Nonreference Medical Image Edge Map Measure€¦ · ResearchArticle Nonreference Medical Image Edge...

Research ArticleNonreference Medical Image Edge Map Measure

Karen Panetta1 Chen Gao1 Sos Agaian2 and Shahan Nercessian3

1 Department of Electrical and Computer Engineering Tufts University Medford MA 02155 USA2Department of Electrical and Computer Engineering The University of Texas at San Antonio San Antonio TX 78249 USA3MIT Lincoln Laboratory Lexington MA 02421 USA

Correspondence should be addressed to Chen Gao cgchengaogmailcom

Received 11 April 2014 Accepted 21 June 2014 Published 15 July 2014

Academic Editor Yicong Zhou

Copyright copy 2014 Karen Panetta et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Edge detection is a key step in medical image processing It is widely used to extract features perform segmentation and furtherassist in diagnosis A poor quality edge map can result in false alarms and misses in cancer detection algorithms Therefore it isnecessary to have a reliable edgemeasure to assist in selecting the optimal edgemap Existing reference based edgemeasures requirea ground truth edge map to evaluate the similarity between the generated edge map and the ground truth However the groundtruth images are not available for medical images Therefore a nonreference edge measure is ideal for medical image processingapplications In this paper a nonreference reconstruction based edge map evaluation (NREM) is proposed The theoretical basisis that a good edge map keeps the structure and details of the original image thus would yield a good reconstructed image TheNREM is based on comparing the similarity between the reconstructed image with the original image using this concept The edgemeasure is used for selecting the optimal edge detection algorithm and optimal parameters for the algorithm Experimental resultsshow that the quantitative evaluations given by the edge measure have good correlations with human visual analysis

1 Introduction

Edge detection is an essential preprocessing step for earlycancer detection and diagnosis in medical image process-ing such as medical image segmentation registration andreconstruction For example accurate edge detection algo-rithms can be used to track the size of a tumor and thisinformation can help to monitor whether the treatment iseffective or not Traditional edge detection algorithms canbe grouped into two categories one utilizes the first ordergradient information and the other uses second derivativezero crossing information Some popular algorithms includeSobel Robert Prewitt Laplacian LoG and Canny algorithm[1] Some other state-of-the-art edge detection algorithmsalso include Partial Derivatives of Boolean Functions [2]and the Alpha Weighted Quadratic Filter [3] Although theperformance of most of these detectors is acceptable forsimple noise free images the case is dramatically differentfor medical images subjected to noises from the acquisitionsystems [4] Unfortunately medical images usually sufferfrom low contrast or poor resolution due to the limitation

of hardware systems or the exposure time Therefore it isnecessary to have a reliable evaluationmethod tomeasure theperformance of different edge detection algorithms and helpselect the optimal algorithm for specificmedical applications

Many edge measures have been proposed including thefull reference edge measure [5] the nonreference measure[6 7] and the subjective evaluation The full reference edgemeasure requires a ground truth image as a reference andcompares the similarity between candidate edge maps andthe ground truth edgemap However the ground truth imageis not available for medical images Subjective evaluationratings by medical experts are the most widely accepted eval-uation method in medical image processing This approachavoids the use of ground truth edge maps However it isimpossible to remove all the bias and the results can still beinconsistent Furthermore subjective evaluation is expensivewith respect to time and resources thus it is difficult to beautomated

The nonreference based method does not require aground truth and it can be automated Unfortunately theexisting nonreference edge measures are still far from ideal

Hindawi Publishing CorporationInternational Journal of Biomedical ImagingVolume 2014 Article ID 931375 8 pageshttpdxdoiorg1011552014931375

2 International Journal of Biomedical Imaging

A nonreference based edge map evaluation should onlyuse the information from the resultant edge map and theoriginal image itself to make an evaluation Yitzhaky andPeli proposed a probabilistic based nonreference measureusing the receiver operating characteristics (ROC) [7] Theirmethod first estimates a ground truth edge map usingautomatic statistical analysis of the correlation of detectionresults produced using different detector parameters Thenthe edge map which is most similar to the estimated groundtruth is selected as the optimal edge detection results Thismethod balances specificity and sensitivity However thismethod suffers from its bias regarding the generation of theestimated ground truth because the candidate edge mapsused can directly affect the estimated ground truthThereforeif the majority of the edge maps used are not of adequatequality or fail to extract certain features this will be reflectedin the derived estimated ground truth Also since the originalimage data is not used there is no way to indicate how wellthe best determined edge detector output from this approachcorresponds to the original image

In this paper we present a reconstruction based nonrefer-ence edgemeasureThe theoretical basis of thismethod is thata good edge map captures the essential structures and detailsof the original imagesTherefore the reconstruction using thepixel information on a better edgemapwould bemore similarto the original image In our method the edge measure iscomposed of two components the first is the gradient basedstructural similarity measure between the original image andthe reconstructed image and the second component is thepenalty factor For instance the reconstructions from edgemaps with the most edge pixels have the greatest similaritymeasure However they utilize more information from theoriginal image To compensate for this a penalty factor whichis inversely proportional to the number of edge pixels is alsoincluded in the formulation of the measure In other wordswe want a measure that chooses the optimal edge map asthe one that shows the structural details in the image withminimal information and minimal false positives

