NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society

Quality evaluation of fuzzy contrast enhancementalgorithms *C

M.A. Wirth, D. NikitenkoDepartment ofComputing & Information Science

University ofGuelphGuelph, Ontario, NIG 2WI, Canada

mwirth(uoguelph.ca

Abstract - A number of algorithms for contrast enhancementincorporating fuzzy reasoning have been proposed in theliterature. This paper evaluates four familiar fuzzy enhancementalgorithms by applying them to the task of mammogramenhancement. MATLAB implementations of the algorithms andperformance metrics are available online athttp://www.uoguelph.ca/kmwirth.

I. INTRODUCTION

With the continued interest in developing imageenhancement algorithms, we have seen a progressive increasein the part fuzzy image processing plays in contrastenhancement. The role of contrast enhancement is to improvethe quality of an image, distinguishing between image detailssuch as fine structures which should be preserved andunwanted artifacts such as noise, which should be suppressed.Although there have been many fuzzy approaches to contrastenhancement, there has been little if any comparison of theirparticular strengths and weaknesses when applied to diversemedical and biological applications. One of the caveats ofmany image enhancement algorithms is the way in which theyare evaluated. A significant difficulty which arises in theevaluation of enhancement algorithms is fmding suitablemetrics which provide an objective measure of performance.There is no single metric which correlates well with imagequality as perceived by the human visual system.

Selection of an appropriate algorithm is dependent on theobjective of the task. In the context of image enhancement,requirements are essentially different for screen-basedenhancement and enhancement which is embedded within analgorithm (as a sub-algofithm). For example, from aradiologists viewpoint, enhancement algorithms are used toachieve enhanced visualizations of anatomical structures , andtherefore detail preservation is a key requirement. Oftenanonymous criteria are used to define the variable success ofeach technique - one that is inherently dependent on theintrinsic characteristics of the image. Algorithms incorporatingfuzzy reasoning are designed for efficiently modelingvagueness and ambiguity - two characteristics oftenassociated with medical or biological images, such asmammograms. A number of fuzzy techniques have beenintroduced for image enhancement [1]. This work exploresthe quantitative evaluation of fuzzy contrast enhancement

algorithms and their ability to improve the quality of imagessuch as mammograms.

II. Fuzzy ENHANCEMENT ALGORITHMS

Fuzzy image enhancement is based in the concept ofmapping a grayscale image onto a fuzzy plane, using someform of membership function such as an S-function [2]. Themembership function characterizes some property of an image(e.g. edginess), and the process is known as imagefuzzification. The membership values are then modified insome manner to improve the contrast. The modifiedmembership values are then inversely transformed through theprocess of defuzzification to produce the enhanced image. Allfuzzy enhancement algorithms follow the same core steps asshown in Fig. 1.

or-iginal linage Membership Image enhancedimage Fuzzification Modification Defuzzification inmage

Fig. 1: Fuzzy enhancement schema

In this investigation, a series of different types ofenhancement algorithms, incorporating fuzzy reasoning [1] arecompared from the literature:

1. fuzzy histogram hyperbolization2. minimization of fuzziness3. fuzzy expected value4. possibility distribution

A. Fuzzy Histogram Hyperbolization (FHH)An extension of histogram hyperbolization [3], this algorithmmodifies the image histogram in a logarithmic manner insteadof flattening it [4]. The algorithm involves four steps:Step 1: Selection of a membership function to fuzzify theimage.Step 2: Selection of the value for the fuzzifer /3: Used tomodify the membership values where 3 -*0 produces brightimages and / -> oo produces dark images.Step 3: Calculate the membership values for each intensityvalue.Step 4: Generate the new gray levels using:

This work is supported by a Discovery Grant from the Canadian National Science and Engineering Research Council (NSERC)

0-7803-91 87-X/05/$20.00 ©2005 IEEE. 436

,4 ) [number of elements x: XF (x) . T]N(5

where L is the maximum number of grey levels in the image.

We examine the use of two membership functions: S-function, and a norma-function. A norma-function is achievedby scaling the intensities (e.g. 0..255) to lie in the range [0,1],such that the gray level of a pixel is representative of itsdegree of membership in the high-intensity pixels. Hence thefuzzifier is a simple N-finction which performs onlynormalization. The norna-function is defined as:where #(gj is the membership value of grey level gj.

