organizing Map(HSOM) for brain tumours using the segmentation techniqueand wavelets packets Accuracy of the results was found to becorrect up to 97 [5] Norihiro Koizumi has proposed highintensity focused ultrasound (HIFU) technique for terminat-ing tumours and stones [6 7] Viswanath and Gunasundaripropose content descriptive multiple stones detection usinglevel set segmentation wavelets processing for identificationof kidney stone and artificial neural network (ANN) forclassification The results yielded a maximum accuracy of9866 [8] The MLP-BP ANN is found to perform better interms of accuracy 92with a speed of 044 sec and it is foundto be very sensitive [9 10] The noninvasive combinationof renal using pulsed cavitation US therapy proposed thatshock wave lithotripsy (ESWL) has become a customary forthe treatment of calculi located in the kidney and ureter[11] Tamilselvi and Thangaraj have proposed seeded regiongrowing based on segmentation and classification of kidneyimages with stone sizes using CAD system [12] Bagleyet al estimate location of urinary stones with unenhancedcomputed tomography (CT) using half-radiation (low) dosecompared with the standard dose Out of the 50 patientsexamined 35 patients were found to have a single stonewhile the rest had multiple stones [13] The solution for localminima and segmentation problem was proposed by ThordAndersson Gunnar Lathen with modified gradient searchand level set segmentation technique [2] Templates basedtechnique was proposed by Emmanouil Skounakis for 3Ddetection of kidneys and their pathology in real time Itsaccuracy was found to be 972 and abnormalities in kidneyshad an accuracy of 961 [7] Gabor function is used forachievement of optimal sharpening and smoothening of 2Dimage in both time and frequency resolutions [14] Chen et alhave proposed the finite element method based 3D tumorgrowth prediction using longitudinal kidney tumor images[15] Using the linear elastic theory Owen et al proposedpressure finding in fluid for calculating the depth of shockwave scattering by kidney stone in water [16] The pH valuebased prediction of stone formation epidemiologically hasbeen proposed by Kok [17] Datar has proposed the seg-mentation of the desired portion using initial seed selectiongrowing and regionmergingwithout any edge detection [18]Multilayer perceptron and back propagation implementationonFPGAandASICdesignwere carried out byRaj andPinjare[19]

This research paper ensues as follows In Section 2 prob-lem statement is demarcated Section 3 defines the proposedmethod in Section 4 image segmentation to locate thekidney stone in Section 5 optimized energy calculation ofsegmented portion is discussed in Section 6 wavelets basedenergy extraction Section 7 explains the artificial neural

networks classifiers used in Section 8 experiments results arediscussed and in the last section conclusion of the paper withscope for future work is given

2 Problem Statement

The kidney malfunctioning can be life intimidating Henceearly detection of kidney stone is essential Precise identi-fication of kidney stone is vital in order to ensure surgicaloperations success The ultrasound images of kidney com-prise speckle noise and are of low contrast which makes theidentification of kidney abnormalities a difficult task As aresult the doctors may find identification of small stones andthe type is difficult and challenging for identify the smallkidney stones and their type appropriately To address thisissue a reaction diffusion level set segmentation is proposedto identify location of the stone it is implemented in real timeon Vertex-2Pro FPGAwith Verilog HDL using Xilinx SystemGenerator blocks from Matlab 2012a which is compatiblewith xilinx134 ISE and lifting scheme wavelets subbands areemployed for extraction of the energy levels of the stoneThe results are analyzed using MLP-BP ANN algorithms forclassification and its type of stone [20]

3 Methodology

Figure 1 shows the overall block diagram of the proposedmethod It consists of the following blocks via kidney imagedatabase image preprocessing image segmentation waveletprocessing and ANN classification

31 Kidney Image Database Kidney image database consistsof nearly 500US kidney images collected from differentindividuals of various hospitals It consists of both normaland abnormal images stored in the database One of theimages is selected from the database and subjected to stonedetection process

32 Image Preprocessing The aim of preprocessing is toimprove the acquired low contrast ultrasound image withspeckle noise It suppresses the undesired distortions andenhances certain image features significant for further pro-cessing and stone detection Without preprocessing the USimage quality may not be good for analyzing For surgicaloperations it is essential to identify the location of kidneystone accurately Preprocessing helps to overcome this issueof low contrast and speckle noise reduction Figure 2 showsthe steps involved in preprocessing of US image which are asfollows

(1) image restoration(2) smoothing and sharpening(3) contrast enhancement

321 Image Restoration Image restoration is meant to mit-igate the degradation of the US image Degradation may bedue to motion blur noise and camera misfocus The mainpurpose of image restoration is to reduce the degradations

VLSI Design 3

Read image text from run command

Store the pixels in IP core RAM memory

Monitor to view kidney image with

stone portion

Counter(2^14)

(14-bit counter)Image

preprocessing

Level set segmentation for

kidney portion

Kidney stone portion segmented by level

set method

Extraction of energy values by using

lifting scheme DWT

MLP-BP ANN

Doctor can view stone size with some color for treatment

Only kidney portion

Only stone portion

Energy values

Displays whether the kidney is normal or abnormal

Write input image pixels into RAM

Read all pixels from RAM

Figure 1 Proposed block diagram for kidney stone detection

Preprocessed image

Smoothening and sharpening by Gabor

Contrast enhancement

Image restoration

US kidney image

Figure 2 Preprocessing of kidney image

that are caused during acquisition of US scanning In thissystem level set function is used for proper orientationUsingplane curve motion curve smoothers shrinks are eventuallyremoved [1]ThusMerriman and Sethian proposed evolutionbetween max(119896 0) and min(119896 0)

119891 (119909) =

max (119896 0) if 119886 (119909 119910) lt 119866 (119909 119910)

min (119896 0) otherwise(1)

where 119886(119909 119910) is average intensity small neighborhood and119866(119909 119910) is median in the same neighborhood

322 Smoothing and Sharpening The restored image isenriched with optimal resolution in both spatial and fre-quency domains using Gabor filter This filter acts as aband pass filter with local spatial frequency distribution [6]Image smoothing and removal of noise is performed usingconvolution operatorThe standard deviation of the Gaussianfunction can be modified to tune the degree of smootheningand its hardware results are shown in Figure 3

323 Contrast Enhancement Histogram equalization isemployed for improvement of the low contrast US image andachievement of the uniform intensity This approach can beused on the image as a whole or to a part of an image Inthis system contrast enhancement of the images is executedby transforming the image intensity values such that thehistogram of the output image approximately matches aspecified histogram and its results are shown in Figure 4Theinput and output signal are of same data type

4 Image Segmentation

In the segmentation process five level set methods in all arediscussed all implemented and compared