The rest of this paper is organized as follows Section 2reviews existing reconstruction methods and the similaritymeasures More details of Yitzhakyrsquos edge measure are alsoreviewed in this section Section 3 presents a new nonrefer-ence edge measure (NREM) Section 4 presents the experi-mental results of using the NREM on choosing the optimaledge detection algorithm and optimal operating parametersfor medical images The comparisons against Yitzhakyrsquos edgemeasure are also presented in this section The conclusionsare discussed in Section 5

2 Background

The new NREM is a reconstruction based edge measureIn this section the existing reconstruction methods arereviewed Similarity measures are used to compare thecorrelation between the reconstructed image and the originalimage Varieties of similarity measures are also reviewed inthis section Lastly as a comparison to the NREM theoretical

analysis and the basic steps of Yitzhakyrsquos measure are shownin this section

21 Reconstruction Interpolation has been widely used toobtain the missed pixels from the original image In thecontext of reconstruction the pixels along edges are usedto predict the pixel values in the smooth areas One of thelinear interpolation methods [8] can be described as followsFor each pixel location (119894 119895) notin 119890

119863 the algorithm searches in

the four horizontal and vertical directions and four diagonaldirections for the nearest pixel in the given direction that isin119890119863 The inverse of the distances of the first pixel encountered

in each direction from the given pixel 119889119896is then used as the

weights for the weighted average of their respective imageintensity values 119905

119896 yielding the reconstructed intensity value

for the given pixelThus reconstruction is carried out for eachpixel location (119894 119895) notin 119890

119863by the following

119903 (119894 119895) =sum8

119896=1(1119889119896) 119905119896

sum8

119896=1(1119889119896) (1)

An improvement of (1) is using a weighted medianinstead of weighted mean to make it more robust to noiseAnother modification utilizes the central weighted medianThe central weighted median of a sequence 119909 with weights 119908is given by (2) where the weights are inversely related to thedistance (3) and is the replication operator representing thefact that intensity value 119905

119894is repeated119908

119894times in the sequence

of median calculation in the following

119903 (119894 119895) = median (1199051 1199081 1199052 1199082 119905

8 1199088) (2)

119908119896= round(100

119889119896

) (3)

Another type of reconstruction methods is based on thepartial differential equation (PDE) discretization proposed byBallester et al [9] In such methods high order PDEs aredesigned to restore smooth regions as well as thin structuresThese reconstruction based methods have clear advantagesfor effectively incorporating the original image informationon the edge pixels In nonreferencemeasures this informationis essential because no ground truth exists

22 Similarity Measures To compare the similarity betweentwo images the most commonly adopted methods are thestatistical methods including the pixel-wised mean squareerror (MSE) and mean absolute error (MAE) The MSE andMAEbetween two images119909 and119910 are defined as shown in (4)In (4) 119909 and 119910 represent the two images for comparison and 119894and 119895 represent the pixel locations These statistical methodshave clear physical meanings and are straightforward Under

International Journal of Biomedical Imaging 3

these definitions two images withmore similarity have lowerMSE or MAE

MSE = 1

119872119873

119872

sum119894=1

119873

sum119895=1

[119909 (119894 119895) minus 119910 (119894 119895)]2

MAE = 1

119872119873

119872

sum119894=1

119873

sum119895=1

1003816100381610038161003816119909 (119894 119895) minus 119910 (119894 119895)1003816100381610038161003816

(4)

However these statistical methods do not take into con-sideration the human visual system (HVS) propertiesThere-fore they are inappropriate to be used as reliable measuresfor medical images Bovikrsquos structural similarity measure(SSIM) [10] is based on the hypothesis that human visualsystem (HVS) is highly adapted for extracting structuralinformation The SSIM measure defines the similarity of twoimages as a function of luminance contrast and structurewhere the luminance contrast and structure are defined as

119897 (119909 119910) =2120583119909120583119910+ 1198621

1205832119909+ 1205832119910+ 1198621

119888 (119909 119910) =2120590119909120590119910+ 1198622

1205902119909+ 1205902119910+ 1198622

119904 (119909 119910) =120590119909119910+ 1198623

120590119909120590119910+ 1198623

(5)

Given two images 119909 and 119910 the 120583119909and 120583

119910represent the

means 120590119909and 120590

119910represent the standard deviation of the 119909

and 119910 image respectively and 120590119909119910

represent the covarianceof 119909 and 119910 119862

1 1198622 and 119862

3represent constant values SSIM is

a combination of luminance contrast and structure measureand it is defined as shown in (6) The SSIM is applied onnonoverlapping windows Thus the mean of the SSIM valuesover the entire image (MSSIM (7)) is used to indicate thesimilarity between two images

SSIM (119909 119910) = (2120583119909120583119910+ 1198621

1205832119909+ 1205832119910+ 1198621

)(2120590119909120590119910+ 1198622

1205902119909+ 1205902119910+ 1198622

) (6)

