Research Article Bilateral Image Subtraction and ...downloads.hindawi.com/journals/bmri/2015/231656.pdfResearch Article Bilateral Image Subtraction and Multivariate Models for the

Research ArticleBilateral Image Subtraction and Multivariate Models forthe Automated Triaging of Screening Mammograms

Joseacute Celaya-Padilla1 Antonio Martinez-Torteya1 Juan Rodriguez-Rojas1

Jorge Galvan-Tejada1 Victor Trevintildeo12 and Joseacute Tamez-Pentildea12

1Grupo de Investigacion en Bioinformatica Escuela de Medicina Tecnologico de Monterrey 64849 Monterrey NL Mexico2Departamento de Investigacion e Innovacion Escuela de Medicina Tecnologico de Monterrey 64710 Monterrey NL Mexico

Correspondence should be addressed to Jose Celaya-Padilla josecpadillagmailcom

Received 4 October 2014 Revised 12 June 2015 Accepted 15 June 2015

Academic Editor Rituraj Purohit

Copyright copy 2015 Jose Celaya-Padilla 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

Mammography is the most common and effective breast cancer screening test However the rate of positive findings is very lowmaking the radiologic interpretationmonotonous andbiased toward errorsThiswork presents a computer-aided diagnosis (CADx)method aimed to automatically triage mammogram sets The method coregisters the left and right mammograms extracts imagefeatures and classifies the subjects into risk of having malignant calcifications (CS) malignant masses (MS) and healthy subject(HS) In this study 449 subjects (197 CS 207 MS and 45 HS) from a public database were used to train and evaluate the CADxPercentile-rank (119901-rank) and 119911-normalizations were used For the 119901-rank the CS versus HS model achieved a cross-validationaccuracy of 0797 with an area under the receiver operating characteristic curve (AUC) of 0882 the MS versus HS model obtainedan accuracy of 0772 and an AUC of 0842 For the 119911-normalization the CS versus HS model achieved an accuracy of 0825 withan AUC of 0882 and the MS versus HS model obtained an accuracy of 0698 and an AUC of 0807 The proposed method has thepotential to rank cases with high probability of malignant findings aiding in the prioritization of radiologists work list

1 Introduction

Breast cancer represents nearly one-third of all female cancercases in the United States [1] and is one of the global leadingcauses of death among women [2] Early detection is impor-tant for survival reducing the mortality rate by up to 65[3ndash5] The screening mammography is the preferred earlydetection method Based on X-ray imaging it is effective invisualizing breast tissue abnormalities such as calcificationsandmasses architectural distortions associatedwith the earlydevelopment of breast cancer [3]

Great efforts have been made to develop computer-aideddetection (CADe) and diagnosis (CADx) systems to assistradiologists in interpreting digital mammograms [6] Com-mercial CADe systems have been shown to be very sensitivein detecting breast abnormalities [7 8] However these sys-tems tend to have low specificities reducing the throughputof expert radiologists [9] Furthermore the presence of falsepositives in CADe systems is increasing the number of

unnecessary biopsy procedures [9]On the other handCADxsystems are helping clinicians in diagnosing complex illnesses(ie detection of aneurysms lung nodules etc) in differentmedical areas [3 10] These systems can be used by radiolo-gists as a second opinion and may help in reaching a correctinterpretation of abnormal findings [6 9 11] Additionallytriaging mammograms by risk of breast cancer using thesesystems might reduce the workload of the radiologists

CADx systems have already been used in breast cancerdiagnosis as a means of assessing the risk of a subjectto develop or have breast cancer [12 13] To do so fea-tures that measure breast abnormalities are extracted fromthe mammograms and the risk is evaluated Among thesefeatures high breast density is recognized as risk featurefor future development of breast cancer [14 15] Howeverthe detection of breast abnormalities can be enhanced bycomparing different images of the same subject either fromthe same breast at different time points [16] or by asymmetryanalyses of the left and right breasts [16 17] The latter

Hindawi Publishing CorporationBioMed Research InternationalVolume 2015 Article ID 231656 12 pageshttpdxdoiorg1011552015231656

2 BioMed Research International

provides clues about the presence of early signs of tumors(eg parenchymal distortion small asymmetric bright spotsand contrast) Asymmetry analysis consists of two mainstages alignment of the images and detection of asymmetrythrough a bilateral image subtraction [17]

Current asymmetry detection methods are often basedon simple bilateral subtraction techniques [16 18] How-ever breasts are composed of highly heterogeneous anddeformable tissue resulting in an unlikely perfect matchbetween both breasts [19] Thus in order to efficientlymeasure asymmetry a registration-based alignment must beperformed [20] It is known that the deviations of the normalsymmetrical architecture between breast images reduce therate of false positive detection of masses from digital mam-mograms [21 22] The alignment is improved by using thenipple as a reference point [23] Coregistration of both breastsusing a robust point matching approach and a novel seriesof features helped to detect abnormal cases with masses [24]In addition feature selection was important in a pool of 20bilateral computed features coupled to a genetic algorithmto select and build an artificial neural network classifier [19]Therefore breast asymmetry can be used to assess the risk ofbreast cancer

The objective of this work was to provide evidence thatfeatures related to asymmetry and derived from bilateralimage subtraction maps might be used to automaticallyclassify mammograms sets by their risk of showing breastcancerThis analysis is based on our previous efforts [25] butit is enhanced by the extraction of hundreds of asymmetry-related features and the use of a more robust automatedregistration algorithm and simplified by the use of a reg-ularization feature selection algorithm Although it followsan approach similar to the ones used for mass detection[22 24] our methodology is also evaluated for the detectionof calcifications

2 Materials

A total of 1796 digitalized film mammograms from 449different subjects were used in this study From those 45 wereclassified as healthy subjects (HS) (mean age of 593 SD of98 years) 197 as subjects with malignant calcifications (CS)(mean age of 58 SD of 109 years) and 207 as subjects withmalignant masses (MS) (mean age of 641 SD of 101 years)Each subject had the four standard mammograms taken leftand right craniocaudal (CC) and left and right mediolateraloblique (MLO) projections

In order to avoid problems associated with intrascannervariability [22 24 26] all mammograms in this study wereobtained from the Howtek dataset of the Digital Database forScreening Mammography public database [27] in which allmammograms were digitalized using a Howtek 960 scannerusing a sampling rate of 435 micrometers per pixel and a 12-bit depth

3 Methodology

Figure 1 shows the seven analysis stages used in this studyBriefly these stages consist of (1) segmentation of soft tissue

Patient

Segmentation

CC CCMLO MLO

Registration

Left Right

ToBilateral subtraction

Enhancement filters

Feature extraction

Feature selection

Model evaluation

Left (l) Right (r)

IΔ

H(lrΔ) L(lrΔ)

120590(lrΔ) F(lrΔ)

l r

T(x y)

Il(T(x y))Δr

Figure 1 Workflow of the proposed methodology

(2) registration of the left images to the right images (3)bilateral subtraction of the coregistered images (4) filteringof the images to enhance the signal and texture (5) featureextraction (6)multivariate models selection using a train setand (7)model evaluation on a test set

31 Segmentation The automatic segmentation of the breasttissue was based on the estimation of the background noiseAn initial segmentation mask was created by estimating thebackgroundnoise in the image and discarding all pixels belowfive standard deviations of the noise level Then holes wereremoved by applying closing morphological operations witha 3 times 3 supporting region

119878 (119860) = (119860 (119909 119910) oplus119861 (119909 119910)) ⊖ 119861 (119909 119910) (1)

where oplus and ⊖ are the grayscale dilation and erosionmorphological operations respectively 119861(119909 119910) is a 3 times 3

structural element119860(119909 119910) is the image being segmented and119878(119860) is the resulting segmentation of the 119860(119909 119910) image Thelargest connected region was used as the segmentation maskwhile all other high intensity regions were removed from theimages Figure 2 shows an example of the final segmentationusing this procedure

32 Registration The left breast mammographic images weremirrored and then registered to their corresponding rightbreast images The registration used a standard image reg-istration framework with a B-Spline multiresolution trans-formation optimizing the Mattes mutual information metric

