Mammogram Enhancement Using Lifting Dyadic Wavelet Transform and Normalized Tsallis Entropy

Hussain M. Mammogram enhancement using lifting dyadic wavelet transform and normalized Tsallis entropy. JOURNAL

OF COMPUTER SCIENCE AND TECHNOLOGY 29(6): 1048–1057 Nov. 2014. DOI 10.1007/s11390-014-1489-7

Mammogram Enhancement Using Lifting Dyadic Wavelet Transform

and Normalized Tsallis Entropy

Muhammad Hussain

Department of Software Engineering, King Saud University, Riyadh 11543, Saudi Arabia

E-mail: [email protected]

Received October 12, 2013; revised July 14, 2014.

Abstract In this paper, we present a new technique for mammogram enhancement using fast dyadic wavelet transform(FDyWT) based on lifted spline dyadic wavelets and normalized Tsallis entropy. First, a mammogram image is decom-posed into a multiscale hierarchy of low-subband and high-subband images using FDyWT. Then noise is suppressed usingnormalized Tsallis entropy of the local variance of the modulus of oriented high-subband images. After that, the waveletcoefficients of high-subbands are modified using a non-linear operator and finally the low-subband image at the first scale ismodified with power law transformation to suppress background. Though FDyWT is shift-invariant and has better poten-tial for detecting singularities like edges, its performance depends on the choice of dyadic wavelets. On the other hand, thenumber of vanishing moments is an important characteristic of dyadic wavelets for singularity analysis because it providesan upper bound measurement for singularity characterization. Using lifting dyadic schemes, we construct lifted spline dyadicwavelets of different degrees with increased number of vanishing moments. We also examine the effect of these waveletson mammogram enhancement. The method is tested on mammogram images, taken from MIAS (Mammographic ImageAnalysis Society) database, having various background tissue types and containing different abnormalities. The comparisonwith the state-of-the-art contrast enhancement methods reveals that the proposed method performs better and the differenceis statistically significant.

Keywords mammogram enhancement, lifting dyadic wavelet transform, Tsallis entropy

1 Introduction

Breast cancer is the second major type of cancer thatcauses mortality among women all over the world[1]. Itsdetection at early stages provides an opportunity of re-covery and assists to decrease the rate of mortalitydue to breast cancer. One of the most reliable tech-niques for the early detection of breast cancer is mam-mography. A mammogram is a low contrast image,which causes difficulties in the detection of masses andmicro-calcifications. The presence of the cluster ofmicro-calcifications and masses is the key sign of breastcancer at its early stages. Micro-calcifications are smallcalcium deposits in the breast tissue, which appear astiny bright spots in mammogram images. Masses arecharacterized by their smooth boundaries, and are of-ten found in the thick regions of breast tissue. Thelow contrast between the background and the inten-sities of micro-calcifications and masses makes theirvisualization harder in mammograms. It motivated theresearch on mammogram enhancement in order to help

radiologists in screening mammograms and to improvethe diagnosis rate[2].

Many techniques have been proposed for the en-hancement of mammograms; for a thorough survey onsuch techniques, the reader is referred to [3-4]. Multi-scale analysis framework has been successfully appliedfor this problem[4]. In this framework, a mammogramimage is decomposed into a multiscale hierarchy of onelow-subband and multiple high-subband images, thenthe coefficients in the high subband images are modi-fied and finally the enhanced mammogram image isreconstructed[5]. The differentiating factors among dif-ferent multiscale methods are 1) the way the multi-scale analysis is performed and 2) the way the coeffi-cients in high-subband images are modified. Commonlyused multiscale analysis techniques are discrete (deci-mated) wavelet transform (DWT)[2], dyadic (undeci-mated) wavelet transform (DyWT)[1], and nonsubsam-pled contourlet transform (NSCT)[6]. DWT is not shift-invariant; it suffers from ringing artifacts and exhibitsvisual artifacts such as Gibbs phenomenon in the neigh-

Regular PaperThis work was supported by the National Science, Technology and Innovation Plan (NSTIP) Strategic Technologies Programs of

the Kingdom of Saudi Arabia under Grant No.08-INF325-02.©2014 Springer Science +Business Media, LLC & Science Press, China

Muhammad Hussain: Mammogram Enhancement Using LDyWT and Normalized Tsallis Entropy 1049

borhood of discontinuities[7]. DyWT is shift-invariantand performs better than DWT. NSCT is also shift-invariant like DyWT and has been applied for mam-mogram enhancement[6].