MSSIM (119909 119910) =1

119873

119873

sum119894=1

SSIM (119909119894 119910119894) (7)

23 Yitzhaky and Pelirsquos Edge Measure Yitzhaky and Peliproposed an objective edge detection evaluation method in[7] In this paper the new measure is compared with thismethod Yitzhakyrsquos edge measure is briefly reviewed in thefollowing section

Yitzhakyrsquos edge measure [7] is a nonreference edgemeasure This method performs statistical analysis of thecorrespondence of detection results produced using differentdetector parameters The statistical measures are used toestimate the ground truth edge map considering the tradeoffbetween the true and false edges and to extract the best detec-torrsquos parameter sets In Yitzhakyrsquos method first an estimatedground truth is automatically constructed by examining the

corresponding threshold receiver operating characteristics(CT-ROC) curve given a range of detection results obtainedfrom different detection parameter sets Then the singleparameter set that provides the most similar edge map tothe estimated ground truth edge map is identifiedThemajorsteps of Yitzhakyrsquos edge measure are summarized in Table 1

The original Yitzhakyrsquos edge measure performs a generalautomatic self-evaluation and parameter selection within arange of examined detector parameters It assumes that thebest detection of a certain edge detector in a given image isthat which is most consistent with the variety of detectionoutputs that can be produced by the detection algorithmwhen different parameters are used Therefore by adopting119873 edge detection results using 119873 sets of parameters of oneedge detection algorithm this algorithm can be used to selectthe optimal operating parameters If the 119873 edge detectionresults are obtained from 119873 edge detectors this algorithmcan be used to compare performances between detectionapproaches

3 New Nonreference Edge Map Measure

A generalized block diagram and intermediate results of theestablished nonreference reconstruction based edge measure(NREM) are shown in Figure 1 It consists of three majorsteps grayscale edge map generation reconstruction andsimilarity measure

(1) Grayscale Edge Map Generation The edge detectionalgorithm to be evaluated is applied in this step Regularedge detection algorithms such as Canny Sobel Log andRoberts can be used Furthermore some state-of-the-art edgedetection algorithms designed specifically for the medicalimage applications such as the CLF [11] morphological gradi-ent operator [12] nonlinear diffusion [13] and mathematicalmorphology [14] can also be used in this step

After the edgemap is subtracted amorphological dilationis applied to generate a continuous edgemapThedilated edgemap is then multiplied with the original image yielding agrayscale edge map In this way the pixels on the dilated edgemap contain information from the original image and thesepixels are used to predict the pixel intensity in the smootharea

(2) Reconstruction In the previous section four major inter-polation based reconstruction methods were reviewed Theweighted average (1) method utilizes all the information fromthe eight neighbors but is sensitive to noise Unfortunatelynoise commonly exists in medical image applications Tobe more robust to noise the weighted median and centralweighted median (2) can be used In this way only oneof the neighbors is used to predict the new pixel valueThis replication solves the noise problem but also results inanother problem That is in some areas with a low gradientchange such as the breast tissue in the mammogram imagethis reconstruction may mistakenly yields a large uniformregion

To get a good balance a weighted alpha trimmed meancan be used in the reconstruction Each of the eight neighbors


Table 1 Basic steps in Yitzhakyrsquos NR edge measure

Yitzhakyrsquos edge measure(1) Generate119873 edge detection results119863

119894 119894 = 1 119873 using119873 combinations of parameters

(2) Generate119873 potential ground truth PGT119894 119894 = 1 119873

(3) Calculate the average true positive (TP) true negative (TN) false positive (FP) and false negative (FN) rate for each potentialground truth

(4) Construct the correspondence threshold ROC curve (CT-ROC)(5) Extract the estimated ground truth using either a diagnosis line or the chi-square estimation(6) Select the best edge map which gives the best match to the estimated ground truth

Original image

Edge map Dilation

Reconstruction

Similarity measure

X Grayscale edge

Figure 1 Flow and the intermediate results of the new nonreference edge measure

is assigned with the weighted intensity 119909119896= (1119889

119896)119905119896 where

119905119896is the actual edge pixel intensity and 119889

119896is the distance

between the pixel to be predicted and edge pixel on a specificdirection Then sort values of all the neighbors in ascendingorder such that 119909

1le 1199092le sdot sdot sdot le 119909

119870 Let 119879

120572= lceil120572119870rceil (the

nearest integer greater than or equal to 120572119870) be the numberof the smallest and largest pixel values to be trimmed ordiscarded from the sorted sequence 119909

1 1199092 119909

119870The alpha

trimmed mean [15] is defined by

119883120572=

1

119870 minus 2119879120572

119870minus119879120572

sum119894=119879120572+1

119909119894 (8)

The alpha trimmed mean will be different when theparameter 120572 changes For example it will be the mean valueof the image for 120572 = 0 and the median value of the image if120572 is close to 05 In this way the parameters can be tuned fordifferent applications In this paper the results are obtained

by discarding the maximum and minimum neighbors in thecalculation of alpha weighted mean