BioMed Research International 3

(a) (b)

Figure 2 Segmentation of breast tissue (a) input raw CC view image (b) segmentationmask of the breastThe red color represents the masksuperimposed to the input image

(a) (b) (c) (d)

Figure 3 B-Spline image registration example Checkerboard visualization of (a) unregistered left and right CC views (b) coregistered leftand right CC views (c) unregistered left and right MLO views and (d) coregistered left and right MLO views Yellow (right image) and green(left image) lines were drawn in the edge of the breast for better visualization

[28 29] The B-Spline transform T(119909 119910) deforms an imagebymodifying a mesh of control points which pinpoints to themoving image to maximize of a similarity measure Brieflythe images are first registered at the lowest resolution TheB-Spline transformation parameters are then moved intothe next resolution and the parameter optimization is runagain The original moving image is lastly deformed usingthe final parameters of the transformT(119909 119910)The registrationalgorithm was implemented using the Insight Toolkit (ITK)libraries [30] Figure 3 shows an example of this process onan abnormal case

33 Image Subtraction Once the images were coregistered apixelwise absolute difference was computed between the leftand right images as follows

119868Δ(119909 119910) =

1003816100381610038161003816119868119903 (119909 119910) minus 119868119897 (T (119909 119910))1003816100381610038161003816 (2)

where 119868119903(119909 119910) represents the right image 119868

119897(T(119909 119910)) repre-

sents the left image registered to the right image space and119868Δ(119909 119910) represents the map of absolute differences

34 Image Enhancement To study the appearance of thearchitectural distortions two enhancing filters were appliedto the images a morphological high frequency enhancementfilter (MoF) designed to enhance fiber-like tissues and aLaplacian of Gaussian filter (LoG) to enhance high frequencypatterns inside the breast tissues Additionally since thetexture between normal and abnormal tissues is different [31]two texture maps were created The first map computed thelocal standard deviation (LSD) of themammographic imagesand the second map computed the local fractal dimension(LFD) Image processing was implemented in c++ using ITKlibraries for image manipulation [30]


341 Morphological High Frequency Enhancement Filter Thefiber enhancement was done by subtracting the output of thegrayscale erosion operation to the original image

119867(119909 119910) = 119868 (119909 119910) minus 119868 (119909 119910) ⊖ 119861 (119909 119910) (3)

where ⊖ represents the grayscale erosion operation 119868(119909 119910)represents the input image 119861(119909 119910) represents a 5 times 5

structural element and119867(119909 119910) represents the output imageThis filter enhances the fine structures by removing theunderlying background signal extracted by the grayscaleerosion operation [32]

342 The Laplacian of Gaussian The image points withhigh frequency intensity were enhanced using this filter Firstconvolving the input image using a Gaussian kernel and thenapplying the Laplacian operator

119871 (119909 119910) = 119868 (119909 119910) lowast 119866120590(119909 119910) lowast ℎ (119909 119910) (4)

where 119866120590(119909 119910) represents a Gaussian kernel with 120590 standard

deviations ℎ(119909 119910) represents a 3 times 3 discrete Laplacian oper-ator [32 33] 119868(119909 119910) represents the input image and 119871(119909 119910)represents the output image Images filtered by the LoG filterwill have all its high frequency components enhanced [33]Therefore high frequency patterns of the breast tissue will bemore prominent after the application of this filter

343 Local Standard Deviation This texture map estimatedthe per-pixel standard deviation as follows

120590 (119909 119910) = radic1119873

sum

119898119899120598R

1198682 (119899119898) minus [1119873

sum

119898119899120598R

119868 (119899119898)]

2

(5)

where 120590(119909 119910) represents the local standard deviation of thesignal within the supporting region R(119909 119910) of 3 times 3 pixelsThis texture map will be bright in areas with large variationsin signal patterns while areas with flat intensities will be black[34]

344 Local Fractal Dimension A triangular prism surfacearea method at three different scales was used to estimate thelocal fractal dimension at each point of the image Furtherdetails of this methodology can be found elsewhere [35] Thefractal dimension map would have higher values in regionswith repeating patterns at the three different resolutions

35 Feature Extraction The enhancement filters and texturemaps were applied to the four screening mammographyimages and to the two bilateral subtraction images whichwould result in a set of 15 images for both the CC and theMLO views 119868

119903 119868119897 119868Δ 119867119903 119867119897 119867Δ 119871119903 119871119897 119871Δ 120590119903 120590119897 120590Δ 119865119903

119865119897 and 119865

Δ where 119868 is the raw image 119867 119871 120590 and 119865 are

the enhanced images described in Section 34 and 119903 119897 andΔ stand for the right left and bilateral subtraction imagesrespectively Features were then extracted from this set ofimages

Forty-three features were extracted from each imageresulting in 1290 image features per subject Additionally

the average and absolute difference of each left-right pair ofmeasurements was also analyzed resulting in 860 additionalfeatures (symmetric features) Finally 2150 features persubject were used Table 4 describes the features extractedfrom each image

36 Feature Selection The first step of the feature selectionprocess consisted of acknowledging for correlations betweenfeatures For any pair of features with a Spearman correla-tion coefficient larger than 096 one feature was randomlyselected to be kept and the other was removed from theselection Two types of normalizations were then applied tothis database resulting in two different datasets The firstdataset was obtained by using a percentile-rank (119901-rank)normalization and the second one by a 119911-normalization Theempirical distribution of the healthy subjects was consideredto perform the 119911-normalization using the rank-based inversenormal transformation [36]

In order to select the most accurate and compact setof features from each dataset a multivariate search strategywas performed using Least Absolute Shrinkage and SelectionOperator (LASSO) [37]The shrinkage and selection methodminimizes the sumof squared errors andpenalizes the regres-sion coefficients The multivariate search was performedusing a class balanced data sample of 100 subjects for trainingand the remaining subjects as a blind test set Models werecalibrated at training using a leave-one-out cross-validation(LOOCV) strategy training the models at every split using119873minus1 subjects and evaluating the model using the remainingsubject [38]The final reported performance was obtained byapplying the final model gathered in the training stage andevaluating it in the blind test set

37 Sensitivity Analysis The pool of features used in thefeature selection procedure was obtained from both the rawand the registered images However features gathered fromthe raw images are side-dependent Therefore a sensitivityanalysis on the effect of using side-dependent features wasperformed Using the final models of HS versus CS andHS versus MS left and right side-dependent features wereswapped with their contralateral counterparts Then wemeasured the change in model performance on the blinddataset

4 Results

All the 1796 films were successfully segmented A total of 9subjectrsquos image sets had to be removed from the experimentdue to problems in the registration process Six were from themalignant mass set two from the calcification set and onefrom the healthy subjects set All the remaining subjects wereincluded in the subsequent stages of the analysis The 2150extracted features were filtered by the correlation processThis filtering removed 826 due to correlation above 096threshold yielding a total of 1324 features per subject Thesefeatures were analyzed by a univariate statistical analysis ofthe unadjusted AUC Table 1 shows a breakdown of the top50 features that achieved the highest AUCs


Table 1 Summary of the top 50 univariate features

Type 119911-normalization 119901-rankHealthy vs Calcifications Healthy vs Masses Healthy vs Calcifications Healthy vs Masses

Raw features 25 25 16 24Symmetric 17 17 20 17Registered 8 8 14 9Number of features by type

Table 2 shows the final model for each dataset afterfeatures selectionThe 21 119901-ranked features model for the HSversus CS subset achieved a blind accuracy of 0797 (95 CI0692ndash0895) and an AUC of 0882 as shown in Figure 4 TheHS versus MSmodel containing 12 features achieved a blindaccuracy of 0772 (95 CI 0617ndash0886) and an AUC of 0842as seen in Figure 4

The 12 feature model obtained for the HS versus CSclassification using the 119911-transformation achieved a blindtest accuracy of 0825 (95 CI 0727ndash0909) and an AUCof 0882 as shown in Figure 5 The HS versus MS with 119911-transformation generated sixteen features and resulted in ablind test accuracy of 0698 (95CI 0557ndash0879) and anAUCof 0807 Table 3 shows the complete set of features of eachmodel