(g, -min) (2)

(max-mmn)where max and min are the maximum and minimum values ofthe original image, and gj and u (ga ) are the intensity valueand fizzified value of the image at the pixel (i, j) in theoriginal and fuzzified images respectively. The S-function isdefined as:

0

21(gy -a)l(r-a)21-22(gii - r)/(r- ax)

if g.. <a

ifa<gi <.f

if/c<g, < Y

ifgy > r

where , is the crossover point, yis the point at which theheight of the S-function is 1, and a = 2,/3- y. The use of thenorma-function does not change global intensitycharacteristics of the image, whilst the use of fuzzifiers suchas the S-function pre-enhance certain intensity ranges, basedon parameters chosen using the parameters a, /3 and r.

B. Equalization using Fuzzy Expected Value (FEV)The fuzzy expected value (FEV) is calculated to improve thequality of an image with respect to the distance of all grey-levels from the FEV [5]. The algorithm involves four steps:Step 1: Calculate the image histogram.Step 2: Calculate the FEV:

where N is the total number of elements in the set. The FEV istherefore defined by:

FEV = sup {min[T,,u(sT )]}O<T<1

(6)

Step 3: Calculate the distance of each grey level from theFEV:

Dij= (FEV)2 -(gij)2Step 4: Generate the new gray levels using the followingrules:

[max (0,FEV -D ) if gi < FEV

gi = min (L - 1 FEV + Du) if gi > FEV[FEV otherwise

(7)

(8)

C. Minimization ofFuzziness (MF)One of the first known fuzzy enhancement algorithms, it isoften known as the contrast intensification operator [6]. The

(3) main aim of this algorithm is to reduce the amount of imagefuzziness. The algorithm is a three step process:Step 1: Perform grey-level fuzzification:

(9)

where

-gmaxF gm] and Fe = 20.L5. i(10)

and Fe and Fd are the exponential and denominationalfuzzifiers that control the amount of grayness ambiguity [6].

Step 2: Modify the membership values using successiveapplication of Zadeh's intensification operator:

aT {xIXF(x) 2 T},

is a subset which represents the number of elements in the setabove and equal to some threshold and ,u is a fuzzy measure

defined over subsets of F:

ju'(g) {2[Y(gy)]2 if 0<,u(g)<0.5

1-2[ - j(gf)2 if 0.5 < u(gu) <I

Step 3: Perform grey-level defuzzification:

437

(1)

0<T<I (4)

(11)

(L 1)(e-,U(gu)" 1)gii = I -Ie

L- -i

(5)

p(gij ) = I+ gmax gmin FF e

d

gi = gmax Fd [(Oguj)) ](2

D. Possibility Distribution (PD)Introduced by Zadeh [7], the possibility distribution can becharacterized using five parameters: (a,A, ,2, max), wherea represents the minimum of the distribution, A6i and 12 are

distribution mid-points, y is the mean intensity and max is themaximum value. The general aim is to decrease intensitiesbelow 81 and above 62 . This is a three-step process:

Step 1: Perform grey-level fuzzification:

2 (gij -a)l(r-a))11-2((gij -r)/(r-a))1- 2((gij - r)/(max- r))2 (gij - at)/(max- r))

if a < g1, </31if ,Aj < gu <7Y

if g.gij /2

if gij .162

where l = (a + y)/2 and 2 = (max+ y)/2

Step 2: Perform the enhancement operation using a modifier,r:

,, (gij) = (ge ), (14

Step 3: Perform image defuzzification:

gi,= /,Ygu (15)

III. PERFORMANCE EVALUATION CR1TEREAThe task of evaluating the accuracy of an enhancement

algorithm is difficult due to the lack of an objective definitionof "good enhancement", beyond visual assessment. Unlikephysically measurable quantities, human judgment issubjective. Subjective evaluation is human-perceived visualquality, and is often measured for a group of observers andreported as a mean opinion score. A significant difficultywhich arises in the quantitative evaluation of such algorithmsis finding suitable metrics which provide an objective measureof performance. There is no single metric which correlateswell with image quality as perceived by the human visualsystem. Without any gold standards for image enhancementevaluation, a number of metrics have been used toquantitatively analyze the enhanced images. We use threequality metrics in addition to visual assessment of thealgorithms. Note that these metrics are classified as full-reference in that they make use of the original image as areference.