Though DyWT performs better than DWT, its per-formance depends on the characteristics of the under-lying decomposition functions (dyadic wavelets). Thenumber of vanishing moments is an important charac-teristic of wavelets for singularity analysis as it providesan upper bound measurement for singularity charac-terization. The greater number of vanishing momentsallows the complex functions to be represented with asparser set of wavelet coefficients. The existing mam-mogram enhancement techniques use DyWT based onquadratic spline dyadic wavelets[5], which are characte-rized by only one vanishing moment, and thus cannotcapture the local regularity and singularities of mam-mograms well. Employing the lifting dyadic schemes[8],we build spline dyadic wavelets with a greater numberof vanishing moments and use them for better mammo-gram enhancement results.

Noise is a high-frequency component and is sepa-rated into high-subband images. Therefore, the high-subband images contain not only edge coefficients butalso noise coefficients, and any effort to emphasize edgecoefficients will also enhance the noise coefficients. Assuch, after decomposing a mammogram into a multi-scale hierarchy, the first issue is to discriminate noiseand edge coefficients so that noise coefficients can besuppressed and edge coefficients can be emphasized. Toaddress this issue, exploiting the fractal-type nature ofmammograms and the observation that the noise coeffi-cients are dominant at the first scale and dilute rapidlywith increasing scales, we use normalized Tsallis en-tropy of the local variance of the modulus of orien-ted high-subbands at the second scale to discriminatethe noise and edge coefficients; using this information,noise coefficients are suppressed across high-subbandsat all scales. After suppressing noise, the wavelet coef-ficients in high-subbands at all scales are modified us-ing a non-linear operator which ensures that the highgraylevel values are not saturated after enhancement.Further for better enhancement effects, we suppress thebackground by modifying low-subband using power lawtransformation at the first scale during the process ofreconstruction. The proposed method works equallywell for micro-calcifications as well as masses. Thecomparison with state-of-the-art similar methods re-veals that the proposed method performs better andthe difference is statistically significant.

The main contributions of the paper are as follows.• It proposes a mammogram enhancement method

based on FDyWT with lifted spline dyadic wavelets

characterized by greater than one vanishing moment,normalized Tsallis entropy of the local variance ofthe modulus of high-subbands instead of graylevels(for noise supersession) and power law transforma-tion (for background suppression). Validation usingmammogram images from well known MIAS (Mamm-graphic Image Analysis Society) database shows thatthis method results in better enhanced mammogramswhere breast pathology is more clear.

• It examines lifted spline dyadic wavelets characte-rized by various number of vanishing moments and findsspline dyadic wavelets that result in the best mammo-gram enhancement performance.

The rest of the paper is organized as follows. InSection 2, we give an overview of FDyWT and presentthe lifted dyadic wavelets. The proposed enhancementmethod is presented in Section 3. Results are presentedand discussed in Section 4. Finally, Section 5 concludesthe paper.

2 Fast Dyadic Wavelet Transform and LiftedSpline Dyadic Wavelets

In this section, first we give an overview of fastdyadic wavelet transform (FDyWT)[8] and then presentlifted spline dyadic wavelets to motivate the proposedenhancement method.