All models included a combination of features extractedfrom raw symmetric and registered images Table 3 summa-rizes the performance achieved by each group of featuresFigures 4 and 5 show the difference in performance by eachtype of features alongwith the combination of all features (fullmodel)

41 Cross-Validation and Sensitivity Analysis Results of sen-sitivity analysis of the side-dependent features are shown inFigure 6The blind performance is presented for both the HSversus CS and HS versus MS with raw and swapped featuresusing the 119911-normalized and 119901-rank normalizations

For the full HS versus CS using 119911-normalization theAUC decreased from 0882 to 0733 by exchanging swappedfeatures For the HS versus MS the AUC had a decreasefrom 0807 to 0760 when exchanging the raw features for theswapped features AUCs are shown in Figures 6(a) and 6(c)respectively

When using the 119901-rank normalization the HS versus CStheAUCdecreased from0882 to 0733 and for theHS versusMS the AUC dropped from 0842 to 0708 when exchangingthe raw features to the swapped features (Figures 6(b) and6(d)) respectively

The decrease in the AUC when exchanging the rawfeatures for the swapped features was a notable decrease whenusing the 119901-rank versus the 119911-normalization (15 versus10)

5 Discussion

51 Image Processing Segmentation Registration and Digital-Subtraction The proposed methodology has multipleimprovements over other techniques It is fully automated

and does not require manual intervention as previousproposals [21 22] Although our approach is similar to others[24] we did not attempt to remove the pectoral muscle fromthe segmentation mask since the presence of abnormalaxillary lymph in this area is an indicator of occult breastcarcinoma [39] However from the computational point ofview the feature extraction process may be affected if theregion processed is not well focused [40] The proposedregistration process achieved a very good performanceand only 20 of the subjects had to be discarded dueto registration issues This performance is remarkable inspite of the amount of tissue deformation induced by themammographic procedure The spline deformation is animprovement over rigid or affine coregistration methods[26] The advantage of the deformable registration hasbeen recognized as key element in breast analysis andhas been successfully used in longitudinal studies [24]Regarding digital subtraction the differences in the X-rayprojection and image acquisition and digitizing artifactsmay affect the detection of asymmetric patterns Our resultsindicate that even in the presence of registration artifacts thedigital subtraction added information that was successfullyincorporated during the feature selection process

52 Feature Extraction The enhanced images and texturemaps enriched the feature set providing a fourfold increase inextracted features per patient which were also incorporatedin the final classification models Regarding symmetry thestrategy of exploring bilateral symmetry has been exploredby other researches where a series of features (signal texturebreast density etc) were computed from each mammo-gram and the absolute difference between both breasts wasobtained tomeasure breast tissue asymmetry and was used topredict the likelihood of developing cancer [19]We extendedthis idea by registering the left and right images using adeformable transformation which increased the number offeatures per patient by 25

53 Model Selection and Triaging The LASSO model selec-tion strategy yields reproducible models of healthy versusmalignant mass with a blind test AUC of 0842 and 0882for the detection of malignant calcifications and massesrespectively Furthermore the detailed analysis of the ROCcurve may give us indications of key triaging points forprioritizing the mammogram reading Priority triaging mayhave real practical usage in regions where expert radiologicalresources are scarce or costly With the aid of the ROC curvewe may define a low priority reading (10 chance of missinga cancer case 90 sensitivity)That group represents the 50


Table 2 Features of the proposed models

119911-normalization 119901-rank normalization

Healthy vs Calcifications Healthy vs Masses Healthy vs Calcifications Healthy vs MassesView Image Feature View Image Feature View Image Feature View Image Feature

1 CC 119867Δ

27 CC 119871Δ

40 CC 119868Δ

2 CC 119871Δ

402 CC 119865

Δ13 CC 119868

11990329 CC 119865

Δ9 CC 119865

Δ12

3 CC 119868119903

29 CC 119871119897

40 CC 119865Δ

12 CC 119868119903

294 CC 119867

11989729 CC 119865

1199036 MLO 119868

Δ42 CC 119867

11990332

5 CC 119867119897

6 MLO 119867119897

11 MLO 119868Δ

13 CC 119871119903

286 MLO 119868

11989728 CC 119868

Δavg 29 MLO 119871Δ

32 MLO 119867119903

327 MLO 119867

11989711 CC 119868

Δ11990428 MLO 119871

Δ6 MLO 119865

11989713

8 MLO 119867119897

21 CC 120590Δ119904

38 CC 119868119903

2 CC 119865Δ119904

289 CC 119868

Δ11990428 CC 119865

Δavg 12 CC 119868119903

29 CC 119865Δavg 12

10 CC 120590Δ119904

38 MLO 119868Δ119904

40 CC 119867119903

14 MLO 119868Δavg 2

11 MLO 119871Δavg 27 MLO 119868

Δ11990428 CC 119865

11989711 MLO 119868

Δ1199045

12 CC 119867Δ

27 MLO 119868Δ119904

29 MLO 119871119903

15 MLO 119867Δ119904

3913 MLO 119867

Δ11990431 MLO 119865

11989716

14 MLO 119867Δ119904

7 CC 119868Δ119904

415 MLO 119871

Δavg 39 CC 119867Δ119904

3916 MLO 119871

Δavg 27 CC 119867Δ119904

1917 CC 119871

Δ11990412

18 CC 120590Δ119904

1719 CC 119865

Δavg 1220 MLO 119867

Δ11990431

21 MLO 119865Δavg 12

Features are grouped by dataset symmetric features are denoted with 119868Δavg = (119868119903 + 119868119897)2119867Δavg = (119867119903 + 119867119897)2 119871Δavg = (119871119903 + 119871119897)2 120590Δavg = (120590119903 + 120590119897)2119865Δavg = (120590119903 + 120590119897)2 119868Δ119904 = |119868119903 minus 119868119897|119867Δ119904 = |119867119903 minus 119867119897| 119871Δ119904 = |119867119903 minus 119867119897| 120590Δ119904 = |119867119903 minus 119867119897| 119865Δ119904 = |119867119903 minus 119867119897|

Table 3 Model AUC by feature type

119911-normalization 119901-rankCALC MASS CALC MASS

RAW-features 0776 0780 0828 0794DIF-features 0765 0767 0767 0725FULL

(RAW+DIF+SYN) 0882 0807 0882 0842RAW stand for raw features DIF stand for digital subtracted features SYNstand for symmetric features The values shown values were obtained usingthe blind test set

and 40 of the screening subjects formalignant calcificationsand masses respectively On the other side of the spectrumthe high priority reading group may be defined by the 90specificity cutoff This 10 of the screening mammogramswill have 60 and 50 of the malignant calcifications andmasses cases By assuming that calcification and masses areindependent events and by applying the 90 specificity to the90 sensitivity criteria for triaging we will have that around19 (1 minus 09 lowast 09) of the subjects will be in a high priorityreview group and around 20 (04 lowast 05) of the subjects willbe in the low priority review group The high priority reviewgroupwill yield around 50 ofmalignant cases while the lowpriority group may have the remaining 10 of the potentialmalignant cases

The results of the work cannot yet be generalized and thepresented findings are limited to plain film mammograms ofa single scanner of the public DDSM dataset Even havingthese strong limitations we believe that the methodology canbe replicated with digital mammography or full-field digitalmammography and with newer advanced technologies liketomosynthesis We believe that in this scenario our resultscould be even higher due to the reduction of noise introducedin the mammography scanning and the higher resolutionreached

54 Sensitivity Analysis Regarding the side dependency ofthe raw features as show in Figure 6 the decrease in the AUCwhen exchanging the raw features for the swapped featureswhen using the 119901-rank versus the 119911-normalization was 15versus 10 For the HS versus CS using119901-rank normalizationandHS versusMS using 119911-normalization the differences werenot significant (119901-value = 07873 and 01841 resp) Howeverthe number of raw-features present in thosemodels was smallcompared to the length of the model (six of twenty-one andfour of sixteen features resp) therefore the impact of specificfeatures is limited