41 Conventional LSS In the conventional level set methodconsider a closed parameterized planar curve or surface

4 VLSI Design

Figure 3 Hardware results of smoothening filter

Figure 4 Hardware result of contrast enhancement

denoted by 119862(119910 119905) [0 1]119909 119877+rarr 119877119899 where 119899 = 2 is for

planar curve and 119899 = 3 is for surface and 119905 is the artificialtime generated by themovement of the initial curve or surface1198620(119910) in its inward normal direction119873simThe curve or surface

evolution equation is as follows [21]

119862 (119910 119905 = 0) = 1198620 (119910)

119862119905= 119865119873

(2)

where 119865 is the force functionIn the above equation intrinsic drawback of interactively

solving (2) lies in its difficulty to handle topological changesof the moving front such as splitting and merging [21] Thisproblem can be eliminated by using the level set method(LSM) by modifying the above equation (2) by taking thederivative with respect to time 119905 on the both sides yieldingthe following equation

120601119905+nabla120601sdot 119862119905= 120601119905+Δ120601sdot 119865119873 = 0

120601 (119909 119905 = 0) = 1206010 (119909) (3)

where gradient operator nabla(sdot) = 120597(sdot)1205971199091 120597(sdot)1205971199092 120597(sdot)120597119909119899and 1206010(119909) is the initial LSF 1198620(119910) = 119909 | 1206010(119909) = 0But (3) fails for too flat or too steep near the zero level set

to address this issue re-initialization is introduced

42 Reinitialization LSS But during evolution the level setfunction (LSF) fails for too flat or too steep near the zero levelset causing serious numerical errors Therefore a procedure

called reinitialization is periodically employed to reshape itto be a signed distance function (SDF) In reinitialization thedistance signed function is 120601(119909) = 1plusmndist2(119909)where dist(sdot) isa distance function and plusmn denotes the sign inside and outsidethe contour [21] But it has many problems such as expensivecomputational cost blocking the emerging of new contours[21] failures when the LSF deviates much from an SDFand inconsistency between theory and implementation usingXSG shown in Figure 5 Therefore some formulation hasbeen proposed to regularize the variational LSF to eliminatethe reinitialization and computational cost The followingreinitialization equation is given by

120601119905+ 119878 (1206010) (

1003816100381610038161003816nabla120601

1003816100381610038161003816) = 0 (4)

where 1206010 = 1206010radic12060120 + Δ1199092 1206010 is the initial LSF and Δ119909 is thespatial step

43 Distance Regularized Level Set Evolution (DRLSE) Liet al proposed a signed distance penalizing energy func-tional is given by

119875 (120601)

12int

Ω

(1003816100381610038161003816nabla120601

1003816100381610038161003816minus 1)2 119889119909 (5)

Equation (5) measures the closeness between an LSF (120601) andan SDF in the domain Ω sub 119877

119899 119899 = 2 or 3 By calculus ofvariation [21] the gradient flow of 119875(120601) is obtained as

120601119905= minus119875120601(120601) = div (1199031 (120601) nabla120601) (6)

Equation (6) is a diffusion equation with rates

1199031 (120601) = 1minus 11003816100381610038161003816nabla120601

1003816100381610038161003816

(7)

However 1199031(120593) rarr minusinfin when |nabla120593| rarr 0 which may

cause oscillation in the final LSF 120593 This problem is solvedby applying a new diffusion rate

1199032 (120601) =

sin (2prod1003816100381610038161003816nabla120601

1003816100381610038161003816)

2prod1003816100381610038161003816nabla120601

1003816100381610038161003816

if 1003816100381610038161003816nabla120601

1003816100381610038161003816le 1

1 minus 11003816100381610038161003816nabla120601

1003816100381610038161003816

if 1003816100381610038161003816nabla120601

1003816100381610038161003816ge 1

(8)

and a constrained level set diffusion rate as

1199033 (120601) = 119867119901 (1003816100381610038161003816nabla120601

1003816100381610038161003816minus 1) (9)

where119867119901(119911) = (12)[1 + (2prod)arctan(119911120588)]

And 120588 is a fixed parameter The DRLSE methods using1199031(120593) 1199032(120593) and 119903

3(120593) are called generalized DRLSE such as

GDRLSE1 GDRLSE2 and GDRLSE3 respectively

44 Reaction Diffusion LSS The RD equation is constructedby adding a diffusion term into the conventional LSE equa-tion Such an introduction of diffusion to LSE makes LSEstable without reinitialization The diffusion term ldquo120576Δ120601rdquo was

VLSI Design 5

Resolution of thegrid at x and y

Euler step

Iterations

System generator

Gateway out

1

05

1000

dx

dyreinit_SD 120601

120572

Iterations

Out

reinit_SD

Figure 5 Hardware implementation of signed distance function using XSG

added to the LSE equation (3) we get the following equationfor RD

120601119905= 120576Δ120601minus

1120576

119871 (120601) 119909120576Ω sub 119877119899

Subject 997888rarr 120601 (119909 119905 = 0 120576) = 1206010 (119909) (10)

where 120576 is a small positive constant 119871(120593) for PDE-based LSMor 119871(120593) = minus119865120575(120593) for variational LSM Δ is the Laplacianoperator defined by Δ(sdot) = sum

119899

119894=1(1205972(sdot)120597119909

2119894) and 1206010(119909) is

the initial LSF Equation (10) has two dynamic processesthe diffusion term 120576Δ120601 gradually regularizes the LSF to bepiecewise constant in each segment domain Ω

119894and the

reaction term ldquominus120576minus1119871(120593)rdquo forces the final stable solution of(10) to 119871(120593) = 0 which determinesΩ

119894

RD Level Set Segmentation Algorithm

(1) Initialization is as follows 120601119899 = 1206010 119899 = 0

(2) Compute 0119899+12 as 120601119899+12=120601119899

=Δ1199052119871(120601119899

)

(3) Compute 0119899+1as 120601119899+12=120601119899

+Δ1199052119871(120601119899

)

(4) If 0119899+1 satisfies stationary condition stop otherwise119899 = 119899 + 1 and return to step (2) 120601119899 = 120601119899+12

From the analysis in DRLSE and RD the equilibriumsolution of (10) is seen t as 120576 rarr 0

+ which is thecharacteristic of phase transition On the other hand the saidequation intrinsic problemof phase transition that is the stiffparameter 120576minus1 makes (10) difficult to implement In TSSMsection we propose a splitting method to implement (10) toreduce the side effect of stiff parameter 120576minus1

441 Two-Step Splitting Method (TSSM) for RD A TSSMalgorithm to implement RD has been proposed in [21] togenerate the curvature-dependent motion In [21] the reac-tion function is first forced to generate a binary function withvalues 0 and 1 and then the diffusion function is applied tothe binary function to generate curvature-dependentmotiondifferent from [21] where the diffusion function is used togenerate curvature-dependent motion in our proposed RDbased LSM the LSE is driven by the reaction function that

is the LSE equation Therefore use of the diffusion functionto regularize the LSF generated by the reaction function isproposed following TSSM to solve the RD The steps are asfollows

(1) Solve the reaction term 120593119905= minus120576minus1119871(120593) with 120593(119909 119905 =