Let f be a square integrable function on R, and φand ψ be scaling and dyadic wavelet functions respec-tively, which are also square integrable on R. FDyWTdecomposes f into a low-subband and multiple high-subbands at scales j = 0, 1, 2, . . . , J , where the coeffi-cients are given by the following formulae[8].

aj+1[n] =∑

k

h[k]aj [n + 2jk], j = 0, 1, . . . , J, (1)

dj+1[n] =∑

k

g[k]aj [n + 2jk], j = 0, 1, . . . , J, (2)

where a0[n] =∫ +∞−∞ f(t)φ(t − n)dt, h[k] and g[k] are

scaling and dyadic wavelet filters respectively. Usi-ng the low-subband and those high-subbands at scalesj = 1, 2, . . . , J , the function f is reconstructed with thefollowing inverse dyadic wavelet transform (IDyWT):

aj [n] =12

∑

k

(h[k]aj+1[n− 2jk] + g[k]dj+1[n− 2jk]),

j = J − 1, J − 2, . . . , 1, 0, (3)

where h[k] and g[k] are dual scaling and dual dyadicwavelet filters respectively. For more details a reader isreferred to [8].

A digital image is a 2D discrete function I[s, t] withs rows and t columns of pixels. It is decomposed into

1050 J. Comput. Sci. & Technol., Nov. 2014, Vol.29, No.6

one low-subband and multiple high-subbands by ap-plying (1) and (2) along rows and columns assuminggraylevel values as a0[n]. Specifically, for scale j = 1decomposition creates:

1) low-subband LL, applying (1) first on rows andthen on columns of I;

2) high-subband LH , applying (1) first on rows andthen applying (2) on columns of I;

3) high-subband HL, applying (2) first on rows andthen applying (1) on columns of I;

4) high-subband HH , applying (2) first on rows andthen on columns of I.One-scale decomposition is shown in Fig.1. Steps 1∼4are repeated on LL for decomposition at other scales(j = 2, 3, . . . , J). Using the hierarchy of a low-subbandand multiple high-subbands, an image is reconstructedwith (3).

Fig.1. One-scale decomposition of a digital image I.

The characteristics of decomposition with FDyWTdepend on the choice of dyadic wavelets. Applicationslike denoising and singularity detection require that thedesign of the wavelets is optimized so that a maximumnumber of wavelet coefficients is close to zero, i.e., thewavelet coefficients of regular parts of a function di-minish along scales. This depends on the number ofvanishing moments of a wavelet function and its sup-port. Increasing the number of vanishing moments de-creases the amplitude of wavelet coefficients in regionsof the functions where it is regular, and results in sparserepresentation[9]. It means that the smooth parts of afunction would decay rapidly if the number of vanishingmoments of a wavelet is large, and the singularities willbe highlighted and can be detected easily.

Spline dyadic wavelets[9] are smooth and compactlysupported, and are suitable for the contrast enhance-ment of mammogram images. The Fourier transformsof the corresponding scaling, dual scaling, wavelet, anddual wavelet filters h[k], h[k], g[k], and g[k] are[9]:

h(ω) =√

2e−iεω/2(

cosω

2

)m+1

, (4)

g(ω) = − i√

2e−iω/2 sinω

2,

h(ω) = h(ω),

g(ω) = − i√

2e−iω/2 sinω

2

m∑

l=0

(cos

ω

2

)2l

,

where m > 0 stands for the degree of spline and

ε ={

1, if m is even,

0, if m is odd.

These dyadic wavelet filters with m = 2, i.e., thequadratic spline dyadic wavelets, which have only onevanishing moment, were used by Mallat and Hwang[10]

for edge detection and employed by Scharacanski andJung[5] for contrast enhancement of mammograms. Be-cause these dyadic wavelet filters have only one vanish-ing moment, they are poor at characterizing the lo-cal regularity of functions. Using the lifting dyadicschemes[8], spline dyadic wavelet filters of different de-grees can be lifted to increase their number of vanishingmoments. The Fourier transforms of the lifted scaling,dual scaling, wavelet and dual wavelet filters h[k], ˆ