On the other hand HS versus CS using 119911-normalizationand HS versus MS using 119901-rank normalization were statisti-cally significant (119901-value lt 005) and marginally significant(0051) respectively those models had a large proportion


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07937AUC = 0725

AUC = 0842

(a)

SpecificitySe

nsiti

vity

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08279AUC = 07667

AUC = 08822

(b)

Figure 4 ROC curves of the models generated using the 119901-rank normalized dataset for (a) HS versus MS (AUC = 0842) and (b) HS versusCS (AUC = 0882) all performances of the models were measured in blind test set Red dashed line = different model black solid line = rawmodel and blue dotted line = full model with DIF SYM and RAW features

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07797AUC = 07673

AUC = 0807

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07841AUC = 07649

AUC = 08822

(b)

Figure 5 ROC curves of the models generated using the 119911-normalized dataset for (a) HS versus MS (AUC = 0807) and (b) HS versus CS(AUC = 0882) all performances of the models were measured in blind test set Red dashed line = different model black solid line = rawmodel blue dotted line = full model with different symmetrical and raw features


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 07333

p-value = 00106

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 08692

p-value = 07873

(b)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0807AUC = 07157

p-value = 01841

(c)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0842AUC = 07083

p-value = 00505

(d)

Figure 6 ROC curves for (a) calcifications versus normal model (119911-normalization) (b) calcifications versus normal model (119901-rank) (c)mass versus normal model (119911-normalization) and (d) mass versus normal model (119901-rank) Solid black line represents the performance ofthe model red dashed line represents the model with the swapped raw features and blue polygon represents the confidence interval of thecurve all performances of the models were measured in blind test set

of raw features present in the model six of twelve and fiveof twelve features respectively and the effect of the side-dependency is more noticeable

Regarding the individual performance of the differentfeature types Table 3 shows the individual blind performance

along with their combination In all the cases of the combina-tion of different types of features we observed an incrementof the blind AUC said increments were from a small 2 inHS versusMSusing 119911-normalization for the lowest incrementto a 98 for the HS versus CS using also 119911-normalization


Table 4

Category Feature Definition

Shape

1 Area 119860119904

Perimeter 119875119904

2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)

4 5 Region centroid(119899 = 2)

x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩

6 7 8 Region scatter(119899 = 3)

RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)

10 Median of the Signal Median = V(05)

11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832

13 Standard deviation 120590119904= radic1205902

119904

14 Dynamic range DR119904= max (119868 (119898 119899)) minusmin (119868 (119898 119899))

15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904

20 21 fraction greater than119911 deviations (119899 = 2)

119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3

22 23 fraction lower than119911 deviations (119899 = 2)

119865 (120583119904minus 119911120590119904) 119911 isin 2 3

24ndash33 Value at fraction(119899 = 10)

V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)

35 5 TrimmedStandard deviation

1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12

36 5 Trimmed 119911Mean

5119904=1205835119904

1205905119904

Morphology

37 Total Signal Mass = 11987200

38 39 Signal centroid(119899 = 2)

x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩

40 41 42 Signal scatter (119899 = 3) RS119868=

11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12


When using the 119901-rank normalization we observed a similarperformance for both HS versus MS and HS versus CSThe HS versus CS achieved the highest AUC this findingis consistent with the literature [7 8] since the masses areharder to find [14]

6 Conclusion

This proof-of-concept study was able to show that healthysubjects subjectswith calcifications and subjectswithmassescan accurately be classified through models generated viaaccurate mammography registration and a feature selectionmethodologyThemethodology demonstrated that the imagesubtraction of registered images generates information thatimproves the identification of subjects with lesions such asmalignant masses and calcification The achieved perfor-mance of the system has the potential to be used to queuecases with high chance of malignant findings or may havethe practical use of triaging mammograms in developingcountries where there is a deficiency of expert readers

Future work will focus on validating this approach inpublic databases like the Breast Cancer Digital Repository[41] and exploring the practical implications of translatingthis methodology to the clinical world

Appendix

Image Features

From the segmented image we can extract a set of featuresrelated to segmentation shape signal distribution signaltexture and signal morphology This section describes theequations required in the computation of the image features

Let us call the segmentation 119904(119898 119899) and 119868(119898 119899) the digitalimage We will define 119878(119896) as the set of order points of thedigital image belonging to a specific tissue 119896

119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)

where each digital point (119898 119899) is associated with a physicalcoordinate x(119898 119899) = ⟨119898Δ119909 + 119909

0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are

the pixel spacing and (1199090 1199100) is the position of the lower left

corner of the image) The physical coordinate represents thelocation inmillimeters of a specific tissue point in the imagingdeviceThe area of the segmented tissue in squaremillimetersis

119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)

where 119886 is the unit area of a pixel and it is given by 119886 = Δ119909Δ119910The perimeter 119875

119904 of the segmentation is the sum of the line

segments lengths that join two neighboring edge pixels

119875119904=

119871

sum

119894=0119863 (A3)

where 119863 = |x119894minus x119895| (x119894 x119895) isin alefsym

2 119909119895isin 119873119894 is the set of

distances between neighboring edge points alefsym2 is the set of

the 119871 unordered pairs of the edge points coordinates |x119894minus x119895|

is the Euclidian distance between the edge point x119894and its

neighboring edge point x119895

The density of intensities are given by the normalizedhistogram

119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)

The fraction of points lower than a given intensity is

119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)

Hence the upper value of the intensity that contains a givenfraction 119901 of pixels is

V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)

The moment generating function of the segmentation shapeis

119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)

while themoment generating function of the signalmorphol-ogy is

119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)

The lengths of the bounding box of the segmentations aregiven by

119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910

= (max119899(x (119898 119899) sdot ⟨0 1⟩) minusmin

119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)

From the above definitions Table 4 shows the extractedfeatures for each segmented image

Conflict of Interests

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


Acknowledgments

This work was partially supported by the CONACyT GrantSSAIMSSISSSTE 140601 and by Tecnologico de MonterreyGrupo de Investigacion y Enfoque Estrategico en Bioinfor-matica

References

[1] C DeSantis J Ma L Bryan and A Jemal ldquoBreast cancerstatistics 2013rdquo CAmdashCancer Journal for Clinicians vol 64 no1 pp 52ndash62 2014

[2] A B Miller C Wall C J Baines P Sun T To and S ANarod ldquoTwenty five year follow-up for breast cancer incidenceandmortality of the CanadianNational Breast Screening Studyrandomised screening trialrdquo British Medical Journal vol 348article g366 2014

[3] M LoslashbergM L Lousdal M Bretthauer andM Kalager ldquoBen-efits and harms of mammography screeningrdquo Breast CancerResearch vol 17 no 1 2015

[4] R M Rangayyan F J Ayres and J E Leo Desautels ldquoAreview of computer-aided diagnosis of breast cancer toward thedetection of subtle signsrdquo Journal of the Franklin Institute vol344 no 3-4 pp 312ndash348 2007

[5] A Bleyer and H GWelch ldquoEffect of three decades of screeningmammography on breast-cancer incidencerdquo The New EnglandJournal of Medicine vol 367 no 21 pp 1998ndash2005 2012

[6] K Doi ldquoComputer-aided diagnosis in medical imaging histor-ical review current status and future potentialrdquo ComputerizedMedical Imaging and Graphics vol 31 no 4-5 pp 198ndash211 2007

[7] J A Baker E L Rosen J Y Lo E I Gimenez RWalsh andMS Soo ldquoComputer-aided detection (CAD) in screening mam-mography sensitivity of commercial CADsystems for detectingarchitectural distortionrdquo American Journal of Roentgenologyvol 181 no 4 pp 1083ndash1088 2003

[8] L H Eadie P Taylor and A P Gibson ldquoA systematic reviewof computer-assisted diagnosis in diagnostic cancer imagingrdquoEuropean Journal of Radiology vol 81 no 1 pp e70ndashe76 2012

[9] C Dromain B Boyer R Ferre S Canale S Delaloge and CBalleyguier ldquoComputed-aided diagnosis (CAD) in the detec-tion of breast cancerrdquo European Journal of Radiology vol 82no 3 pp 417ndash423 2013