(3) Similarity Measure NREM The reconstructed image isthen compared to the original image using a similaritymeasure which is then used as an assessment of the edgemap The SSIM [10] is widely used in clean images but itis noted that the performance of the SSIM index degradedsubstantially when assessing Gaussian blurred images Thenoise in medical images is very prevalent and difficult tomodel In the experiments the SSIM does not performwell when the images are subjected to other distortionssuch as low contrast and blurring effects To measure thesimilarity between the original image and the reconstructedimage the GSSIM [16 17] is used GSSIM suggests that thegradients of the images to be compared be integrated intothe image similarity assessment to penalize dissimilarity inimage contours and edges Thus the GSSIM index makescomparisons between both 119909 and 119910 and the gradients of 119909and 119910 The gradients of 119909 and 119910 specifically indicate the


(a) (b) (c)

(d) (e) (f)

Figure 2 Reconstruction results using different interpolation methods (a) Original CT kidney image (b)ndash(f) Reconstructed results from(b) weighted average (c) weighted median (d) central weighted median (e) PDE and (f) alpha trimmed weighted average

similarity between edges In the expression of GSSIM thecontrast and structure terms of SSIM are modified as in (9)where 120590

1199091015840 and 120590

1199101015840 represent the standard deviation of the

gradient magnitude of 119909 and 119910 respectively

119888 (1199091015840 1199101015840) =

212059011990910158401205901199101015840 + 1198622

12059021199091015840+ 12059021199101015840+ 1198622

119904 (1199091015840 1199101015840) =

12059011990910158401199101015840 + 1198623

12059011990910158401205901199101015840 + 1198623

(9)

Using similar methods to fuse luminance gradient con-trast and gradient structure together the GSSIM over sub-blocks can be shown in the following

GSSIM (119909 119910) = [119897 (119909 119910)]120572[119888 (1199091015840 1199101015840)]120573

[119904 (1199091015840 1199101015840)]120574

(10)

Therefore the mean of GSSIM over the entire image canbe used to indicate the similarity between the reconstructedimage and the original image

MGSSIM (119909 119910) =1

119873

119873

sum119894=1

GSSIM (119909119894 119910119894) (11)

It is worth noting that the similarity measure itself is notaccurate enough tomeasure the reconstruction performance

The reason is that when more edge pixels exist in an edgemap more information from the original image is used inthe reconstruction which will definitely yield more similarresults Therefore a penalty factor 119891

119901which is formulated as

a decreasing function of the total number of edge pixels isintroduced in (12) where 119873

119890represents the total number of

edge pixels in the dilated edge map and119872119873 represents thetotal number of pixels in the original image

119891119901=

1

1 + 119873119890119872119873

(12)

The final nonreference based edge measure (NREM) iscomprised as the alpha weighted product of these two termsIn this paper the results are shown with 120572 = 1 and 120573 = 3which were obtained experimentally

NREM (119894 119890) = (MGSSIM)120572119891120573119901 (13)

4 Experimental Results

Edge detection plays an important role in medical imageprocessing as it determines the structure of objects in imagesIn this section we demonstrate some applications of the newnonreference edge measures NREM on medical image pro-cessing The testing images are obtained from the FrederickNational Library for Cancer Research Database [18]


(a) (b) NREM = 01917 Yitzhakyrsquos = minus11953 (c) NREM = 08506 Yitzhakyrsquos = 05773

(d) NREM = 07443 Yitzhakyrsquos = minus03462 (e) NREM = 06905 Yitzhakyrsquos = minus06754 (f) NREM = 06905 Yitzhakyrsquos = 05866

Figure 3 Using measures to select optimal edge detection algorithms (a) Original CT abdomen image (b)ndash(f) Edge detection results from(b) Canny (c) Sobel (d) Roberts (e) LoG and(f) Prewitt The optimal edge maps with highest NREM value and Yitzhakyrsquos measure valueare in bold

The first example compares the reconstruction resultsusing the weighted mean weighted median central weightedmedian PDE and alpha trimmed weighted mean basedinterpolation Figure 2 shows the original CT kidney imageand five reconstructions It is seen from the results that forthe low quality medical images the mean based reconstruc-tion is not as sharp as the median based reconstructionHowever the median based reconstruction introduces someartificial lines As analyzed before the alpha trimmed meancan be converted to mean or median filter with differentparameter alpha In Figure 3 the alpha trimmed weightedmean reconstruction achieves a good balance The centralweighted median retrieves details but also introduces falsedetails especially around the edge of the real tissuesThe PDEbased painting method suffers from severe blurring effects

The second example is using the nonreference edgemeasures selecting the optimal edge detection algorithm InFigure 3 multiple edge detection results from the CannySobel Roberts Log and Prewitt for a CT abdomen imageare shown in Figures 3(b)ndash3(f) These edge detection algo-rithms shown in Figure 3 are commonly used edge detectionalgorithms and each has its advantages and disadvantagesFor example gradient based edge detection algorithms suchas Sobel and Prewitt are simple but sensitive to noise TheCanny edge detector improves the signal to noise ratio by

smoothing the image however the smoothing may lead toloss of corners and detection of double edges Therefore itis necessary to have a reliable edge measure that can helpto decide the optimal edge detection algorithm for a specificimage The NREM selects the Sobel edge detection result asthe optimal and Yitzhakyrsquos method selects the Prewitt Thesetwo edge detection results agree with the visual assessmentAs a comparison the Canny and LoG edge subtract all thesoft tissues inside the abdomen while the Roberts edge hasthe disconnection problem on the key edges