h[k],g[k], and ˆg[k] for m = 0, 2, 4 are

h(ω) =√

2e−iω/2(

cosω

2

)m+1

, (5)

g(ω) = −i√

2e−iω/2 sinω

2

(1− cosm+2 ω

2

),

ˆh(ω) =

√2e−iω/2 cos

ω

2

(cosm ω

2+ sin2 ω

2

m∑

l=0

cos2l ω

2

),

ˆg(ω) = −i√

2e−iω/2 sinω

2

m∑

l=0

(cos

ω

2

)2l

,

and for m = 1, 3

h(ω) =√

2e−iω/2(

cosω

2

)m+1

, (6)

g(ω) = −i√

2 sinω

2

(e−iω/2 − cosm+2 ω

2

),

ˆh(ω) =

√2 cos

ω

2

(cosm ω

2+ e−iω/2 sin2 ω

2

m∑

l=0

cos2l ω

2

),

ˆg(ω) = −i√

2e−iω/2 sinω

2

m∑

l=0

(cos

ω

2

)2l

.

It is easy to verify that the lifted spline dyadic wavelethas three vanishing moments when m = 0, 2, 4 whereasthe number of vanishing moments is 2 when m = 1, 3.We increased the number of vanishing moments onlyto 3 because increasing the number of vanishing mo-ments also increases the wavelet support, which causes


to increase the number of large coefficients producedby isolated singularities[9]. It is shown in [8] that theselifted spline dyadic wavelets perform better in denoisingnatural images. Hussain et al.[11] have shown that liftedspline dyadic wavelet transform with m = 4 possesbetter potential for edge detection. In this study, weexamine the effect of these filters for mammogram en-hancement and find the ones that result in the bestenhancement performance.

3 Enhancement of Mammograms

Using FDyWT based on lifted spline dyadic waveletsand normalized Tsallis entropy, we propose a new en-hancement method in this section. The flowchart of themethod is shown in Fig.2; there are four main modules:pre-processing, decomposition with FDyWT, process-ing low-frequency and high-frequency subbands, andreconstruction with IDyWT. In the following subsec-tions, we give the detail of these steps.

Fig.2. Main steps of the contrast enhancement method.

3.1 Pre-Processing

Mammogram images usually include artifacts in theform of labels and wedges in the background area. Thepreprocessing stage removes these artifacts and the pec-

toral muscle. For this purpose, we adopt the methodproposed by Nagi et al.[12].

3.2 Decomposition with FDyWT

Using FDyWT, a mammogram image I is decom-posed upto scale 4. Micro-calcifications are capturedat lower scales whereas masses are encoded by higherscales. At each scale j (= 1, 2, 3, 4), one low-subbandimage LLj and three high-subband images LH j ,HLj

and HH j are obtained. Noise is a high-frequency com-ponent and is filtered in high-subbands at lower scales.Our idea for the contrast enhancement of mammogramsis first to suppress noise-related wavelet coefficientsin high-subbands, and then to emphasize edge-relatedwavelet coefficients in high-subbands at all scales andfinally to modify the low-subband to suppress the back-ground.

3.3 Noise Suppression Using NormalizedTsallis Entropy

Mammogram images contain grain and structurenoise[13]; this noise tends to enhance with pixel intensitymaking the discrimination of local digital contents moredifficult, specially in dense areas[5]. Any effort for en-hancing the contrast of mammogram images increasesthe noise making the discrimination of local detail evenmore difficult. As such, the suppression of this noise isan essential part of the contrast enhancement of mam-mograms.

For noise suppression, the wavelet coefficients re-lated to noise need to be separated from those corre-sponding to edges in high-subbands. It is a segmenta-tion problem and an appropriate solution is threshold-ing, but in this approach the challenge is to find theoptimal threshold that can separate noise and edge co-efficients successfully. Mammograms are characterizedby fractal-type structures and thus involve a kind ofnon-extensive information content[14]. On the otherhand, Tsallis entropy is associated with the amount ofnon-extensiveness in a physical system, which entailsfractal-type structures and has been successfully ap-plied for image thresholding[15]. It has shown promis-ing results for segmentation[16] and enhancement[17]. Inview of this, we employ Tsallis entropy for thresholdcalculation using the local variance of wavelet coeffi-cients instead of graylevel values to discriminate noisyand edge pixels.