0) = 120593119899 till some time 119879

119903to obtain the intermediate

solution denoted by 120593119899+12 = 120593(119909 119879119903)

(2) Solve the diffusion term 120593119905= 120576Δ120593 120593(119909 119905 = 0) =

120593119899+12 till some time 119879

119889 and then the final level set

is 120593119899+1 = 120593(119909 119879119889)

Although the second step faces the rush of moving the zerolevel set away from its original position But this can beeliminated through the choice of a td small enough comparedto the spatial resolutions

In the above two terms by choosing small 119879119903and 119879

119889

we can discretely approximate 120593119899+12 and 120593119899+1 as 120593119899+12 =

120593119899+ Δ1199051(minus120576minus1119871(120593119899)) and 120593

119899+1= 120593119899+12

+ Δ1199052(120576Δ120593119899+12

)respectively where the time steps Δ119905

1and Δ119905

2represent

the times 119879119903and 119879

119889 respectively Obviously we can inte-

grate the parameter 120576 into the time steps Δ1199051and Δ119905

2as

Δ1199051larr Δ119905

1(minus120576minus1) and Δ119905

2larr Δ119905

2120576 and hence similar to

the diffusion-generated or convolution-generated curvaturemotion we only need to consider the two time steps Δ119905

1and

Δ1199052to keep numerical stability

Speed of Segmentation For the reinitialization methods (4)should be iterated several times to make the LSF be an SDFwhile keeping the zero level set stationary This is highlytime-consuming for the reinitialization methods [21] TheGDRLSE methods are computationally much more efficientthan reinitialization method Equation (8) in each iterationof the computation ofGDRLSE includes two components theregularization term and LSE term driven by force 119865 in eachiteration of RD method the computation also includes twosimilar components The only difference is that we split thecomputation into two steps first compute the LSE term andthen compute the diffusion termTherefore the computationcomplexity of RD is similar to that of GDRLSE methods andusing Xilinx system generator implemented on hardwareits XSG are shown in the Figure 6 The proposed design isimplemented using Verilog HDL configured on Vertex-2Pro

6 VLSI Design

Curvature central

Reg Xie

Regularization function

Curvature 3D

Delta function

Heavisible

Signed distance function

Constant

Signed distance function to circle

Cv 2D

Reinitialization for signed distance for 3D

NeumanBoundCond

Constant

reinit_SD_3D Out

Gateway out

dx

dyreinit_SD120601120572

Iterations

nrowncol

ic sdf2circlef

F

jc

r

l120583

120582_1 CV_2D120582_2Timestepdelt2

1000

Κ

120601 Curvature_central

120601 Curvature_3D

absR

120601 Reg_Xie Κ_H

120601 RegularizeF r

120601Δ Δ_h

120598

120601Heaviside

120598H

10

Img Top_main 120601InGateway in

System generator

dx

dydz120572Iterations

120601

120601

fNeumanBoundCond g

120581

Figure 6 Curvature central regularization delta signed distance signed distance function to circle and reinitialization of signed distanceof reaction and diffusion level set function segmentation

(a) (b)

Figure 7 The FPGA output in the monitor through VGA The first image shows the kidney portion segmented from the US image andsecond image witnesses the detected stone in that image indicated with red color

FPGA and output of FPGA is applied to monitor throughVGA for displaying input image and processed image asshown Figure 7

5 Lifting Scheme Wavelets Processing

The segmented image (only stone) obtained from the previ-ous block is applied to the lifting scheme wavelet processingblockThis block consists ofDaubechies filter (Db12) Symletsfilter (sym12) and Biorthogonal filter (bio37 bio39 and

bio43) In Daubechies filter (Db12) the number 12 denotesthe number of vanishing moments The higher the numberof vanishing moments the smoother the wavelet (and longerthe wavelet filter) and the length of the wavelet (and scaling)filter should be twice that of the number [5] Symlets filter(sym12) extracts the kidney image features and analysesthe discontinuities and abrupt changes contained in thesignals One of the 12th-order Symlets wavelets is used forfeature extraction Biorthogonal filter (bio37 bio39 andbio44) filterrsquos wavelet energy signatures were considered andaverages of horizontal and vertical coefficients details were

VLSI Design 7

Stone portion image

Daubechies (Db 12)

Energy values from different filters

Symlets (sym 12)Biorthogonal (bio 12)

Figure 8 Wavelets filters to extract energy features

Dh12Kidney stone image

Cv12Split Predict Update

Figure 9 2D lifting scheme DWT

calculated Figure 8 shows different filter used in the liftingscheme that gives different energy levels or energy featuresThese energy features will have significant difference if thereis any stone present in the particular region or location Theidentification of type of stone is explained in next section

In 2D lifting scheme wavelets transformation consists ofupdate and predictor to get Db12 sym12 bio37 bio39 andbio43 as shown in Figure 9

The equations of predict and update are given by

1198891119894= 120572 (1199092119894 +1199092119894+2) + 1199092119894+1

1198861119894= 120573 (119889

1119894+119889

1119894minus1) + 1199092119894

1198892119894= 120574 (119886

1119894+ 119886

1119894+1) + 119889

1119894

1198862119894= 120575 (119889

2119894+119889

2119894minus1) + 119886

1119894

119889119894=

1198892119894

120576

(11)

where 1199092119894and 1199092119894+2

are even pixels 1199092119894+1

is odd pixels of stoneimage and 120572 120573 120574 120575 120576 are the constants

6 ANN Classification

Two architectures are used in the ANN classification namelymultilayer perceptron and back propagation which aredescribed in detail in the following sections

61 Multilayer Perceptron (MLP) A multilayer perceptronis a feedforward artificial neural network algorithm thathelps in the mapping of different sets of energy and averagevalues obtained from the wavelets subbands energy extrac-tion shown in Table 1 These energy values are given to theinput layer and multiplied with initial weights The backpropagation is the modified version of linear perceptronwhich uses three or more hidden layers with the nonlinearactivation function The back propagation is the most exten-sively used learning algorithm for multilayer perceptron in

Table 1 Min and max features of kidney images database which areenlarged table of the table in the GUI of lifting scheme wavelets

Min-max

Db12Dh1average

00026ndash00169

Db12cVenergy

00011ndash90990e minus 04

Sym12Dh1average

00026ndash00169

Sym12cVenergy


rbio37Dh1average

00052ndash00255

rbio37cDenergy


rbio37cVenergy


rbio37Dh1average

00066ndash00272

rbio39cDenergy


rbio39cVenergy


rbio39cVaverage

00039ndash00061

rbio44Dh1average


rbio44cHenergy

14336e minus 04ndash87336e minus 04

rbio44cVenergy


8 VLSI Design

Figure 10 Lifting scheme wavelets subband decomposition energyfeature extraction and classifications

neural networks and it employs gradient descent tominimizethe mean squared error between the network output valueand the desired output value These error signals are takenfor completion of the weight updates which represent thepower of knowledge learnt by the back propagation [22]Multilayer perceptron with back propagation (MLP-BP) isthe core algorithm Based on the literature survey MLP-BPalgorithm was found to be better than the other algorithmsin terms of accuracy speed and performance