[10] K Doi ldquoCurrent status and future potential of computer-aideddiagnosis in medical imagingrdquoThe British Journal of Radiologyvol 78 supplement 1 2014

[11] K Doi ldquoCurrent status and future potential of computer-aideddiagnosis in medical imagingrdquoThe British Journal of Radiology2014

[12] J Tang R M Rangayyan J Xu I El Naqa and Y YangldquoComputer-aided detection and diagnosis of breast cancerwith mammography recent advancesrdquo IEEE Transactions onInformation Technology in Biomedicine vol 13 no 2 pp 236ndash251 2009

[13] J Dheeba and N A Singh ldquoComputer aided intelligentbreast cancer detection second opinion for radiologistsmdashaprospective studyrdquo inComputational Intelligence Applications inModeling and Control pp 397ndash430 Springer 2015

[14] V A McCormack and I dos Santos Silva ldquoBreast density andparenchymal patterns as markers of breast cancer risk a meta-analysisrdquoCancer Epidemiology Biomarkers amp Prevention vol 15no 6 pp 1159ndash1169 2006

[15] C M Checka J E Chun F R Schnabel J Lee and HToth ldquoThe relationship of mammographic density and ageimplications for breast cancer screeningrdquoTheAmerican Journalof Roentgenology vol 198 no 3 pp W292ndashW295 2012

[16] B Zheng J H Sumkin M L Zuley X Wang A H Klymand D Gur ldquoBilateral mammographic density asymmetry andbreast cancer risk a preliminary assessmentrdquo European Journalof Radiology vol 81 no 11 pp 3222ndash3228 2012

[17] D Scutt G A Lancaster and J T Manning ldquoBreast asymmetryandpredisposition to breast cancerrdquoBreast Cancer Research vol8 no 2 article R14 2006

[18] J S Suri and R M Rangayyan Recent Advances in BreastImaging Mammography and Computer-Aided Diagnosis ofBreast Cancer vol 155 SPIE Press 2006

[19] X Wang D Lederman J Tan X H Wang and B ZhengldquoComputerized prediction of risk for developing breast cancerbased on bilateral mammographic breast tissue asymmetryrdquoMedical Engineering and Physics vol 33 no 8 pp 934ndash9422011

[20] Y Dıez A Oliver X Llado et al ldquoRevisiting intensity-basedimage registration applied to mammographyrdquo IEEE Transac-tions on Information Technology in Biomedicine vol 15 no 5pp 716ndash725 2011

[21] F-F Yin M L Giger C J Vyborny K Doi and R ASchmidt ldquoComparison of bilateral-subtraction and single-image processing techniques in the computerized detection ofmammographic massesrdquo Investigative Radiology vol 28 no 6pp 473ndash481 1993

[22] F-F Yin M L Giger K Doi C E Metz C J Vybornyand R A Schmidt ldquoComputerized detection of masses indigital mammograms analysis of bilateral subtraction imagesrdquoMedical Physics vol 18 no 5 pp 955ndash963 1991

[23] A J Mendez P G Tahoces M J Lado M Souto and J J VidalldquoComputer-aided diagnosis automatic detection of malignantmasses in digitized mammogramsrdquoMedical Physics vol 25 no6 p 957 1998

[24] R Martı Y Dıez A Oliver M Tortajada R Zwiggelaar and XLlado ldquoDetecting abnormal mammographic cases in temporalstudies using image registration featuresrdquo in Breast Imaging pp612ndash619 Springer 2014

[25] J M Celaya-Padilla J Rodriguez-Rojas J I Galvan-Tejada AMartınez-Torteya V Trevino and J G Tamez-Pena ldquoBilateralimage subtraction features for multivariate automated classifi-cation of breast cancer riskrdquo inMedical Imaging 2014 Computer-Aided Diagnosis vol 9035 of Proceedings of SPIE San DiegoCalif USA February 2014

[26] F-F Yin M L Giger K Doi C J Vyborny and R A SchmidtldquoComputerized detection of masses in digital mammogramsautomated alignment of breast images and its effect on bilateral-subtraction techniquerdquoMedical Physics vol 21 no 3 pp 445ndash452 1994

[27] M Heath K Bowyer D Kopans R Moore and P KegelmeyerldquoThe digital database for screening mammographyrdquo in Proceed-ings of the 5th InternationalWorkshop on Digital Mammography(IWDM rsquo00) pp 212ndash218 Toronto Canada June 2000

[28] J M Celaya-Padilla J Rodriguez-Rojas V Trevino and JG Tamez-Pena ldquoLocal image registration a comparison forbilateral registration mammographyrdquo in Proceedings of the 9thInternational Seminar on Medical Information Processing andAnalysis p 892210 Mexico City Mexico 2013


[29] D Rueckert L I Sonoda C Hayes D L Hill M O Leach andD J Hawkes ldquoNonrigid registration using free-form deforma-tions application to breast mr imagesrdquo IEEE Transactions onMedical Imaging vol 18 no 8 pp 712ndash721 1999

[30] L Ibanez W Schroeder L Ng and J Cates The ITK SoftwareGuide Kitware 2003

[31] R M Rangayyan S Banik and J E L Desautels ldquoComputer-aided detection of architectural distortion in prior mammo-grams of interval cancerrdquo Journal of Digital Imaging vol 23 no5 pp 611ndash631 2010

[32] R Duits T D Haije E Creusen andA Ghosh ldquoMorphologicaland linear scale spaces for fiber enhancement in DW-MRIrdquoJournal of Mathematical Imaging and Vision vol 46 no 3 pp326ndash368 2013

[33] G E Sotak Jr and K L Boyer ldquoThe Laplacian-of-Gaussiankernel a formal analysis and design procedure for fast accurateconvolution and full-frame outputrdquo Computer Vision Graphicsand Image Processing vol 48 no 2 pp 147ndash189 1989

[34] S S Singh T T SinghHMDevi andT Sinam ldquoLocal contrastenhancement using local standard deviationrdquo InternationalJournal of Computer Applications vol 47 no 15 pp 39ndash44 2012

[35] K C Clarke ldquoComputation of the fractal dimension oftopographic surfaces using the triangular prism surface areamethodrdquo Computers amp Geosciences vol 12 no 5 pp 713ndash7221986

[36] T M Beasley S Erickson and D B Allison ldquoRank-basedinverse normal transformations are increasingly used but arethey meritedrdquo Behavior Genetics vol 39 no 5 pp 580ndash5952009

[37] R Tibshirani ldquoRegression shrinkage and selection via the lassordquoJournal of the Royal Statistical Society Series B Methodologicalvol 58 no 1 pp 267ndash288 1996

[38] J Friedman T Hastie and R Tibshirani ldquoGlmnet lasso andelastic-net regularized generalized linear modelsrdquo R packageVersion vol 1 2009

[39] K Ganesan U R Acharya K C Chua L C Min and K TAbraham ldquoPectoral muscle segmentation a reviewrdquo ComputerMethods and Programs in Biomedicine vol 110 no 1 pp 48ndash572013

[40] D Raba A Oliver J Martı M Peracaula and J EspunyaldquoBreast segmentation with pectoral muscle suppression on dig-ital mammogramsrdquo in Pattern Recognition and Image AnalysisJ S Marques N P de la Blanca and P Pina Eds Lecture Notesin Computer Science pp 471ndash478 Springer Berlin Germany2005

[41] D C Moura and M A G Lopez ldquoAn evaluation of imagedescriptors combined with clinical data for breast cancerdiagnosisrdquo International Journal of Computer Assisted Radiologyand Surgery vol 8 no 4 pp 561ndash574 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of


Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology


Molecular Biology International

GenomicsInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


BioinformaticsAdvances in

Marine BiologyJournal of



Signal TransductionJournal of


BioMed Research International

Evolutionary BiologyInternational Journal of



Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Genetics Research International


Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational



Enzyme Research



Microbiology


provides clues about the presence of early signs of tumors(eg parenchymal distortion small asymmetric bright spotsand contrast) Asymmetry analysis consists of two mainstages alignment of the images and detection of asymmetrythrough a bilateral image subtraction [17]