The wavelet coefficients corresponding to edge pixelshave higher local variance than those related to noisepixels. Thus, we use local variance estimates for cal-culating the optimal threshold for separating noise andedge coefficients. It was noted in [18] that orientationdistortion is introduced when the oriented wavelet coef-


ficients LH j and HLj are independently processed. Inview of this observation, the magnitude M of these co-efficients is calculated and the local variance estimatesSTDj

M are calculated using a window of size w; weperform experiments with w = 3. The local varianceestimates STDj

M are quantized into L levels, and theirprobability distribution p = {p1, p2, . . . , pL} is obtainedas a normalized histogram of quantized local varianceestimates with L bins; in our experiments L = 512 isused. The reason to use L = 512 is to capture thecharacteristics of the local variance in a better way; asmaller number of bins have smoothing effect whereasa larger number introduces many empty bins. Fromthis distribution, we derive two probability distribu-tions, one for noise coefficients { p1

Pk, p2

Pk, . . . , pk

Pk} and

another for edge coefficients { pk+11−Pk

, pk+21−Pk

, . . . , pL

1−Pk}

where Pk =k∑

i=1

pi. The prior Tsallis entropy for each

class (noise and edge) is defined as:

Snoiseq (k) =

1q − 1

(1−

k∑

i=1

( pi

Pk

)q)

,

Sedgeq (k) =

1q − 1

(1−

L∑

i=k+1

( pi

1− Pk

)q)

,

where q is a real number in the range (0, 1) and isan entropic index that characterizes the degree of non-extensiveness; in our experiments, we find that formammograms, the acceptable value of q is 0.99.

Tsallis entropy depends on the threshold value kfor noise and edge classes. According to the pseudo-additive law for statistically independent systems, it isdefined as follows:

Sq(k) = (Snoiseq (k) + Sedge

q (k)+

(1− q)Snoiseq (k)Sedge

q (k)).

The optimal threshold value T is computed by maxi-mizing the information measure between the two classes(noise and edge). It is obtained by solving the followingcheap optimization problem:

T = arg max(Snoiseq (k) + Sedge

q (k)+

(1− q)Snoiseq (k)Sedge

q (k)).

The wavelet coefficients with local variance estimatesless than T are assumed to be noisy coefficients whilethe others are considered as edge coefficients.

One approach for noise suppression is to calculateoptimal threshold for high-subbands at each scale. Butit is not fine because of the observation given in [10].As noted in [10], the Lipschitz regularities of edges in

an image are greater than or equal to zero and thusthe amplitudes of corresponding wavelet coefficients in-crease or remain constant when the scale increases,whereas the Lipschitz regularity of noise is less thanzero and thus the amplitudes of wavelet coefficientscorresponding to noise decrease with increasing scale.In view of this, at the first scale, the wavelet coeffi-cients are almost dominated by noise and it is difficultto discriminate the wavelet coefficients correspondingto noise from those corresponding to edges. At scaleshigher than j = 2, though noise diluting rapidly the ac-curacy of edge locations decreases[10]. Thus the secondscale is a good choice for the discrimination of noiseand edges. Using the wavelet coefficients LH 2 and HL2

and the technique for optimal threshold value calcula-tion described above, locations of noise and edge pixelsare computed, the wavelet coefficients corresponding tothese locations are treated as noise and edge coefficientsat all scales. The noisy coefficients are suppressed atall scales j = 1, 2, 3, 4 using the following operator:

S(e) ={

e, if e is an edge coefficient,

λe, if e is a noise coefficient,(7)

where λ is the factor for suppression; in our experi-ments, we use λ = j/10, which depends on scale j.Noise is a high frequency content and is mostly fil-tered in high-subbands, i.e., the noise coefficients arestronger in high-subbands and get weaker with increas-ing scale j, thus noise coefficients must be suppressedstrongly using smaller values of suppression factor atlower scales. That is why λ increases with scale j.