7 Implementation and Results

The implementation of the proposed work is completedusing Verilog on Vertex-2Pro FPGA and Matlab 2012a TheGraphical User Interface (GUI) is created for the developedsystem as shown in Figure 10 From the database of the USkidney images one kidney image is uploaded through theGUI The uploaded image is preprocessed and is shown inthe GUI The image segmentation option present in the GUIis executed as the next step to segment the kidney stoneportion from the image The segmented image is performedwith wavelet processing by picking one of the lifting waveletfilters shown in the GUI After selecting the filter for energylevel extraction a specific wavelet code will be invoked toget the subsequent image Then the feature extraction optionis selected to get list of energy levels extracted from thesegmented image

In the GUI shown in Figure 10 there is another tablewhich lists energy levels of all the kidney images present inthe database This is performed for testing the accuracy ofMLP-BP ANN system in identifying the kidney images asnormal or abnormal and to mention the type of the detectedstone Essentially the database should have both normal andabnormal images in which we should have knowledge of thenumber of normal and abnormal image count During thetest it is found that our system can classify the kidney images

0

30

60

90

120

150

180

210

240

270

300

330

004

003

002

001

Compass plot for the all energy and average features of database kidney stone detection

Figure 11 Energy and average feature values are within 0 to 1 range

Table 2 Design summary of proposed hardware implementation

Parameters Used Available UtilizationNumber of slices Register 377 28800 1Number of flip flops used 376Number of latches used 507 28200 1Mo of slice LUTs 424 28200 1Dynamic power 0488WGate delay 165 ns

as normal and abnormal almost with accuracy of 988 Theenergy levels of all kidney images from database are extractedand plotted and are shown in Figure 12 The maximum peakplot indicates presence of stone All extracted features arefrom range of 0 to 1 as shown in Figure 11

Table 1 shows the lists of energy levels extracted fromthe segmented image This table is the enlarged version ofthe table shown in the GUI The rows of the table give theindividual energy levels of each kidney image in the databaseThe columns of the table give the energy level extracted fromthe images in the database with respect to each wavelet filterThe first two columns correspond to Daubechies filter thethird and the fourth columns correspond to symlets12 Thefifth sixth and seventh columns correspond to Biorthogonalfilter (Bio37) The eighth ninth and tenth columns corre-spond to Biorthogonal filter (Bio39) The eleventh twelfthand thirteenth columns correspond to Biorthogonal filter(Bio44)

The proposed work is implemented on Vertex-2ProFPGA and the device speed is increased by 35 with a gatedelay of 3765 ns The number of slices LUTs are deceased by23 in comparison with the existing methods The designsummary table of the proposed hardware model is shown inTable 2

VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de

times10minus3 Energy values

Energy featuresStone detection

CenterMaxmin

Figure 12 Lifting scheme filters energy and average features of database kidney images

8 Conclusion and Scope for Future Work

The proposed work is implemented on Vertex-2Pro FPGAemploying level set segmentation with momentum andresilient propagation parameters It is found to be capable ofany satisfactory achievement in identifying the stones in theUS kidney image The device performance is also pleasingwith very low utilization of resources The energy levelsextracted from the lifting scheme wavelet subbands thatis Daubechies (Db12) Symlets (sym12) and Biorthogonalfilterers (bio37 bio39 and bio44) give the perfect indicationof the difference in the energy levels of the stone portion com-pared to that of normal kidney region The ANN is trainedwith normal kidney image and classified image input for nor-mal or abnormal conditions by considering extracted energylevels fromwavelets filtersThedeveloped system is examinedfor different kidney images from the database and the resultsare effective in classifying the types of stone successfully withthe accuracy of 988 [23] Thus this system can be readilyutilized in the hospitals for patients with abnormality inkidney This work proves that the combination of level setsegmentation lifting scheme wavelet filters and multilayerperceptron with back propagation means a better approachfor the detection of stones in the kidney In the future workthe system will be designed for real time implementation byplacing biomedical sensors in the abdomen region to capturekidney portion The captured kidney image is subjected tothe proposed algorithm to process and detect stone on FPGAusing hardware description language (HDL) The identifiedkidney stone in the image is displayed with colour for easyidentification and visibility of stone in monitor

Conflict of Interests

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

References

[1] T Rahman and M S Uddin ldquoSpeckle noise reduction andsegmentation of kidney regions from ultrasound imagerdquo inProceedings of the 2nd International Conference on InformaticsElectronics and Vision (ICIEV rsquo13) pp 1ndash5 IEEE DhakaBangladesh May 2013

[2] W G Robertson ldquoMethods for diagnosing the risk factors ofstone formationrdquoArab Journal of Urology vol 10 no 3 pp 250ndash257 2012

[3] B Hess ldquoMetabolic syndrome obesity and kidney stonesrdquoArabJournal of Urology vol 10 no 3 pp 258ndash264 2012

[4] WMHafizah ldquoFeature extraction of kidney ultrasound imagesbased on intensity histogram and gray level co-occurrencematrixrdquo in Proceedings of the 6th Asia Modeling Symposium(AMS rsquo12) pp 115ndash120 IEEE May 2012

[5] V P G P Rathi and S Palani ldquoDetection and characterizationof brain tumor using segmentation based on HSOM waveletpacket feature spaces and ANNrdquo in Proceedings of the 3rdInternational Conference on Electronics Computer Technology(ICECT rsquo11) vol 6 pp 274ndash277 IEEE Kanyakumari IndiaApril 2011

[6] N Koizumi J Seo D Lee et al ldquoRobust kidney stone trackingfor a non-invasive ultrasound theragnostic systemmdashservoingperformance and safety enhancementrdquo in Proceedings of theIEEE International Conference on Robotics and Automation(ICRA rsquo11) pp 2443ndash2450 Shanghai China May 2011

[7] M E Abou El-Ghar A A Shokeir H F Refaie and A REl-Nahas ldquoLow-dose unenhanced computed tomography fordiagnosing stone disease in obese patientsrdquo Arab Journal ofUrology vol 10 no 3 pp 279ndash283 2012

[8] K Viswanath and R Gunasundari ldquoKidney stone detectionfrom ultrasound images by Level Set Segmentation and mul-tilayer perceptron ANNrdquo in Proceedings of the InternationalConference on Communication and Comuting (IMCIET-ICCErsquo14) pp 38ndash48 Elsevier 2014

10 VLSI Design

[9] N Dheepa ldquoAutomatic seizure detection using higher ordermoments amp ANNrdquo in Proceedings of the 1st International Con-ference on Advances in Engineering Science and Management(ICAESM rsquo12) pp 601ndash605 March 2012

[10] K Kumar ldquoArtificial neural network for diagnosis of kidneystone diseaserdquo International Journal of Information Technologyand Computer Science vol 7 pp 20ndash25 2012