Current asymmetry detection methods are often basedon simple bilateral subtraction techniques [16 18] How-ever breasts are composed of highly heterogeneous anddeformable tissue resulting in an unlikely perfect matchbetween both breasts [19] Thus in order to efficientlymeasure asymmetry a registration-based alignment must beperformed [20] It is known that the deviations of the normalsymmetrical architecture between breast images reduce therate of false positive detection of masses from digital mam-mograms [21 22] The alignment is improved by using thenipple as a reference point [23] Coregistration of both breastsusing a robust point matching approach and a novel seriesof features helped to detect abnormal cases with masses [24]In addition feature selection was important in a pool of 20bilateral computed features coupled to a genetic algorithmto select and build an artificial neural network classifier [19]Therefore breast asymmetry can be used to assess the risk ofbreast cancer

The objective of this work was to provide evidence thatfeatures related to asymmetry and derived from bilateralimage subtraction maps might be used to automaticallyclassify mammograms sets by their risk of showing breastcancerThis analysis is based on our previous efforts [25] butit is enhanced by the extraction of hundreds of asymmetry-related features and the use of a more robust automatedregistration algorithm and simplified by the use of a reg-ularization feature selection algorithm Although it followsan approach similar to the ones used for mass detection[22 24] our methodology is also evaluated for the detectionof calcifications

2 Materials

A total of 1796 digitalized film mammograms from 449different subjects were used in this study From those 45 wereclassified as healthy subjects (HS) (mean age of 593 SD of98 years) 197 as subjects with malignant calcifications (CS)(mean age of 58 SD of 109 years) and 207 as subjects withmalignant masses (MS) (mean age of 641 SD of 101 years)Each subject had the four standard mammograms taken leftand right craniocaudal (CC) and left and right mediolateraloblique (MLO) projections

In order to avoid problems associated with intrascannervariability [22 24 26] all mammograms in this study wereobtained from the Howtek dataset of the Digital Database forScreening Mammography public database [27] in which allmammograms were digitalized using a Howtek 960 scannerusing a sampling rate of 435 micrometers per pixel and a 12-bit depth

3 Methodology

Figure 1 shows the seven analysis stages used in this studyBriefly these stages consist of (1) segmentation of soft tissue

Patient

Segmentation

CC CCMLO MLO

Registration

Left Right

ToBilateral subtraction

Enhancement filters

Feature extraction

Feature selection

Model evaluation

Left (l) Right (r)

IΔ

H(lrΔ) L(lrΔ)

120590(lrΔ) F(lrΔ)

l r

T(x y)

Il(T(x y))Δr

Figure 1 Workflow of the proposed methodology

(2) registration of the left images to the right images (3)bilateral subtraction of the coregistered images (4) filteringof the images to enhance the signal and texture (5) featureextraction (6)multivariate models selection using a train setand (7)model evaluation on a test set

31 Segmentation The automatic segmentation of the breasttissue was based on the estimation of the background noiseAn initial segmentation mask was created by estimating thebackgroundnoise in the image and discarding all pixels belowfive standard deviations of the noise level Then holes wereremoved by applying closing morphological operations witha 3 times 3 supporting region

119878 (119860) = (119860 (119909 119910) oplus119861 (119909 119910)) ⊖ 119861 (119909 119910) (1)

where oplus and ⊖ are the grayscale dilation and erosionmorphological operations respectively 119861(119909 119910) is a 3 times 3

structural element119860(119909 119910) is the image being segmented and119878(119860) is the resulting segmentation of the 119860(119909 119910) image Thelargest connected region was used as the segmentation maskwhile all other high intensity regions were removed from theimages Figure 2 shows an example of the final segmentationusing this procedure

32 Registration The left breast mammographic images weremirrored and then registered to their corresponding rightbreast images The registration used a standard image reg-istration framework with a B-Spline multiresolution trans-formation optimizing the Mattes mutual information metric


(a) (b)


(a) (b) (c) (d)




119868Δ(119909 119910) =

1003816100381610038161003816119868119903 (119909 119910) minus 119868119897 (T (119909 119910))1003816100381610038161003816 (2)


119897(T(119909 119910)) repre-





119867(119909 119910) = 119868 (119909 119910) minus 119868 (119909 119910) ⊖ 119861 (119909 119910) (3)




119871 (119909 119910) = 119868 (119909 119910) lowast 119866120590(119909 119910) lowast ℎ (119909 119910) (4)




120590 (119909 119910) = radic1119873

sum

119898119899120598R

1198682 (119899119898) minus [1119873

sum

119898119899120598R

119868 (119899119898)]

2

(5)




119903 119868119897 119868Δ 119867119903 119867119897 119867Δ 119871119903 119871119897 119871Δ 120590119903 120590119897 120590Δ 119865119903

119865119897 and 119865








4 Results













5 Discussion









1 CC 119867Δ

27 CC 119871Δ

40 CC 119868Δ

2 CC 119871Δ

402 CC 119865

Δ13 CC 119868

11990329 CC 119865

Δ9 CC 119865

Δ12

3 CC 119868119903

29 CC 119871119897

40 CC 119865Δ

12 CC 119868119903

294 CC 119867

11989729 CC 119865

1199036 MLO 119868

Δ42 CC 119867

11990332

5 CC 119867119897

6 MLO 119867119897

11 MLO 119868Δ

13 CC 119871119903

286 MLO 119868

11989728 CC 119868


32 MLO 119867119903

327 MLO 119867

11989711 CC 119868

Δ11990428 MLO 119871

Δ6 MLO 119865

11989713

8 MLO 119867119897

21 CC 120590Δ119904

38 CC 119868119903

2 CC 119865Δ119904

289 CC 119868

Δ11990428 CC 119865

Δavg 12 CC 119868119903

29 CC 119865Δavg 12

10 CC 120590Δ119904

38 MLO 119868Δ119904

40 CC 119867119903

14 MLO 119868Δavg 2

11 MLO 119871Δavg 27 MLO 119868

Δ11990428 CC 119865

11989711 MLO 119868

Δ1199045

12 CC 119867Δ

27 MLO 119868Δ119904

29 MLO 119871119903

15 MLO 119867Δ119904

3913 MLO 119867

Δ11990431 MLO 119865

11989716

14 MLO 119867Δ119904

7 CC 119868Δ119904

415 MLO 119871

Δavg 39 CC 119867Δ119904

3916 MLO 119871

Δavg 27 CC 119867Δ119904

1917 CC 119871

Δ11990412

18 CC 120590Δ119904

1719 CC 119865

Δavg 1220 MLO 119867

Δ11990431

21 MLO 119865Δavg 12











Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07937AUC = 0725

AUC = 0842

(a)

SpecificitySe

nsiti

vity

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08279AUC = 07667

AUC = 08822

(b)


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07797AUC = 07673

AUC = 0807

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07841AUC = 07649

AUC = 08822

(b)



Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 07333

p-value = 00106

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 08692

p-value = 07873

(b)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0807AUC = 07157

p-value = 01841

(c)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0842AUC = 07083

p-value = 00505

(d)






Table 4


Shape

1 Area 119860119904


2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)


x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩


RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)


11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832


119904


15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904


119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3


119865 (120583119904minus 119911120590119904) 119911 isin 2 3


V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)


1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12


5119904=1205835119904

1205905119904

Morphology



x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩


11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a) (b)


(a) (b) (c) (d)




119868Δ(119909 119910) =

1003816100381610038161003816119868119903 (119909 119910) minus 119868119897 (T (119909 119910))1003816100381610038161003816 (2)


119897(T(119909 119910)) repre-





119867(119909 119910) = 119868 (119909 119910) minus 119868 (119909 119910) ⊖ 119861 (119909 119910) (3)




119871 (119909 119910) = 119868 (119909 119910) lowast 119866120590(119909 119910) lowast ℎ (119909 119910) (4)




120590 (119909 119910) = radic1119873

sum

119898119899120598R

1198682 (119899119898) minus [1119873

sum

119898119899120598R

119868 (119899119898)]