3.4 Contrast Enhancement

After suppressing noise, wavelet coefficients aremodified for contrast enhancement. One way for en-hancement is to linearly map the wavelet coefficients ateach scale and each subband, but it causes saturationand loss of detail. Instead, we adopt a non-linear func-tion α(x) defined in the light of the following designguidelines proposed by Laine et al.[18]

• An area of low contrast has to be enhanced morethan an area of high contrast to minimize the saturationeffects.

• A sharp edge should not be blurred.• The non-linear function α has to be monotoni-

cally increasing to insure that no artifacts are intro-duced during the reconstruction.

Following these considerations, Laine et al.[18] de-fined the following non-linear function:

α(x) =

x− (G− 1)T, if x < −T,

Gx, if − T < x < T,

s + (G− 1)T, if x > T,

(8)


where gain G and threshold T are two free parameters.Different choices for these parameters are possible[5,18].As the scale increases, the amplitude of wavelet coeffi-cients corresponding to noise dilutes rapidly and thatof wavelet coefficients related to edges either increasesor remains invariant[10], thus the probability of non-zero wavelet coefficients with small amplitudes to benoise coefficients decreases whereas that to be edge co-efficients increases as scale increases. It leads us to usegreater value of gain G for higher scales to enhanceweak edges. We use G = jG∗ where j is the scale andfind by experiment that G∗ = 10 gives the acceptableresults. We take T to be the median of the wavelet co-efficients of the corresponding high-subband as in [5].Applying this function on each high-subband at eachscale j = 1, 2, 3, 4, the wavelet coefficients are modifiedas follows:

LHj

= α(LH j),

HLj

= α(HLj),

HHj

= α(HH j).

3.5 Background Suppression

After the wavelet coefficients are modified, InverseDyadic Wavelet Transform (IDyWT) is applied to getthe image with enhanced contrast. During the recon-struction process of the enhanced image, we suppressbackground for further enhancing breast tissue and le-sion regions so that the lesions are more visible. Forthis purpose, the scaling coefficients LL1 at the firstscale are mapped using power law intensity transforma-tion x3. This transformation expands the bright areasand de-emphasizes the background. The scaling coef-ficients LL1 are selected to avoid the enhancement ofnoise; the dominant noise is separated into wavelet co-efficients. The mapping of the scaling coefficients atscales j = 2, 3, 4 enhances only larger scale objectsand edges. Note that most of the enhancement me-thods based on multiscale approach, perform enhance-ment modifying only wavelet coefficients. In contrast,our method modifies scaling coefficients in addition towavelet coefficients.

4 Results and Discussion

In this section, we present the results, discuss them,and compare the proposed method with similar state-of-the-art methods. For validation, MIAS database[19]

has been used. This database includes mammogramimages with three background tissue types: fatty (F),fatty-glandular (G), and dense-glandular (D). The mainabnormality types existing in these images are micro-calcifications and masses. Each mammogram image in

the database is annotated by expert radiologists. Forevaluation, we give a subjective and objective compa-rison.

We compare the proposed method with three state-of-the-art enhancement methods: adaptive histogramequalization (AHE), direct enhancement method(DE)[2], and nonsubsampled contourlet transform(NSCT)[6]. The first one is the best classical methodwhereas the other two are based on multiscale frame-work.

For objective comparison, we employ evaluationtechnique for the contrast enhancement of mammogramimages proposed in [20]; this metric combines threeother metrics and is shown to be stable and robust.It is defined as follows:

D =√

(1−DSM )2 + (1− TBC s)2 + (1− TBC e)2,

where

DSM =∣∣µE

T − µEB

∣∣− ∣∣µOT − µO

B

∣∣,

TBC s =(µE

T

µEB

− µOT

µOB

)σOT

σET

,

TBC e =(µE

T

µEB

− µOT

µOB

)εOT

εET

.