Another example of using the edge measure as a meansof selecting optimal parameter values is shown in Figure 4In this experiment the Sobel edge detection algorithm withdifferent threshold ranging from 001 to 008 is used Thetesting image is an X-Ray chest image which suffers from lowcontrastTherefore lower threshold values tend to keepmoresoft tissue or other noise components in the edge map whilehigher threshold values discard essential edgesThe proposedmeasure selects the optimal parameter at threshold = 003 andachieves the best tradeoff between noise removal and featureextraction In contrast Yitzhakyrsquos method selects threshold =006 which losses some ribs in the edge map Figure 4(k) alsoillustrates the need for the edge pixel density function in theformulation of NREM as the use of MGSSIM alone results inthe discussed edge pixel bias


(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

001 002 003 004 005 006 007 008

035

04

045

05

055

Threshold

Mea

sure

val

ue

NREM

(j)

001 002 003 004 005 006 007 008

04

05

06

07

08

09

1

Threshold

Mea

sure

val

ue

MGSSIM

(k)

001 002 003 004 005 006 007 008

02

Threshold

Mea

sure

val

ue

Yitzhakyrsquos measure

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

(l)

Figure 4 Applying edge measures in assisting in selecting optimal operating parameters (a) Original X-ray chest image (b)ndash(i) Edgedetection results using the Sobel edge detector with the threshold ranging from 001 to 008 (j) Presented measure plot indicating 119879 = 003 asthe optimal parameter value (k) Measure plot of using MGSSIM alone (l) Yitzhakyrsquos method indicating 119879 = 006 as the optimal parametervalue


5 Conclusions

Nonreference edge measure is very useful in medical imagesegmentation registration and reconstruction A new non-reference edge map evaluation NREM for medical applica-tions is proposed in this paper This measure is based on thefact that the best edge map results consist of the least numberof edge pixels at their correct locations needed to characterizeall the relevant structures in the reconstruction image Com-parison with state-of-the-art nonreference edge detectionmeasure shows the advantages of the new measure theNREM utilizes the information from the original image andthus can achieve better performance Experimental resultson using the NREM on selecting the optimal edge detectionalgorithm and optimal operating parameters show that themeasure coincides with subjective evaluation validating theusefulness of the measure

Conflict of Interests

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

References

[1] D Ziou and S Tabbone ldquoEdge detection techniques anoverviewrdquo Pattern Recognition and Image Analysis CC ofRaspoznavaniye Obrazov I Analiz Izobrazhenii vol 8 pp 537ndash559 1998

[2] E E Danahy S S Agaian and K A Panetta ldquoDirectional edgedetection using the logical transform for binary and grayscaleimagesrdquo inMobileMultimediaImage Processing forMilitary andSecurity Applications vol 6250 of Proceedings of SPIE pp 1ndash122006

[3] C Gao K Panetta and S Agaian ldquoNew edge detectionalgorithms using alpha weighted quadratic filterrdquo in Proceedingsof the IEEE International Conference on Systems Man andCybernetics (SMCrsquo11) pp 3167ndash3172 Anchorage Alaska USAOctober 2011

[4] M Bennamoun ldquoEdge detection problems and solutionsrdquo inProceedings of the IEEE International Conference on SystemsMan and Cybernetics pp 3164ndash3169 October 1997

[5] S C Nercessian S S Agaian and K A Panetta ldquoA newreference-based measure for objective edge map evaluationrdquo inMobileMultimediaImage Processing Security and Applicationsvol 7351 of Proceedings of SPIE April 2009

[6] S Nercessian K Panetta and S Agaian ldquoA non-referencemeasure for objective edgemap evaluationrdquo in Proceeding of theIEEE International Conference on Systems Man and Cybernetics(SMCrsquo09) pp 4563ndash4568 San Antonio Tex USA October2009

[7] Y Yitzhaky and E Peli ldquoA method for objective edge detectionevaluation and detector parameter selectionrdquo IEEETransactionson Pattern Analysis and Machine Intelligence vol 25 no 8 pp1027ndash1033 2003

[8] B Govindarajan K A Panetta and S Agaian ldquoImage recon-struction for quality assessment of edge detectorsrdquo in Proceed-ings of the IEEE International Conference on Systems Man andCybernetics (SMC rsquo08) pp 691ndash696 October 2008

[9] C Ballester M Bertalmio V Caselles and J Verdera ldquoFilling-in by joint interpolation of vector fields and gray levelsrdquo IEEE

Transactions on Image Processing vol 10 no 8 pp 1200ndash12112001

[10] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[11] J Quintanilla-Domınguez M G Cortina-Januchs A Jevtic DAndina J M Barron-Adame and A Vega-Corona ldquoCombina-tion of nonlinear filters and ANN for detection of microcalcifi-cations in digitized mammographyrdquo in Proceedings of the IEEEInternational Conference on SystemsMan andCybernetics (SMCrsquo09) pp 1516ndash1520 October 2009