2

(5)




119903 119868119897 119868Δ 119867119903 119867119897 119867Δ 119871119903 119871119897 119871Δ 120590119903 120590119897 120590Δ 119865119903

119865119897 and 119865








4 Results













5 Discussion









1 CC 119867Δ

27 CC 119871Δ

40 CC 119868Δ

2 CC 119871Δ

402 CC 119865

Δ13 CC 119868

11990329 CC 119865

Δ9 CC 119865

Δ12

3 CC 119868119903

29 CC 119871119897

40 CC 119865Δ

12 CC 119868119903

294 CC 119867

11989729 CC 119865

1199036 MLO 119868

Δ42 CC 119867

11990332

5 CC 119867119897

6 MLO 119867119897

11 MLO 119868Δ

13 CC 119871119903

286 MLO 119868

11989728 CC 119868


32 MLO 119867119903

327 MLO 119867

11989711 CC 119868

Δ11990428 MLO 119871

Δ6 MLO 119865

11989713

8 MLO 119867119897

21 CC 120590Δ119904

38 CC 119868119903

2 CC 119865Δ119904

289 CC 119868

Δ11990428 CC 119865

Δavg 12 CC 119868119903

29 CC 119865Δavg 12

10 CC 120590Δ119904

38 MLO 119868Δ119904

40 CC 119867119903

14 MLO 119868Δavg 2

11 MLO 119871Δavg 27 MLO 119868

Δ11990428 CC 119865

11989711 MLO 119868

Δ1199045

12 CC 119867Δ

27 MLO 119868Δ119904

29 MLO 119871119903

15 MLO 119867Δ119904

3913 MLO 119867

Δ11990431 MLO 119865

11989716

14 MLO 119867Δ119904

7 CC 119868Δ119904

415 MLO 119871

Δavg 39 CC 119867Δ119904

3916 MLO 119871

Δavg 27 CC 119867Δ119904

1917 CC 119871

Δ11990412

18 CC 120590Δ119904

1719 CC 119865

Δavg 1220 MLO 119867

Δ11990431

21 MLO 119865Δavg 12











Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07937AUC = 0725

AUC = 0842

(a)

SpecificitySe

nsiti

vity

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08279AUC = 07667

AUC = 08822

(b)


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07797AUC = 07673

AUC = 0807

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07841AUC = 07649

AUC = 08822

(b)



Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 07333

p-value = 00106

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 08692

p-value = 07873

(b)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0807AUC = 07157

p-value = 01841

(c)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0842AUC = 07083

p-value = 00505

(d)






Table 4


Shape

1 Area 119860119904


2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)


x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩


RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)


11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832


119904


15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904


119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3


119865 (120583119904minus 119911120590119904) 119911 isin 2 3


V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)


1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12


5119904=1205835119904

1205905119904

Morphology



x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩


11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology



119867(119909 119910) = 119868 (119909 119910) minus 119868 (119909 119910) ⊖ 119861 (119909 119910) (3)




119871 (119909 119910) = 119868 (119909 119910) lowast 119866120590(119909 119910) lowast ℎ (119909 119910) (4)




120590 (119909 119910) = radic1119873

sum

119898119899120598R

1198682 (119899119898) minus [1119873

sum

119898119899120598R

119868 (119899119898)]

2

(5)




119903 119868119897 119868Δ 119867119903 119867119897 119867Δ 119871119903 119871119897 119871Δ 120590119903 120590119897 120590Δ 119865119903

119865119897 and 119865








4 Results













5 Discussion









1 CC 119867Δ

27 CC 119871Δ

40 CC 119868Δ

2 CC 119871Δ

402 CC 119865

Δ13 CC 119868

11990329 CC 119865

Δ9 CC 119865

Δ12

3 CC 119868119903

29 CC 119871119897

40 CC 119865Δ

12 CC 119868119903

294 CC 119867

11989729 CC 119865

1199036 MLO 119868

Δ42 CC 119867

11990332

5 CC 119867119897

6 MLO 119867119897

11 MLO 119868Δ

13 CC 119871119903

286 MLO 119868

11989728 CC 119868


32 MLO 119867119903

327 MLO 119867

11989711 CC 119868

Δ11990428 MLO 119871

Δ6 MLO 119865

11989713

8 MLO 119867119897

21 CC 120590Δ119904

38 CC 119868119903

2 CC 119865Δ119904

289 CC 119868

Δ11990428 CC 119865

Δavg 12 CC 119868119903

29 CC 119865Δavg 12

10 CC 120590Δ119904

38 MLO 119868Δ119904

40 CC 119867119903

14 MLO 119868Δavg 2

11 MLO 119871Δavg 27 MLO 119868

Δ11990428 CC 119865

11989711 MLO 119868

Δ1199045

12 CC 119867Δ

27 MLO 119868Δ119904

29 MLO 119871119903

15 MLO 119867Δ119904

3913 MLO 119867

Δ11990431 MLO 119865

11989716

14 MLO 119867Δ119904

7 CC 119868Δ119904

415 MLO 119871

Δavg 39 CC 119867Δ119904

3916 MLO 119871

Δavg 27 CC 119867Δ119904

1917 CC 119871

Δ11990412

18 CC 120590Δ119904

1719 CC 119865

Δavg 1220 MLO 119867

Δ11990431

21 MLO 119865Δavg 12











Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07937AUC = 0725

AUC = 0842

(a)

SpecificitySe

nsiti

vity

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08279AUC = 07667

AUC = 08822

(b)


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07797AUC = 07673

AUC = 0807

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07841AUC = 07649

AUC = 08822

(b)



Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 07333

p-value = 00106

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 08692

p-value = 07873

(b)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0807AUC = 07157

p-value = 01841

(c)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0842AUC = 07083

p-value = 00505

(d)






Table 4


Shape

1 Area 119860119904


2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)


x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩


RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)


11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832


119904


15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904


119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3


119865 (120583119904minus 119911120590119904) 119911 isin 2 3


V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)


1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12


5119904=1205835119904

1205905119904

Morphology



x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩


11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology












5 Discussion









1 CC 119867Δ

27 CC 119871Δ

40 CC 119868Δ

2 CC 119871Δ

402 CC 119865

Δ13 CC 119868

11990329 CC 119865

Δ9 CC 119865

Δ12

3 CC 119868119903

29 CC 119871119897

40 CC 119865Δ

12 CC 119868119903

294 CC 119867

11989729 CC 119865

1199036 MLO 119868

Δ42 CC 119867

11990332

5 CC 119867119897

6 MLO 119867119897

11 MLO 119868Δ

13 CC 119871119903

286 MLO 119868

11989728 CC 119868


32 MLO 119867119903

327 MLO 119867

11989711 CC 119868

Δ11990428 MLO 119871

Δ6 MLO 119865

11989713

8 MLO 119867119897

21 CC 120590Δ119904

38 CC 119868119903

2 CC 119865Δ119904

289 CC 119868

Δ11990428 CC 119865

Δavg 12 CC 119868119903

29 CC 119865Δavg 12

10 CC 120590Δ119904

38 MLO 119868Δ119904

40 CC 119867119903

14 MLO 119868Δavg 2

11 MLO 119871Δavg 27 MLO 119868

Δ11990428 CC 119865

11989711 MLO 119868

Δ1199045

12 CC 119867Δ

27 MLO 119868Δ119904

29 MLO 119871119903

15 MLO 119867Δ119904

3913 MLO 119867

Δ11990431 MLO 119865

11989716

14 MLO 119867Δ119904

7 CC 119868Δ119904

415 MLO 119871

Δavg 39 CC 119867Δ119904

3916 MLO 119871

Δavg 27 CC 119867Δ119904

1917 CC 119871

Δ11990412

18 CC 120590Δ119904

1719 CC 119865

Δavg 1220 MLO 119867

Δ11990431

21 MLO 119865Δavg 12











Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07937AUC = 0725

AUC = 0842

(a)

SpecificitySe

nsiti

vity

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08279AUC = 07667

AUC = 08822

(b)


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07797AUC = 07673

AUC = 0807

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07841AUC = 07649

AUC = 08822

(b)



Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 07333

p-value = 00106

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 08692

p-value = 07873

(b)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0807AUC = 07157

p-value = 01841

(c)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0842AUC = 07083

p-value = 00505

(d)






Table 4


Shape

1 Area 119860119904


2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)


x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩


RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)


11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832


119904


15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904


119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3


119865 (120583119904minus 119911120590119904) 119911 isin 2 3


V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)


1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12


5119904=1205835119904

1205905119904

Morphology



x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩


11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





1 CC 119867Δ

27 CC 119871Δ

40 CC 119868Δ

2 CC 119871Δ

402 CC 119865

Δ13 CC 119868

11990329 CC 119865

Δ9 CC 119865

Δ12

3 CC 119868119903

29 CC 119871119897

40 CC 119865Δ

12 CC 119868119903

294 CC 119867

11989729 CC 119865

1199036 MLO 119868

Δ42 CC 119867

11990332

5 CC 119867119897

6 MLO 119867119897

11 MLO 119868Δ

13 CC 119871119903

286 MLO 119868

11989728 CC 119868


32 MLO 119867119903

327 MLO 119867

11989711 CC 119868

Δ11990428 MLO 119871

Δ6 MLO 119865

11989713

8 MLO 119867119897

21 CC 120590Δ119904

38 CC 119868119903

2 CC 119865Δ119904

289 CC 119868

Δ11990428 CC 119865

Δavg 12 CC 119868119903

29 CC 119865Δavg 12

10 CC 120590Δ119904

38 MLO 119868Δ119904

40 CC 119867119903

14 MLO 119868Δavg 2

11 MLO 119871Δavg 27 MLO 119868

Δ11990428 CC 119865

11989711 MLO 119868

Δ1199045

12 CC 119867Δ

27 MLO 119868Δ119904

29 MLO 119871119903

15 MLO 119867Δ119904

3913 MLO 119867

Δ11990431 MLO 119865

11989716

14 MLO 119867Δ119904

7 CC 119868Δ119904

415 MLO 119871

Δavg 39 CC 119867Δ119904

3916 MLO 119871

Δavg 27 CC 119867Δ119904

1917 CC 119871

Δ11990412

18 CC 120590Δ119904

1719 CC 119865

Δavg 1220 MLO 119867

Δ11990431

21 MLO 119865Δavg 12











Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07937AUC = 0725

AUC = 0842

(a)

SpecificitySe

nsiti

vity

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08279AUC = 07667

AUC = 08822

(b)


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07797AUC = 07673

AUC = 0807

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07841AUC = 07649

AUC = 08822

(b)



Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 07333

p-value = 00106

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 08692

p-value = 07873

(b)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0807AUC = 07157

p-value = 01841

(c)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0842AUC = 07083

p-value = 00505

(d)






Table 4


Shape

1 Area 119860119904


2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)


x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩


RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)


11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832


119904


15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904


119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3


119865 (120583119904minus 119911120590119904) 119911 isin 2 3


V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)


1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12


5119904=1205835119904

1205905119904

Morphology



x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩


11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07937AUC = 0725

AUC = 0842

(a)

SpecificitySe

nsiti

vity

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08279AUC = 07667

AUC = 08822

(b)


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07797AUC = 07673

AUC = 0807

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 07841AUC = 07649

AUC = 08822

(b)



Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 07333

p-value = 00106

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 08692

p-value = 07873

(b)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0807AUC = 07157

p-value = 01841

(c)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0842AUC = 07083

p-value = 00505

(d)






Table 4


Shape

1 Area 119860119904


2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)


x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩


RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)


11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832


119904


15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904


119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3


119865 (120583119904minus 119911120590119904) 119911 isin 2 3


V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)


1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12


5119904=1205835119904

1205905119904

Morphology



x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩


11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 07333

p-value = 00106

(a)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 08822AUC = 08692

p-value = 07873

(b)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0807AUC = 07157

p-value = 01841

(c)

Specificity

Sens

itivi

ty

00

02

04

06

08

10

10 08 06 04 02 00

AUC = 0842AUC = 07083

p-value = 00505

(d)






Table 4


Shape

1 Area 119860119904


2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)


x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩


RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)


11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832


119904


15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904


119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3


119865 (120583119904minus 119911120590119904) 119911 isin 2 3


V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)


1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12


5119904=1205835119904

1205905119904

Morphology



x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩


11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Table 4


Shape

1 Area 119860119904


2 Compactness 119862119904=1198752

119904

119860119904

3 Elongation 119864119904=max (119871

119909 119871119910)

min (119871119909 119871119910)


x = ⟨119909 =11989810

11989800

119910 =11989801

11989800

⟩


RS119878=

11989820

11989800

minus 119909211989811

11989800

minus 11990911991011989802

11989800

minus 1199102

Signal

9 Mean 120583119904=

max(119868)

sum

119894=0

119894119891(119894)


11 Energy 119864119904=

max(119868)

sum

119894=0

1198942119891(119894)

12 Variance 1205902

119904= 1198642minus 1205832


119904


15 119911mean 119904=120583119904

120590119904

16 Entropy 119867119904=

max(119868)

sum

119894=0

log(119891(119894))119891(119894)

17 Skewness 120574119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

3

119891 (119894)]

18 Kurtosis 120573119904=

max(119868)

sum

119894=0

[(119894 minus 120583119904

120590119904

)

4

119891 (119894)] minus 3

19 119911 Range 119911DR =DR119904

120590119904


119901119911= 10 minus 119865 (120583

119904+ 119911120590119904) 119911 isin 2 3


119865 (120583119904minus 119911120590119904) 119911 isin 2 3


V119901= V (119901) 119901 isin 00001 0001 001 005 025 075 095 099 0999 09999

34 5 Trimmed Mean 1205835119904=

V(095)

sum

119894=V(005)119894119891(119894)


1205905119904= [

V(095)

sum

119894=V(005)(119894 minus 120583

5119904)2

119891 (119894)]

12


5119904=1205835119904

1205905119904

Morphology



x119868= ⟨119909

119868=11987210

11987200

119910119868=11987201

11987200

⟩


11987220

11987200

minus 1199092

11986811987211

11987200

minus 11990911986811991011986811987202

11987200

minus 1199102

119868

43 Signal Surface 119860119868= Δ119909119910

sum

(119898119899)isin119878(119896)

(Δ119909119910

2+ 4 lowast (119868 (119898 119899) minus 119868 (119898 119899))

2

)12



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology



6 Conclusion



Appendix

Image Features



119878 (119896) = (119898 119899) isinZ2 119904 (119898 119899) = 119896 (A1)


0 119899Δ119910 + 119910

0⟩ (Δ119909 and Δ119910 are



119860119904= 119886 sum

(119898119899)isin119878(119896)

119904 (119898 119899) (A2)




119875119904=

119871

sum

119894=0119863 (A3)


2 119909119895isin 119873119894 is the set of






119891 (119894) =119886

119860119904

sum

(119898119899)isin119878(119896)

[119868 (119898 119899) = 119894] (A4)


119901 (119868 lt V) = 119865 (V) =V

sum

119894=0119891 (119894) (A5)


V (119901) = 119865minus1 (119901) = arg minV

(1003816100381610038161003816119865 (V) minus 119901

1003816100381610038161003816) (A6)


119898119894119895= sum

(119898119899)isin119878(119896)

1003816100381610038161003816119898Δ119909+11990901003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A7)


119872119894119895= sum

(119898119899)isin119878(119896)

119868 (119898 119899)1003816100381610038161003816119898Δ119909+1199090

1003816100381610038161003816119894 1003816100381610038161003816119899Δ119910+1199100

1003816100381610038161003816119895 (A8)


119871119909

= (max119898

(x (119898 119899) sdot ⟨1 0⟩) minusmin119898

(x (119898 119899) sdot ⟨1 0⟩))

forall (119898 119899) isin 119878 (119896)

119871119910


119899(x (119898 119899) sdot ⟨0 1⟩))

forall (119898 119899) isin 119878 (119896)

(A9)





Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Acknowledgments


References


















































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology






















Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology








Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

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