µOB , σO

B , εOB , µO

T , σOT , εO

T are the mean, the standarddeviation, and the entropy of the graylevels of the back-ground and those of the target area (lesion region)of the original image before enhancement respectively;µE

B , σEB , εE

B , µET , σE

T , εET represent the mean, the stan-

dard deviation, and the entropy of the graylevels afterenhancement. Note that DSM, TBCs, and TBCe arenot normalized, i.e., the values of these measures arenot between 0 and 1. When there is no enhancement,the value of each of DSM, TBCs, and TBCe is zero, andin this case the value of D is

√3. When the value of each

of these measures is 1, then there is an enhancement inthe image and the D value is zero. On the other handwhen the value of these measures is −1, then there isalso an enhancement and the value of D is 2

√3. When

the value of D is greater than 2√

3, it indicates over-enhancement or under-enhancement. For the validationof the proposed method, we select 18 mammogram ima-ges (6 from each type of background tissue: fatty (F),fatty-glandular (G), and dense-glandular (D)), half ofwhich contain micro-calcifications and the other half in-clude masses. Using the information about the locationof each type of abnormality provided by the annotationof each mammogram image, we extract the lesion re-gion (target area) and the background from the mam-mogram image before and after enhancement. We ex-tract the target area using the MIAS database groundtruth and the background area using the surrounding


region. In case of micro-calcifications, the target areais not continuous as in case of masses but consists ofa cloud of points. Using ground truth, we define theregion containing this cloud as target area and its sur-rounding region as background area.

First we show the effect of different spline dyadicwavelets (with and without lifting), described in Sec-tion 2, on mammogram enhancement. Fig.3 gives thebar graph of the average D values for six different splinedyadic wavelets (with and without lifting); in each casethe average D is computed over ROIs taken from 18mammogram images. The bar graph indicates that thelifted spline dyadic wavelets with degree 4 (LDyWT 41)perform better than other spline dyadic wavelets. Inour onward discussion, we will concentrate only on lift-ing dyadic wavelet transform based on this wavelet andrefer to it as LDyWT 41.

Fig.3. Bar graph of average D value obtained after enhancing

18 mammogram images with 6 different types of spline dyadic

wavelets. Here DyWT ml stands for dyadic wavelet transform

based on spline dyadic wavelets with degree m and lifting (l = 1)

or without lifting (l = 0) as described in (4), (5) and (6).

Fig.4 shows the D values for the four enhance-ment methods computed over ROIs of 18 mammo-gram images. This graph reveals that LDyWT 41 per-forms better than other enhancement methods. ForROIs from mammograms mdb019 (containing mass andFatty-glandular (G) background tissue) and mdb209(having micro-calcification cluster and Fatty-glandular(G) background tissue), AHE performs slightly better.Also, in Fig.5, the bar graph shows average D values forthe four methods. It is obvious that LDyWT 41 excelsother methods on average in terms of D value.

To see whether the observed difference between theperformance of different methods is significant, we usestatistical analysis, which tells us whether the methods

Fig.4. Plots of D values for the four enhancement methods ap-

plied on 18 mammogram images.

Fig.5. Average D values for four enhancement methods computed

over ROIs taken from 18 mammogram images.

differ significantly. For statistical analysis, we use one-tail t-test; the goal of this test is to determine which ofthe following two hypotheses is true:Ho: m1 = m2, i.e., the mean performances of two me-thods are same;Ha: m1 < m2, i.e., the mean performance of method 1is better than that of method 2.