[11] P M Morse and H Feshbach ldquoThe variational integral and theEuler equationsrdquo in Methods of Theoretical Physics Part I pp276ndash280 1953

[12] P R Tamilselvi and P Thangaraj ldquoComputer aided diagnosissystem for stone detection and early detection of kidney stonesrdquoJournal of Computer Science vol 7 no 2 pp 250ndash254 2011

[13] D H Bagley K A Healy and N Kleinmann ldquoUreteroscopictreatment of larger renal calculi (gt2 cm)rdquo Arab Journal ofUrology vol 10 no 3 pp 296ndash300 2012

[14] L Shen and S Jia ldquoThree-dimensional gabor wavelets for pixel-based hyperspectral imagery classificationrdquo IEEE Transactionson Geoscience and Remote Sensing vol 49 no 12 pp 5039ndash5046 2011

[15] X Chen R Summers and J Yao ldquoFEM-based 3-D tumorgrowth prediction for kidney tumorrdquo IEEE Transactions onBiomedical Engineering vol 58 no 3 pp 463ndash467 2011

[16] N R Owen O A Sapozhnikov M R Bailey L Trusov and LA Crum ldquoUse of acoustic scattering to monitor kidney stonefragmentation during shock wave lithotripsyrdquo in Proceedingsof the IEEE Ultrasonics Symposium pp 736ndash739 VancouverCanada October 2006

[17] D J KokMetaphylaxis Diet and Lifestyle in Stone Disease vol10 Arab Association of Urology Production and Hosting byElsevier BV 2012

[18] D S Datar ldquoColor image segmentation based on Initial seedselection seeded region growing and region mergingrdquo Interna-tional Journal of Electronics Communication amp Soft ComputingScience and Engineering vol 2 no 1 pp 13ndash16 2012

[19] P C P Raj and S L Pinjare ldquoDesign and analog VLSI imple-mentation of neural network architecture for signal processingrdquoEuropean Journal of Scientific Research vol 27 no 2 pp 199ndash216 2009

[20] J Martınez-Carballido C Rosas-Huerta and J M Ramırez-Cortes ldquoMetamyelocyte nucleus classification using a setof morphologic templatesrdquo in Proceedings of the ElectronicsRobotics and Automotive Mechanics Conference (CERMA rsquo10)pp 343ndash346 IEEE Morelos Mexico September-October 2010

[21] C Li C Xu C Gui and M D Fox ldquoDistance regularized levelset evolution and its application to image segmentationrdquo IEEETransactions on Image Processing vol 19 no 12 pp 3243ndash32542010

[22] M Stevenson R Winter and B Widrow ldquoSensitivity of feed-forward neural networks to weight errorsrdquo IEEE Transactionson Neural Networks vol 1 no 1 pp 71ndash80 1990

[23] K Viswanath and R Gunasundari ldquoDesign and analysis per-formance of kidney stone detection from ultrasound image bylevel set segmentation and ANN classificationrdquo in Proceedingsof the International Conference on Advances in ComputingCommunications and Informatics (ICACCI rsquo14) pp 407ndash414IEEE New Delhi India September 2014

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


2 VLSI Design

Rahman andUddin have proposed diminution of specklenoise and segmentation from US image It not only detectsproblem in the kidney region but also provides image qualityenhancement [1] Hafizah proposed kidney US images anddivides them into four dissimilar categories normal bacte-rial infection cystic disease and kidney stones using graylevel cooccurrencematrix (GLCM)This categorization helpsdoctors to identify the abnormalities in kidney [4] Rathi andPalani have proposed a Hierarchical Self-Organizing Map(HSOM) for brain tumours using the segmentation techniqueand wavelets packets Accuracy of the results was found to becorrect up to 97 [5] Norihiro Koizumi has proposed highintensity focused ultrasound (HIFU) technique for terminat-ing tumours and stones [6 7] Viswanath and Gunasundaripropose content descriptive multiple stones detection usinglevel set segmentation wavelets processing for identificationof kidney stone and artificial neural network (ANN) forclassification The results yielded a maximum accuracy of9866 [8] The MLP-BP ANN is found to perform better interms of accuracy 92with a speed of 044 sec and it is foundto be very sensitive [9 10] The noninvasive combinationof renal using pulsed cavitation US therapy proposed thatshock wave lithotripsy (ESWL) has become a customary forthe treatment of calculi located in the kidney and ureter[11] Tamilselvi and Thangaraj have proposed seeded regiongrowing based on segmentation and classification of kidneyimages with stone sizes using CAD system [12] Bagleyet al estimate location of urinary stones with unenhancedcomputed tomography (CT) using half-radiation (low) dosecompared with the standard dose Out of the 50 patientsexamined 35 patients were found to have a single stonewhile the rest had multiple stones [13] The solution for localminima and segmentation problem was proposed by ThordAndersson Gunnar Lathen with modified gradient searchand level set segmentation technique [2] Templates basedtechnique was proposed by Emmanouil Skounakis for 3Ddetection of kidneys and their pathology in real time Itsaccuracy was found to be 972 and abnormalities in kidneyshad an accuracy of 961 [7] Gabor function is used forachievement of optimal sharpening and smoothening of 2Dimage in both time and frequency resolutions [14] Chen et alhave proposed the finite element method based 3D tumorgrowth prediction using longitudinal kidney tumor images[15] Using the linear elastic theory Owen et al proposedpressure finding in fluid for calculating the depth of shockwave scattering by kidney stone in water [16] The pH valuebased prediction of stone formation epidemiologically hasbeen proposed by Kok [17] Datar has proposed the seg-mentation of the desired portion using initial seed selectiongrowing and regionmergingwithout any edge detection [18]Multilayer perceptron and back propagation implementationonFPGAandASICdesignwere carried out byRaj andPinjare[19]

This research paper ensues as follows In Section 2 prob-lem statement is demarcated Section 3 defines the proposedmethod in Section 4 image segmentation to locate thekidney stone in Section 5 optimized energy calculation ofsegmented portion is discussed in Section 6 wavelets basedenergy extraction Section 7 explains the artificial neural

networks classifiers used in Section 8 experiments results arediscussed and in the last section conclusion of the paper withscope for future work is given

2 Problem Statement

The kidney malfunctioning can be life intimidating Henceearly detection of kidney stone is essential Precise identi-fication of kidney stone is vital in order to ensure surgicaloperations success The ultrasound images of kidney com-prise speckle noise and are of low contrast which makes theidentification of kidney abnormalities a difficult task As aresult the doctors may find identification of small stones andthe type is difficult and challenging for identify the smallkidney stones and their type appropriately To address thisissue a reaction diffusion level set segmentation is proposedto identify location of the stone it is implemented in real timeon Vertex-2Pro FPGAwith Verilog HDL using Xilinx SystemGenerator blocks from Matlab 2012a which is compatiblewith xilinx134 ISE and lifting scheme wavelets subbands areemployed for extraction of the energy levels of the stoneThe results are analyzed using MLP-BP ANN algorithms forclassification and its type of stone [20]

