Multi Scale Morpho

*Corresponding author.E-mail address: [email protected] (B. Chanda).

Signal Processing 80 (2000) 685}696

A multiscale morphological approach to localcontrast enhancement

Susanta Mukhopadhyay, Bhabatosh Chanda*

Electronics and Communication Sciences Unit, Indian Statistical Institute, Calcutta 700035, India

Received 15 March 1999; received in revised form 2 November 1999

Abstract

A scheme for enhancing local contrast of raw images based on multiscale morphology is presented in this paper. Theconventional theoretical concept of local contrast enhancement has been extended in the regime of mathematicalmorphology. The intensity values of the scale-speci"c features of the image extracted using multiscale tophat transforma-tion are modi"ed for achieving local contrast enhancement. Locally enhanced features are combined to reconstruct the"nal image. The proposed algorithm has been executed on a set of raw images for testing its e$cacy and the result hasbeen compared with that of other standard methods for getting idea about its relative performance. ( 2000 ElsevierScience B.V. All rights reserved.

Zusammenfassung

In diesem Beitrag wird ein Verfahren zur Verbesserung des lokalen Kontrastes von Rohbildern, basierend aufmultiskalarer Morphologie vorgestellt. Das konventionelle theoretische Konzept zur lokalen Kontrastverbesserungwurde durch mathematische Morphologie erweitert. Die durch multiskale Zylindertransformation extrahierten Inten-sitaK tswerte der skalenspezi"schen Eigenschaften des Bildes werden zur lokalen Kontrastverbesserung modi"ziert. Lokalverbesserte Eigenschaften werden zur Rekonstruktion des Ergebnisbildes kombiniert. Der vorgeschlagene Algorithmuswurde an einem Satz Rohbilder zum Test seiner E$ziens angewandt und das Resultat wurde mit denen andererStandardverfahren verglichen, um einen Eindruck seiner relativen Leistung zu erhalten. ( 2000 Elsevier Science B.V.All rights reserved.

Re2 sume2

Nous preH sentons dans cet article un scheHma de rehaussement du contraste local dans des images, reposant sur de lamorphologie multi-eH chelle. Le concept theH orique conventionne du rehaussement de contraste local a eH teH eH tendu dans lereH gime de la morphologie matheHmatique. Les valeurs dintensiteH des caracteH ristiques speH ci"ques de leH chelle dans limage,extraites en utilisant la transformation du chapeau haut-de-forme multi-eH chelle, sont modi"eH es pour atteindre unrehaussement du contraste local. Less caracteH ristiques rehausseH es localement sont combineH es pour reconstruire limage"nale. Lalgorithme proposeH a eH teH exeH cuteH sur un ensemble dimages a"n de tester sont e$caciteH et les reH sultats ont eH teH

0165-1684/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.PII: S 0 1 6 5 - 1 6 8 4 ( 9 9 ) 0 0 1 6 1 - 9

compareH s avec ceux dautres meH thodes standard a"n davoir une ideH e de ses performances relatives. ( 2000 ElsevierScience B.V. All rights reserved.

Keywords: Mathematical morphology; Multiscale morphology; Morphological towers; Tophat transformation; Local contrast en-hancement

1. Introduction

The formation of a digital image of an object ora scene involves several intermediate steps like cap-turing the image, digitization, transmission, etc.The visual quality and the information content ofthe image so formed therefore su!er at almost allthe steps in its formation. The image as a whole isfound to have undergone a degradation and isunable to present the exact replica of the object orthe scene. For example, a poor illumination of theobject or the scene to be imaged causes a lowcontrast in the image whereas, the camera or themedium may introduce noise in the image data.Such a degraded image cannot render itself success-fully for subsequent processing toward image un-derstanding and interpretation. The techniqueusually adopted for improving the quality of thedegraded image is broadly termed as image en-hancement. Image enhancement is an ad-hoc pro-cess [27,10,14] for improving the quality of animage by which a degraded image is made to ac-quire a pre-requisite quality for subsequent ap-plication speci"c processing. An enhancementtechnique performing well in enhancing biomedicalimages may not be identically e$cient in enhancingsatellite images. Conventional image enhancementtechniques are broadly classi"ed into two catego-ries viz. the spatial domain techniques and the fre-quency domain techniques.