[12] C Santhaiah G A Babu andM U Rani ldquoGray-level morpho-logical operations for image segmentation and tracking edgeson medical applicationsrdquo International Journal of ComputerScience and Network Security vol 9 pp 131ndash136 2009

[13] F Catte P-L Lions J-M Morel and T Coll ldquoImage selectivesmoothing and edge detection by nonlinear diffusionrdquo SIAMJournal on Numerical Analysis vol 29 no 1 pp 182ndash193 1992

[14] Y Zhao W Gui Z Chen J Tang and L Li ldquoMedicalimages edge detection based on mathematical morphologyrdquo inProceedings of the 27th Annual International Conference of theEngineering in Medicine and Biology Society (IEEE-EMBS rsquo05)pp 6492ndash6495 September 2005

[15] J B Bednar and T L Watt ldquo120572-trimmed means and theirrelationship to median filtersrdquo IEEE Transactions on AcousticsSpeech and Signal Processing vol 32 no 1 pp 145ndash153 1984

[16] G-H Chen C-L Yang and S-L Xie ldquoGradient-based struc-tural similarity for image quality assessmentrdquo in Proceedingsof the IEEE International Conference on Image Processing(ICIPrsquo06) pp 2929ndash2932 Atlanta Ga USA October 2006

[17] S Nercessian S S Agaian and K A Panetta ldquoAn imagesimilarity measure using enhanced human visual system char-acteristicsrdquo in Mobile MultimediaImage Processing Securityand Applications 806310 vol 8063 of Proceedings of SPIE SPIEDefense Security and Sensing Orlando Fla USA April 2011

[18] E Rosten andTDrummond ldquoMachine learning for high-speedcorner detectionrdquo in Proceedings of the 9th European Conferenceon Computer Vision (ECCVrsquo06) pp 430ndash443 Springer 2006


A nonreference based edge map evaluation should onlyuse the information from the resultant edge map and theoriginal image itself to make an evaluation Yitzhaky andPeli proposed a probabilistic based nonreference measureusing the receiver operating characteristics (ROC) [7] Theirmethod first estimates a ground truth edge map usingautomatic statistical analysis of the correlation of detectionresults produced using different detector parameters Thenthe edge map which is most similar to the estimated groundtruth is selected as the optimal edge detection results Thismethod balances specificity and sensitivity However thismethod suffers from its bias regarding the generation of theestimated ground truth because the candidate edge mapsused can directly affect the estimated ground truthThereforeif the majority of the edge maps used are not of adequatequality or fail to extract certain features this will be reflectedin the derived estimated ground truth Also since the originalimage data is not used there is no way to indicate how wellthe best determined edge detector output from this approachcorresponds to the original image

In this paper we present a reconstruction based nonrefer-ence edgemeasureThe theoretical basis of thismethod is thata good edge map captures the essential structures and detailsof the original imagesTherefore the reconstruction using thepixel information on a better edgemapwould bemore similarto the original image In our method the edge measure iscomposed of two components the first is the gradient basedstructural similarity measure between the original image andthe reconstructed image and the second component is thepenalty factor For instance the reconstructions from edgemaps with the most edge pixels have the greatest similaritymeasure However they utilize more information from theoriginal image To compensate for this a penalty factor whichis inversely proportional to the number of edge pixels is alsoincluded in the formulation of the measure In other wordswe want a measure that chooses the optimal edge map asthe one that shows the structural details in the image withminimal information and minimal false positives

The rest of this paper is organized as follows Section 2reviews existing reconstruction methods and the similaritymeasures More details of Yitzhakyrsquos edge measure are alsoreviewed in this section Section 3 presents a new nonrefer-ence edge measure (NREM) Section 4 presents the experi-mental results of using the NREM on choosing the optimaledge detection algorithm and optimal operating parametersfor medical images The comparisons against Yitzhakyrsquos edgemeasure are also presented in this section The conclusionsare discussed in Section 5

2 Background

The new NREM is a reconstruction based edge measureIn this section the existing reconstruction methods arereviewed Similarity measures are used to compare thecorrelation between the reconstructed image and the originalimage Varieties of similarity measures are also reviewed inthis section Lastly as a comparison to the NREM theoretical

analysis and the basic steps of Yitzhakyrsquos measure are shownin this section

21 Reconstruction Interpolation has been widely used toobtain the missed pixels from the original image In thecontext of reconstruction the pixels along edges are usedto predict the pixel values in the smooth areas One of thelinear interpolation methods [8] can be described as followsFor each pixel location (119894 119895) notin 119890

119863 the algorithm searches in

the four horizontal and vertical directions and four diagonaldirections for the nearest pixel in the given direction that isin119890119863 The inverse of the distances of the first pixel encountered

in each direction from the given pixel 119889119896is then used as the

weights for the weighted average of their respective imageintensity values 119905

119896 yielding the reconstructed intensity value

for the given pixelThus reconstruction is carried out for eachpixel location (119894 119895) notin 119890