3 Methodology

Figure 1 shows the overall block diagram of the proposedmethod It consists of the following blocks via kidney imagedatabase image preprocessing image segmentation waveletprocessing and ANN classification

31 Kidney Image Database Kidney image database consistsof nearly 500US kidney images collected from differentindividuals of various hospitals It consists of both normaland abnormal images stored in the database One of theimages is selected from the database and subjected to stonedetection process

32 Image Preprocessing The aim of preprocessing is toimprove the acquired low contrast ultrasound image withspeckle noise It suppresses the undesired distortions andenhances certain image features significant for further pro-cessing and stone detection Without preprocessing the USimage quality may not be good for analyzing For surgicaloperations it is essential to identify the location of kidneystone accurately Preprocessing helps to overcome this issueof low contrast and speckle noise reduction Figure 2 showsthe steps involved in preprocessing of US image which are asfollows

(1) image restoration(2) smoothing and sharpening(3) contrast enhancement

321 Image Restoration Image restoration is meant to mit-igate the degradation of the US image Degradation may bedue to motion blur noise and camera misfocus The mainpurpose of image restoration is to reduce the degradations

VLSI Design 3




stone portion

Counter(2^14)


preprocessing


kidney portion


set method


lifting scheme DWT

MLP-BP ANN


Only kidney portion

Only stone portion

Energy values





Preprocessed image



Image restoration

US kidney image



119891 (119909) =

max (119896 0) if 119886 (119909 119910) lt 119866 (119909 119910)








4 VLSI Design






119862 (119910 119905 = 0) = 1198620 (119910)

119862119905= 119865119873

(2)



120601119905+nabla120601sdot 119862119905= 120601119905+Δ120601sdot 119865119873 = 0

120601 (119909 119905 = 0) = 1206010 (119909) (3)





120601119905+ 119878 (1206010) (

1003816100381610038161003816nabla120601

1003816100381610038161003816) = 0 (4)



119875 (120601)

12int

Ω

(1003816100381610038161003816nabla120601

1003816100381610038161003816minus 1)2 119889119909 (5)



120601119905= minus119875120601(120601) = div (1199031 (120601) nabla120601) (6)


1199031 (120601) = 1minus 11003816100381610038161003816nabla120601

1003816100381610038161003816

(7)



1199032 (120601) =

sin (2prod1003816100381610038161003816nabla120601

1003816100381610038161003816)

2prod1003816100381610038161003816nabla120601

1003816100381610038161003816

if 1003816100381610038161003816nabla120601

1003816100381610038161003816le 1

1 minus 11003816100381610038161003816nabla120601

1003816100381610038161003816

if 1003816100381610038161003816nabla120601

1003816100381610038161003816ge 1

(8)


1199033 (120601) = 119867119901 (1003816100381610038161003816nabla120601

1003816100381610038161003816minus 1) (9)






VLSI Design 5


Euler step

Iterations

System generator

Gateway out

1

05

1000

dx

dyreinit_SD 120601

120572

Iterations

Out

reinit_SD



120601119905= 120576Δ120601minus

1120576

119871 (120601) 119909120576Ω sub 119877119899

Subject 997888rarr 120601 (119909 119905 = 0 120576) = 1206010 (119909) (10)


119899

119894=1(1205972(sdot)120597119909

2119894) and 1206010(119909) is


119894and the


119894



(2) Compute 0119899+12 as 120601119899+12=120601119899

=Δ1199052119871(120601119899

)

(3) Compute 0119899+1as 120601119899+12=120601119899

+Δ1199052119871(120601119899

)







0) = 120593119899 till some time 119879




120593119899+12 till some time 119879


is 120593119899+1 = 120593(119909 119879119889)



119889


120593119899+ Δ1199051(minus120576minus1119871(120593119899)) and 120593

119899+1= 120593119899+12

+ Δ1199052(120576Δ120593119899+12


1and Δ119905

2represent

the times 119879119903and 119879



2as

Δ1199051larr Δ119905


2larr Δ119905



1and



6 VLSI Design

Curvature central

Reg Xie


Curvature 3D

Delta function

Heavisible


Constant


Cv 2D


NeumanBoundCond

Constant

reinit_SD_3D Out

Gateway out

dx


Iterations

nrowncol

ic sdf2circlef

F

jc

r

l120583


1000

Κ


120601 Curvature_3D

absR

120601 Reg_Xie Κ_H


120601Δ Δ_h

120598

120601Heaviside

120598H

10


System generator

dx


120601

120601

fNeumanBoundCond g

120581


(a) (b)






VLSI Design 7

Stone portion image

Daubechies (Db 12)










1198891119894= 120572 (1199092119894 +1199092119894+2) + 1199092119894+1

1198861119894= 120573 (119889

1119894+119889

1119894minus1) + 1199092119894

1198892119894= 120574 (119886

1119894+ 119886

1119894+1) + 119889

1119894

1198862119894= 120575 (119889

2119894+119889

2119894minus1) + 119886

1119894

119889119894=

1198892119894

120576

(11)

where 1199092119894and 1199092119894+2







Min-max

Db12Dh1average

00026ndash00169

Db12cVenergy


Sym12Dh1average

00026ndash00169

Sym12cVenergy


rbio37Dh1average

00052ndash00255

rbio37cDenergy


rbio37cVenergy


rbio37Dh1average

00066ndash00272

rbio39cDenergy


rbio39cVenergy


rbio39cVaverage

00039ndash00061

rbio44Dh1average


rbio44cHenergy


rbio44cVenergy


8 VLSI Design






0

30

60

90

120

150

180

210

240

270

300

330

004

003

002

001








VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de



CenterMaxmin






References









10 VLSI Design


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









VLSI Design 3




stone portion

Counter(2^14)


preprocessing


kidney portion


set method


lifting scheme DWT

MLP-BP ANN


Only kidney portion

Only stone portion

Energy values





Preprocessed image



Image restoration

US kidney image



119891 (119909) =

max (119896 0) if 119886 (119909 119910) lt 119866 (119909 119910)








4 VLSI Design






119862 (119910 119905 = 0) = 1198620 (119910)

119862119905= 119865119873

(2)



120601119905+nabla120601sdot 119862119905= 120601119905+Δ120601sdot 119865119873 = 0

120601 (119909 119905 = 0) = 1206010 (119909) (3)





120601119905+ 119878 (1206010) (

1003816100381610038161003816nabla120601

1003816100381610038161003816) = 0 (4)



119875 (120601)

12int

Ω

(1003816100381610038161003816nabla120601

1003816100381610038161003816minus 1)2 119889119909 (5)



120601119905= minus119875120601(120601) = div (1199031 (120601) nabla120601) (6)


1199031 (120601) = 1minus 11003816100381610038161003816nabla120601

1003816100381610038161003816

(7)