The hypothesis test is carried out against the signifi-cance level 0.05. Statistical analysis results are shownin Table 1. In this table, the last column shows the95% confidence interval about difference mean. It re-veals that the difference between the performance ofLDyWT 41 and the other three methods in terms of Dvalue is significant at significance level 0.05. For subjec-tive comparison, see Figs. 6∼10. Fig.6 shows the origi-nal ROI of the mammogram image mdb252, which con-tains a cluster of micro-calcifications at the center, andits enhanced versions by the four methods. LDyWT 41enhances the contrast moderately in such a way thatnot only has the cluster of micro-calcifications becomemore visible, but other microstructures of the paren-


Table 1. Statistical Significance Test Results

Mean of the Standard t Degree p 95% Confidence

Difference Deviation Interval of the Difference

LDyWT vs DE −4.66 1.81 −2.57 17 0.009 8 (−8.47,−0.84)

LDyWT vs AHE −4.77 1.27 −3.75 17 0.000 7 (−7.45,−2.09)

LDyWT vs NSCT −10.47 2.45 −4.27 17 0.000 2 (−15.64,−5.29)

Fig.6. (a) Original ROI extracted from the mammogram image

mdb252 and its versions enhanced by (b) LDyWT 41, (c) AHE,

(d) NSCT, and (e) DE.




Fig.8. (a) Original ROI extracted from the mammogram image mdb145 and its versions enhanced by (b) LDyWT 41, (c) AHE, (d)

NSCT, and (e) DE.


Fig.9. (a) Original ROI extracted from the normal mammogram

image mdb050 and its versions enhanced by (b) LDyWT 41, (c)

AHE, (d) NSCT, and (e) DE.




chyma have become more pronounced (i.e., the breastpathology is more clear), which makes the analysisof mammogram images and the detection of abnor-malities easier. In contrast, though other three me-thods also emphasize the cluster of micro-calcifications,AHE does over-enhancement (i.e., it enhances the back-ground and breast tissues unnecessarily along withmicro-calcifications) whereas DE and NSCT result inunder-enhancement (i.e., the microstructures of theparenchyma have been suppressed). ROIs taken frommammogram images mdb010 and mdb145 containmasses at their centers; again LDyWT 41 performs theenhancement moderately, and mass regions are morepronounced. The response of the other algorithmsagain is similar. AHE performs over-enhancementwhereas DE and NSCT do under-enhancement. In caseof DE, mass regions are not visible at all. Also, seeingthe ROIs (original and enhanced) of two normal mam-mogram images (mdb050 and mdb086) shown in Figs. 9and 10, one can have similar observations about the en-hancement performance of the four methods.

5 Conclusions

A new method was proposed for the enhancementof mammogram images. The method uses FDyWT formultiresolution analysis, normalized Tsallis entropy fornoise suppression, a non-linear operator for contrast en-hancement and a power law transformation for back-ground suppression. It was tested with mammogramimages taken from MIAS database and was comparedwith state-of-the-art enhancement techniques for mam-mogram images. Objective and subjective comparisonsreveal that the proposed method outperforms the state-of-the-art enhancement techniques and the differencein performance is statistically significant. The effect ofdifferent dyadic wavelet filters with and without liftingwas investigated and it was found that the lifted splinedyadic wavelets of degree 4 perform better than otherdyadic wavelet filters.

Acknowledgement We are thankful to theanonymous reviewers for their valuable comments toimprove the quality of this paper.

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Muhammad Hussain is a pro-fessor in the Department of Soft-ware Engineering, King Saud Uni-versity, Saudi Arabia. He receivedhis M.S. and M.Phil. degrees, bothfrom University of the Punjab, La-hore, Pakistan, in 1990 and 1993respectively. In 2003, He receivedhis Ph.D. degree in computer sciencefrom Kyushu University, Fukuoka,

Japan. He worked as a researcher at Japan Science andTechnology Agency from April 2003 to September 2005. InSeptember 2005, he joined King Saud University as an assis-tant professor. His current research interests include imageprocessing, computer graphics, and computer vision.

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Mammogram Enhancement Using Lifting Dyadic Wavelet Transform and Normalized Tsallis Entropy