119863by the following

119903 (119894 119895) =sum8

119896=1(1119889119896) 119905119896

sum8

119896=1(1119889119896) (1)

An improvement of (1) is using a weighted medianinstead of weighted mean to make it more robust to noiseAnother modification utilizes the central weighted medianThe central weighted median of a sequence 119909 with weights 119908is given by (2) where the weights are inversely related to thedistance (3) and is the replication operator representing thefact that intensity value 119905

119894is repeated119908

119894times in the sequence

of median calculation in the following

119903 (119894 119895) = median (1199051 1199081 1199052 1199082 119905

8 1199088) (2)

119908119896= round(100

119889119896

) (3)

Another type of reconstruction methods is based on thepartial differential equation (PDE) discretization proposed byBallester et al [9] In such methods high order PDEs aredesigned to restore smooth regions as well as thin structuresThese reconstruction based methods have clear advantagesfor effectively incorporating the original image informationon the edge pixels In nonreferencemeasures this informationis essential because no ground truth exists

22 Similarity Measures To compare the similarity betweentwo images the most commonly adopted methods are thestatistical methods including the pixel-wised mean squareerror (MSE) and mean absolute error (MAE) The MSE andMAEbetween two images119909 and119910 are defined as shown in (4)In (4) 119909 and 119910 represent the two images for comparison and 119894and 119895 represent the pixel locations These statistical methodshave clear physical meanings and are straightforward Under



MSE = 1

119872119873

119872

sum119894=1

119873

sum119895=1

[119909 (119894 119895) minus 119910 (119894 119895)]2

MAE = 1

119872119873

119872

sum119894=1

119873

sum119895=1

1003816100381610038161003816119909 (119894 119895) minus 119910 (119894 119895)1003816100381610038161003816

(4)


119897 (119909 119910) =2120583119909120583119910+ 1198621

1205832119909+ 1205832119910+ 1198621

119888 (119909 119910) =2120590119909120590119910+ 1198622

1205902119909+ 1205902119910+ 1198622

119904 (119909 119910) =120590119909119910+ 1198623

120590119909120590119910+ 1198623

(5)


119910represent the

means 120590119909and 120590




1 1198622 and 119862



SSIM (119909 119910) = (2120583119909120583119910+ 1198621

1205832119909+ 1205832119910+ 1198621

)(2120590119909120590119910+ 1198622

1205902119909+ 1205902119910+ 1198622

) (6)

MSSIM (119909 119910) =1

119873

119873

sum119894=1

SSIM (119909119894 119910119894) (7)


















Original image

Edge map Dilation

Reconstruction

Similarity measure

X Grayscale edge



119896)119905119896 where





119870 Let 119879

120572= lceil120572119870rceil (the


1 1199092 119909

119870The alpha


119883120572=

1

119870 minus 2119879120572

119870minus119879120572

sum119894=119879120572+1

119909119894 (8)





(a) (b) (c)

(d) (e) (f)



1199091015840 and 120590



119888 (1199091015840 1199101015840) =

212059011990910158401205901199101015840 + 1198622

12059021199091015840+ 12059021199101015840+ 1198622

119904 (1199091015840 1199101015840) =

12059011990910158401199101015840 + 1198623

12059011990910158401205901199101015840 + 1198623

(9)


GSSIM (119909 119910) = [119897 (119909 119910)]120572[119888 (1199091015840 1199101015840)]120573

[119904 (1199091015840 1199101015840)]120574

(10)


MGSSIM (119909 119910) =1

119873

119873

sum119894=1

GSSIM (119909119894 119910119894) (11)







119891119901=

1

1 + 119873119890119872119873

(12)


NREM (119894 119890) = (MGSSIM)120572119891120573119901 (13)












(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

001 002 003 004 005 006 007 008

035

04

045

05

055

Threshold

Mea

sure

val

ue

NREM

(j)

001 002 003 004 005 006 007 008

04

05

06

07

08

09

1

Threshold

Mea

sure

val

ue

MGSSIM

(k)

001 002 003 004 005 006 007 008

02

Threshold

Mea

sure

val

ue


minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

(l)



5 Conclusions




References






















MSE = 1

119872119873

119872

sum119894=1

119873

sum119895=1

[119909 (119894 119895) minus 119910 (119894 119895)]2

MAE = 1

119872119873

119872

sum119894=1

119873

sum119895=1

1003816100381610038161003816119909 (119894 119895) minus 119910 (119894 119895)1003816100381610038161003816

(4)


119897 (119909 119910) =2120583119909120583119910+ 1198621

1205832119909+ 1205832119910+ 1198621

119888 (119909 119910) =2120590119909120590119910+ 1198622

1205902119909+ 1205902119910+ 1198622

119904 (119909 119910) =120590119909119910+ 1198623

120590119909120590119910+ 1198623

(5)


119910represent the

means 120590119909and 120590




1 1198622 and 119862



SSIM (119909 119910) = (2120583119909120583119910+ 1198621

1205832119909+ 1205832119910+ 1198621

)(2120590119909120590119910+ 1198622

1205902119909+ 1205902119910+ 1198622

) (6)