The first metric we use is the Noise Amplification Index(NAI) [8]which represents the amount of image noiseremoved through enhancement. It uses Rank's algorithm fornoise estimation [Rank 1999] by calculating the noise contentfor the original, and enhanced images. The value of NAIincreases as the contrast in the image improves.

B. Universal Quality IndexIntroduced by Wang et al. [9], the Universal Quality Index(UQI) models image distortion as a combination of threefactors: loss of correlation, luminance distortion and contrastdistortion. The dynamic range of UQI is [-1,1], with 1providing the best estimate of quality.

C. Distance/background VarianceThe measure used here is formed by two figures of meritrepresenting an estimate of the local variance of an image[10]. The estimate is performed separately in detail regions(detail variance, DV) and in relatively uniform regions(background variance, BV) of an image. Here we expectreasonably high values of DV in the enhanced images, whilethe BV value should remain low in order to indicate limitednoise amplification. We use a region-of-interest basedadaptation of the DV/BV metric.

IV. EXPERIMENTAL RESULTS

We examine how each algorithm performs on differenttypes of mammograms. We also compare the algorithmsagainst classical algorithms for contrast enhancement such asContrast-Limited-Adaptive-Histogram-Equalization (CLAHE)[11]. Parameters used for each algorithm are shown in Table I.

TABLE IPARAMETERS FOR FUZZY ALGoRiTHMs

ParametersFHH S-function:

a = min(g), / = mean(g), y= max(g)PD r=2

A. Experiment 1: Nonspecific Mammogram Enhancement

This experiment concentrates on global contrast improvementof tissue regions within mammograms of different densitytypes, namely fatty, fatty-fibroglandular and dense-fibroglandular. Techniques are investigated, both to (i)improve the contrast along the periphery of the mammogram,and (ii) to enhance structures within the breast. Mammogramswere selected from the Mammographic Image AnalysisSociety (MIAS) [12] mammogram database. The results areshown visually, with the performance metrics for UQI andNAI in Table II and III respectively. The first result is shownin Fig.2 for the mammogram classified as fatty.

A. Noise Amplification Index

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contrast along the periphery of the mammogram, however thealgorithm based on the norma membership function seemsmore prone to amplifying noise in the background region ofthe mammogram (e.g. Fig. 3b). This is confirmed by lookingat the UQI metrics in Table II. In all three instances the FHHusing the S-function outperformed all other fuzzy algorithmsin terms of image quality. The MF algorithm seems to havethe best ability to improve the contrast of dense-tissue regions.For example, in both Fig. 3d and Fig. 4d, the regionsrecognized as the pectoral muscle, and fibroglandular tissue(FGT) are quite distinct as compared to the original image.

_l

Ita)

Fig. 2: Example of a fatty mamunogram (a) Original mammogram; (b) HH(/1 = 0.5, norma): (c) (/1 = 0.5, S); (d) MF; (e) FEV; and (f) PD

(e)

(D)

(t)

Fig. 4: Example of a dense-glandular mammogram (a) Original mamunogram;(b) HH (fi = 0.5, nonra); (c) (fi = 0.5 ,S); (d) MF; (e) FEV; and (f) PD

Fig. 3: Example of a fatty-glandular mammogram (a) Original mammogram;(b) HH (f, = 0.5, normia); (c) ()6 = 0.5 ,S); (d) MF; (e) FEV: and (f) PD

In a global context, both FHH algorithms equally produce thebest enhancement results with respect to improving the

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TABLE II

UQI RESULTS FOR MAMMOGRAMS

l__ _UQIFatty | Fatty-G | Dense-G

FHH (S-function) 0.7074 0.5985 0.7387FHH (norma-fiuction) 0.5656 0.5110 0.6943

FEV 0.5237 0.4615 0.6349MY 0.4640 0.3745 0.5489PD 0.0129 0.2993 0.3529

CLAHE 0.5796 0.5076 0.5102

TABLE HINAI RESULTS FOR MAMMOGRAMS

Fatty Fatty-G Dense-GFHH (S-function) 0.9464 0.9064 1.0573

FIHH (norna-fimction) 0.7753 0.7373 0.9183FEV 1.0495 1.1572 1.3338MF 1.0662 1.2961 1.2212PD 1.1410 0.9704 0.8407