1199032 (120601) =

sin (2prod1003816100381610038161003816nabla120601

1003816100381610038161003816)

2prod1003816100381610038161003816nabla120601

1003816100381610038161003816

if 1003816100381610038161003816nabla120601

1003816100381610038161003816le 1

1 minus 11003816100381610038161003816nabla120601

1003816100381610038161003816

if 1003816100381610038161003816nabla120601

1003816100381610038161003816ge 1

(8)


1199033 (120601) = 119867119901 (1003816100381610038161003816nabla120601

1003816100381610038161003816minus 1) (9)






VLSI Design 5


Euler step

Iterations

System generator

Gateway out

1

05

1000

dx

dyreinit_SD 120601

120572

Iterations

Out

reinit_SD



120601119905= 120576Δ120601minus

1120576

119871 (120601) 119909120576Ω sub 119877119899

Subject 997888rarr 120601 (119909 119905 = 0 120576) = 1206010 (119909) (10)


119899

119894=1(1205972(sdot)120597119909

2119894) and 1206010(119909) is


119894and the


119894



(2) Compute 0119899+12 as 120601119899+12=120601119899

=Δ1199052119871(120601119899

)

(3) Compute 0119899+1as 120601119899+12=120601119899

+Δ1199052119871(120601119899

)







0) = 120593119899 till some time 119879




120593119899+12 till some time 119879


is 120593119899+1 = 120593(119909 119879119889)



119889


120593119899+ Δ1199051(minus120576minus1119871(120593119899)) and 120593

119899+1= 120593119899+12

+ Δ1199052(120576Δ120593119899+12


1and Δ119905

2represent

the times 119879119903and 119879



2as

Δ1199051larr Δ119905


2larr Δ119905



1and



6 VLSI Design

Curvature central

Reg Xie


Curvature 3D

Delta function

Heavisible


Constant


Cv 2D


NeumanBoundCond

Constant

reinit_SD_3D Out

Gateway out

dx


Iterations

nrowncol

ic sdf2circlef

F

jc

r

l120583


1000

Κ


120601 Curvature_3D

absR

120601 Reg_Xie Κ_H


120601Δ Δ_h

120598

120601Heaviside

120598H

10


System generator

dx


120601

120601

fNeumanBoundCond g

120581


(a) (b)






VLSI Design 7

Stone portion image

Daubechies (Db 12)










1198891119894= 120572 (1199092119894 +1199092119894+2) + 1199092119894+1

1198861119894= 120573 (119889

1119894+119889

1119894minus1) + 1199092119894

1198892119894= 120574 (119886

1119894+ 119886

1119894+1) + 119889

1119894

1198862119894= 120575 (119889

2119894+119889

2119894minus1) + 119886

1119894

119889119894=

1198892119894

120576

(11)

where 1199092119894and 1199092119894+2







Min-max

Db12Dh1average

00026ndash00169

Db12cVenergy


Sym12Dh1average

00026ndash00169

Sym12cVenergy


rbio37Dh1average

00052ndash00255

rbio37cDenergy


rbio37cVenergy


rbio37Dh1average

00066ndash00272

rbio39cDenergy


rbio39cVenergy


rbio39cVaverage

00039ndash00061

rbio44Dh1average


rbio44cHenergy


rbio44cVenergy


8 VLSI Design






0

30

60

90

120

150

180

210

240

270

300

330

004

003

002

001








VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de



CenterMaxmin






References









10 VLSI Design


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









4 VLSI Design






119862 (119910 119905 = 0) = 1198620 (119910)

119862119905= 119865119873

(2)



120601119905+nabla120601sdot 119862119905= 120601119905+Δ120601sdot 119865119873 = 0

120601 (119909 119905 = 0) = 1206010 (119909) (3)





120601119905+ 119878 (1206010) (

1003816100381610038161003816nabla120601

1003816100381610038161003816) = 0 (4)



119875 (120601)

12int

Ω

(1003816100381610038161003816nabla120601

1003816100381610038161003816minus 1)2 119889119909 (5)



120601119905= minus119875120601(120601) = div (1199031 (120601) nabla120601) (6)


1199031 (120601) = 1minus 11003816100381610038161003816nabla120601

1003816100381610038161003816

(7)



1199032 (120601) =

sin (2prod1003816100381610038161003816nabla120601

1003816100381610038161003816)

2prod1003816100381610038161003816nabla120601

1003816100381610038161003816

if 1003816100381610038161003816nabla120601

1003816100381610038161003816le 1

1 minus 11003816100381610038161003816nabla120601

1003816100381610038161003816

if 1003816100381610038161003816nabla120601

1003816100381610038161003816ge 1

(8)


1199033 (120601) = 119867119901 (1003816100381610038161003816nabla120601

1003816100381610038161003816minus 1) (9)






VLSI Design 5


Euler step

Iterations

System generator

Gateway out

1

05

1000

dx

dyreinit_SD 120601

120572

Iterations

Out

reinit_SD



120601119905= 120576Δ120601minus

1120576

119871 (120601) 119909120576Ω sub 119877119899

Subject 997888rarr 120601 (119909 119905 = 0 120576) = 1206010 (119909) (10)


119899

119894=1(1205972(sdot)120597119909

2119894) and 1206010(119909) is


119894and the


119894



(2) Compute 0119899+12 as 120601119899+12=120601119899

=Δ1199052119871(120601119899

)

(3) Compute 0119899+1as 120601119899+12=120601119899

+Δ1199052119871(120601119899

)







0) = 120593119899 till some time 119879




120593119899+12 till some time 119879


is 120593119899+1 = 120593(119909 119879119889)



119889


120593119899+ Δ1199051(minus120576minus1119871(120593119899)) and 120593

119899+1= 120593119899+12

+ Δ1199052(120576Δ120593119899+12


1and Δ119905

2represent

the times 119879119903and 119879



2as

Δ1199051larr Δ119905


2larr Δ119905



1and



6 VLSI Design

Curvature central

Reg Xie


Curvature 3D

Delta function

Heavisible


Constant


Cv 2D


NeumanBoundCond

Constant

reinit_SD_3D Out

Gateway out

dx


Iterations

nrowncol

ic sdf2circlef

F

jc

r

l120583


1000

Κ


120601 Curvature_3D

absR

120601 Reg_Xie Κ_H


120601Δ Δ_h

120598

120601Heaviside

120598H

10


System generator

dx


120601

120601

fNeumanBoundCond g

120581


(a) (b)






VLSI Design 7

Stone portion image

Daubechies (Db 12)