MSSIM (119909 119910) =1

119873

119873

sum119894=1

SSIM (119909119894 119910119894) (7)


















Original image

Edge map Dilation

Reconstruction

Similarity measure

X Grayscale edge



119896)119905119896 where





119870 Let 119879

120572= lceil120572119870rceil (the


1 1199092 119909

119870The alpha


119883120572=

1

119870 minus 2119879120572

119870minus119879120572

sum119894=119879120572+1

119909119894 (8)





(a) (b) (c)

(d) (e) (f)



1199091015840 and 120590



119888 (1199091015840 1199101015840) =

212059011990910158401205901199101015840 + 1198622

12059021199091015840+ 12059021199101015840+ 1198622

119904 (1199091015840 1199101015840) =

12059011990910158401199101015840 + 1198623

12059011990910158401205901199101015840 + 1198623

(9)


GSSIM (119909 119910) = [119897 (119909 119910)]120572[119888 (1199091015840 1199101015840)]120573

[119904 (1199091015840 1199101015840)]120574

(10)


MGSSIM (119909 119910) =1

119873

119873

sum119894=1

GSSIM (119909119894 119910119894) (11)







119891119901=

1

1 + 119873119890119872119873

(12)


NREM (119894 119890) = (MGSSIM)120572119891120573119901 (13)












(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

001 002 003 004 005 006 007 008

035

04

045

05

055

Threshold

Mea

sure

val

ue

NREM

(j)

001 002 003 004 005 006 007 008

04

05

06

07

08

09

1

Threshold

Mea

sure

val

ue

MGSSIM

(k)

001 002 003 004 005 006 007 008

02

Threshold

Mea

sure

val

ue


minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

(l)



5 Conclusions




References



























Original image

Edge map Dilation

Reconstruction

Similarity measure

X Grayscale edge



119896)119905119896 where





119870 Let 119879

120572= lceil120572119870rceil (the


1 1199092 119909

119870The alpha


119883120572=

1

119870 minus 2119879120572

119870minus119879120572

sum119894=119879120572+1

119909119894 (8)





(a) (b) (c)

(d) (e) (f)



1199091015840 and 120590



119888 (1199091015840 1199101015840) =

212059011990910158401205901199101015840 + 1198622

12059021199091015840+ 12059021199101015840+ 1198622

119904 (1199091015840 1199101015840) =

12059011990910158401199101015840 + 1198623

12059011990910158401205901199101015840 + 1198623

(9)


GSSIM (119909 119910) = [119897 (119909 119910)]120572[119888 (1199091015840 1199101015840)]120573

[119904 (1199091015840 1199101015840)]120574

(10)


MGSSIM (119909 119910) =1

119873

119873

sum119894=1

GSSIM (119909119894 119910119894) (11)







119891119901=

1

1 + 119873119890119872119873

(12)


NREM (119894 119890) = (MGSSIM)120572119891120573119901 (13)












(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

001 002 003 004 005 006 007 008

035

04

045

05

055

Threshold

Mea

sure

val

ue

NREM

(j)

001 002 003 004 005 006 007 008

04

05

06

07

08

09

1

Threshold

Mea

sure

val

ue

MGSSIM

(k)

001 002 003 004 005 006 007 008

02

Threshold

Mea

sure

val

ue


minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

(l)



5 Conclusions




References





















(a) (b) (c)

(d) (e) (f)



1199091015840 and 120590



119888 (1199091015840 1199101015840) =

212059011990910158401205901199101015840 + 1198622

12059021199091015840+ 12059021199101015840+ 1198622

119904 (1199091015840 1199101015840) =

12059011990910158401199101015840 + 1198623

12059011990910158401205901199101015840 + 1198623

(9)


GSSIM (119909 119910) = [119897 (119909 119910)]120572[119888 (1199091015840 1199101015840)]120573

[119904 (1199091015840 1199101015840)]120574

(10)


MGSSIM (119909 119910) =1

119873

119873

sum119894=1

GSSIM (119909119894 119910119894) (11)







119891119901=

1

1 + 119873119890119872119873

(12)


NREM (119894 119890) = (MGSSIM)120572119891120573119901 (13)












(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

001 002 003 004 005 006 007 008

035

04

045

05

055

Threshold

Mea

sure

val

ue

NREM

(j)

001 002 003 004 005 006 007 008

04

05

06

07

08

09

1

Threshold

Mea

sure

val

ue

MGSSIM

(k)

001 002 003 004 005 006 007 008

02

Threshold

Mea

sure

val

ue


minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

(l)



5 Conclusions




References





























(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

001 002 003 004 005 006 007 008

035

04

045

05

055

Threshold

Mea

sure

val

ue

NREM

(j)

001 002 003 004 005 006 007 008

04

05

06

07

08

09

1

Threshold

Mea

sure

val

ue

MGSSIM

(k)

001 002 003 004 005 006 007 008

02

Threshold

Mea

sure

val

ue


minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

(l)



5 Conclusions




References





















5 Conclusions




References




















Nonreference Medical Image Edge Map Measure€¦ · ResearchArticle Nonreference Medical Image Edge...

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