CLAHE 1.0206 1 .0935 1.0965

The second experiment involves investigating the ability offuzzy algorithms to enhance abnormalities such as masses.Consider the example mammogram shown in Fig. 6, amammogram which contains a (spiculated) mass surroundedby fatty tissue. Whilst such a mass is obvious to the humanobserver, a CADe system nonetheless has to identify theregion containing the mass. So the purpose of enhancement inthe context of this algorithm is the enhancement of regionscontaining conspicuous ROI. Viewing the results shown inFig. 7 and the associated metric in Table IV, it can beconcluded that the PD algorithm proved most effective indifferentiating the mass from the surrounding region.

Overall, the following inferences can be made:1. MF is good for separating high-density regions if

they are surrounded by diffuse tissue. e.g. pectoralmuscle and FGT.

2. FHH is well suited to providing global contrastimprovement of mammograms, i.e. improvement ofcontrast along the breast periphery.

3. PD is well suited to enhancing the highest densityregions of a mammogram.

B. Effect ofArtifacts

One of the caveats of some of these algorithms such as PD isthat artifacts present in an image, such as the radiopaque labelsand high-intensity wedge artifacts adjacent to the breast regioncan influence the behavior of the algorithm. For example, thedense-glandular tissue mammogram is shown in Fig. 5 afterhaving the artifacts suppressed [13]. Enhancement using thePD algorithm shows increased enhancement if the centraltissue region, compared to Fig.4.

Fig. 6: Example of a mammogram containing an "obvious" mass (spiculated)surrounded by fatty tissue: (a) Original mammogram; (b) Ground truth image

Fig. 5: Effect of removing artifacts

Fig. 7: Example of a fatty-glandular mammogram (a) CLAHE; (b) HH(,8 = 0.5, norma); (c) (fi = 0.5 ,S); (d) MF; (e) FEV; and (f) PD

C. Experiment 2: Enhancement ofMasses

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Therefore such a fuzzy algorithm may be well suited to thetask of enhancing an object which has a higher density thanthe surrounding area.

TABLE IVENHANCEMENT METRICS FOR MAMMOGRAMS CONTAING A MASS

Performance MetricNAI DV/BV

Original (no enhancement) 5.32/13.85FHH (S-function) 0.9084 0.29/17.78

FHH (nonna-fumction) 1.0624 0.75/20.86FEV 0.9308 0.03/56.98MF 0.9336 0.92/47.78PD 1.1583 192.00/36.56

CLAHE 1.0441 27.57/63.58

IV. CONCLUSION

The purpose of this work was to concisely evaluate a series offuzzy contrast enhancement algorithms in an applicationspecific context. There is no one "quintessential" enhancementalgorithm which is capable of improving the acuity of anytype of image. Fuzzy enhancement algorithms are certainlysuited to certain applications, but it is often difficult toascertain a priori what these are. As with many enhancementalgorithms, those of a fuzzy nature often contain some level ofadjustable parameters, for instance the choice of membershipfunction, which may contribute to the quality of the result. Forexample, consider the FHH algorithm with /3= 2, and thefollowing membership function:

O if gj <S1

Agij) I[gi Io- if S, < gi < 52 (16)

1 ~~~if 52 < gij < 255

(a)

function. It is also difficult to reliably measure theperformance of contrast enhancement algorithms. Much ofthis evaluation has to be targeted towards a particular rationalefor enhancement. If enhancement is performed to amplify aspecific structure, then its perfonnance can be calibrated usinga GT and metrics such as BV/DV, however if enhancement isfor the purpose of visualization, a more realistic enhancementschema may be appropriate, and therefore the UQI or NAImetrics may be useful. Are fuzzy enhancement algorithmsbetter? This will be challenging to answer until large-scaleevaluation of image enhancement algorithms are performed,encompassing both quantitative metrics and subjectiveassessments.

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Fig. 8: Effect of different membership functions on FHH: (a) Fig 3a, and (b)Fig 4a after enhancement

An application of this combination is shown in Fig.8 using theoriginal mammograms from Fig 3 and Fig 4. The effects arenoticeably different from those using either the norna- or 5-

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