1198891119894= 120572 (1199092119894 +1199092119894+2) + 1199092119894+1

1198861119894= 120573 (119889

1119894+119889

1119894minus1) + 1199092119894

1198892119894= 120574 (119886

1119894+ 119886

1119894+1) + 119889

1119894

1198862119894= 120575 (119889

2119894+119889

2119894minus1) + 119886

1119894

119889119894=

1198892119894

120576

(11)

where 1199092119894and 1199092119894+2







Min-max

Db12Dh1average

00026ndash00169

Db12cVenergy


Sym12Dh1average

00026ndash00169

Sym12cVenergy


rbio37Dh1average

00052ndash00255

rbio37cDenergy


rbio37cVenergy


rbio37Dh1average

00066ndash00272

rbio39cDenergy


rbio39cVenergy


rbio39cVaverage

00039ndash00061

rbio44Dh1average


rbio44cHenergy


rbio44cVenergy


8 VLSI Design






0

30

60

90

120

150

180

210

240

270

300

330

004

003

002

001








VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de



CenterMaxmin






References









10 VLSI Design


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









VLSI Design 5


Euler step

Iterations

System generator

Gateway out

1

05

1000

dx

dyreinit_SD 120601

120572

Iterations

Out

reinit_SD



120601119905= 120576Δ120601minus

1120576

119871 (120601) 119909120576Ω sub 119877119899

Subject 997888rarr 120601 (119909 119905 = 0 120576) = 1206010 (119909) (10)


119899

119894=1(1205972(sdot)120597119909

2119894) and 1206010(119909) is


119894and the


119894



(2) Compute 0119899+12 as 120601119899+12=120601119899

=Δ1199052119871(120601119899

)

(3) Compute 0119899+1as 120601119899+12=120601119899

+Δ1199052119871(120601119899

)







0) = 120593119899 till some time 119879




120593119899+12 till some time 119879


is 120593119899+1 = 120593(119909 119879119889)



119889


120593119899+ Δ1199051(minus120576minus1119871(120593119899)) and 120593

119899+1= 120593119899+12

+ Δ1199052(120576Δ120593119899+12


1and Δ119905

2represent

the times 119879119903and 119879



2as

Δ1199051larr Δ119905


2larr Δ119905



1and



6 VLSI Design

Curvature central

Reg Xie


Curvature 3D

Delta function

Heavisible


Constant


Cv 2D


NeumanBoundCond

Constant

reinit_SD_3D Out

Gateway out

dx


Iterations

nrowncol

ic sdf2circlef

F

jc

r

l120583


1000

Κ


120601 Curvature_3D

absR

120601 Reg_Xie Κ_H


120601Δ Δ_h

120598

120601Heaviside

120598H

10


System generator

dx


120601

120601

fNeumanBoundCond g

120581


(a) (b)






VLSI Design 7

Stone portion image

Daubechies (Db 12)










1198891119894= 120572 (1199092119894 +1199092119894+2) + 1199092119894+1

1198861119894= 120573 (119889

1119894+119889

1119894minus1) + 1199092119894

1198892119894= 120574 (119886

1119894+ 119886

1119894+1) + 119889

1119894

1198862119894= 120575 (119889

2119894+119889

2119894minus1) + 119886

1119894

119889119894=

1198892119894

120576

(11)

where 1199092119894and 1199092119894+2







Min-max

Db12Dh1average

00026ndash00169

Db12cVenergy


Sym12Dh1average

00026ndash00169

Sym12cVenergy


rbio37Dh1average

00052ndash00255

rbio37cDenergy


rbio37cVenergy


rbio37Dh1average

00066ndash00272

rbio39cDenergy


rbio39cVenergy


rbio39cVaverage

00039ndash00061

rbio44Dh1average


rbio44cHenergy


rbio44cVenergy


8 VLSI Design






0

30

60

90

120

150

180

210

240

270

300

330

004

003

002

001








VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de



CenterMaxmin






References









10 VLSI Design


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









6 VLSI Design

Curvature central

Reg Xie


Curvature 3D

Delta function

Heavisible


Constant


Cv 2D


NeumanBoundCond

Constant

reinit_SD_3D Out

Gateway out

dx


Iterations

nrowncol

ic sdf2circlef

F

jc

r

l120583


1000

Κ


120601 Curvature_3D

absR

120601 Reg_Xie Κ_H


120601Δ Δ_h

120598

120601Heaviside

120598H

10


System generator

dx


120601

120601

fNeumanBoundCond g

120581


(a) (b)






VLSI Design 7

Stone portion image

Daubechies (Db 12)










1198891119894= 120572 (1199092119894 +1199092119894+2) + 1199092119894+1

1198861119894= 120573 (119889

1119894+119889

1119894minus1) + 1199092119894

1198892119894= 120574 (119886

1119894+ 119886

1119894+1) + 119889

1119894

1198862119894= 120575 (119889

2119894+119889

2119894minus1) + 119886

1119894

119889119894=

1198892119894

120576

(11)

where 1199092119894and 1199092119894+2







Min-max

Db12Dh1average

00026ndash00169

Db12cVenergy


Sym12Dh1average

00026ndash00169

Sym12cVenergy


rbio37Dh1average

00052ndash00255

rbio37cDenergy


rbio37cVenergy


rbio37Dh1average

00066ndash00272

rbio39cDenergy


rbio39cVenergy


rbio39cVaverage

00039ndash00061

rbio44Dh1average


rbio44cHenergy


rbio44cVenergy


8 VLSI Design






0

30

60

90

120

150

180

210

240

270

300

330

004

003

002

001








VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de



CenterMaxmin






References









10 VLSI Design


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









VLSI Design 7

Stone portion image

Daubechies (Db 12)










1198891119894= 120572 (1199092119894 +1199092119894+2) + 1199092119894+1

1198861119894= 120573 (119889

1119894+119889

1119894minus1) + 1199092119894

1198892119894= 120574 (119886

1119894+ 119886

1119894+1) + 119889

1119894

1198862119894= 120575 (119889

2119894+119889

2119894minus1) + 119886

1119894

119889119894=

1198892119894

120576

(11)

where 1199092119894and 1199092119894+2







Min-max

Db12Dh1average

00026ndash00169

Db12cVenergy


Sym12Dh1average

00026ndash00169

Sym12cVenergy


rbio37Dh1average

00052ndash00255

rbio37cDenergy


rbio37cVenergy


rbio37Dh1average

00066ndash00272

rbio39cDenergy


rbio39cVenergy


rbio39cVaverage

00039ndash00061

rbio44Dh1average


rbio44cHenergy


rbio44cVenergy


8 VLSI Design






0

30

60

90

120

150

180

210

240

270

300

330

004

003

002

001








VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de



CenterMaxmin






References









10 VLSI Design


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









8 VLSI Design






0

30

60

90

120

150

180

210

240

270

300

330

004

003

002

001








VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de



CenterMaxmin






References









10 VLSI Design


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









VLSI Design 9

12

10

8

6

4

2

0

minus25 10 15 20 25 30 35 40

Am

plitu

de



CenterMaxmin






References









10 VLSI Design


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









10 VLSI Design


















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









Research Article Analysis and Implementation of Kidney ...downloads.hindawi.com/archive/2015/581961.pdf · kidney image with stone portion Counter (2^14) (14-bit counter) Image preprocessing

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