One of the most common degradations in therecorded image is its poor contrast. The contrast ofan image may roughly be de"ned as the di!erencebetween its highest and lowest intensity values. Theproblem of poor contrast in the degraded image isusually solved by histogram stretching [11,27] or byhistogram equalization technique [27,10]. There arefew variations of histogram equalization technique,e.g. histogram modi"cation [8,9]. The conventionalhistogram equalization technique treats the image

globally. Since the image characteristics di!er con-siderably from one region to another in the sameimage, it is reasonable to adopt a context-sensitivetechnique based on local contrast variation espe-cially when the local histogram does not follow theglobal histogram. Dorst [4] adapted histogramstretching method over a neighborhood around thecandidate pixel for local contrast stretching. While,various modi"cations [26,25,23] of histogramequalization (or modi"cation) are suggested basedon adapting the same over a subregion of the im-age. Contrast stretching methods using local statis-tics are also reported [16,17,24]. Attas et al. [1]have devised a variational approach to local con-trast enhancement through a suitable optimizationof some desirable characteristics of graylevel histo-gram of output image. Similar approach for con-strained local histogram equalization has beenadopted by Zhu et al. [31]. Boccignone andPicariello [2] have suggested a multiscale approachto contrast enhancement using a non-linearscale-space representation of image generated byanisotropic di!usion. Another multiscale contrastenhancement technique is developed by Toet [30]through non-linear pyramid recombination.

Mathematical morphology [20,28] is a relativelynew approach to image processing and analysis.This approach is based on set-theoretic concepts ofshape. In morphology objects present in an imageare treated as sets. As the identi"cation of objectsand object features directly depend on their shape,mathematical morphology is becoming an obviousapproach for various machine vision and recogni-tion processes. Several machine vision hardwaremanufacturers have started including morphologi-cal processors. These machines include Golay logicprocessor [7], Leitz Texture Analysis System TAS[15], the CLIP processor arrays [5], and the DelftImage Processor DIP [18]. Initially morphologydealt with binary images only, and basic operation

686 S. Mukhopadhyay, B. Chanda / Signal Processing 80 (2000) 685}696

were dilation and erosion, also known as Min-kowski addition and subtraction [22], respectively.Natural extension of morphologic transformationsfrom binary image processing to gray scale process-ing using max and min operations is done by Ster-nberg [29] and Haralick et al. [13]. Concept ofmultiscale morphology is introduced by Serra [28]followed by Maragos [19] and many other re-searchers. Multiscale morphologic techniques arealso used in various types of image processingproblems. Floreby et al. [6] have developed a noiseremoval technique using morphological pyramiddecomposition and modi"ed reconstruction. Multi-scale morphologic edge detector is suggested byChanda et al. [3].

In this paper we present a local contrast en-hancement technique using multiscale morphology.We use usual notations of digital image processingand mathematical morphology [12] in the follow-ing description. Section 2 gives a brief discussion onconventional local contrast enhancement methodsbased on local statistics and local histogram equal-ization. Mathematical morphology alongwithmultiscale morphology and tophat transfomationhave been discussed in Section 3. In Section 4.1 wehave "rst presented the theoretical formulation oflocal contrast enhancement using multiscale mor-phology. Section 4.2 presents elaborately varioussteps of the implementational aspects of the pro-posed alogorithm. Section 5 gives a discussion onthe result and its comparison with that of otherwell-known techniques. Finally, concluding re-marks are cited in Section 6.

2. Local contrast stretching

A good ambience of light illuminating the objector scene to be imaged may give rise to exhaustiveutilization of the entire dynamic range of grayscalein the image, but the contrast over a small regionmay be very poor. Second, a relatively smallernumber of pixels in such areas are insu$cient tohave any signi"cant in#uence on the computationof global transformation. So the conventional his-togram stretching or histogram equalization tech-nique fail to serve the purpose. Such images need

local enhancement and the technique by which thiscan be achieved is called local contrast stretching.

A contrast stretching method using local statis-tics suggested by Lee [16,17] ampli"es the di!er-ence between graylevel g(r, c) and mean graylevelg6 (r, c) over a prede"ned neighborhood surroundingthe pixel (r, c). Thus the modi"ed graylevel g8 (r, c) isgiven by

g8 (r, c)"g6 (r, c)#k[g(r, c)!g6 (r, c)] (1)

where k is a global ampli"cation factor and isgreater than one. In another approach Narendraand Fitch [24] have considered the ampli"cationfactor also be a function of (r, c) based on the localgraylevel statistics over the same neighborhood asis used to de"ne the mean graylevel g6 (r, c). Supposegraylevel variance over that neighborhood isp2(r, c). Then the factor k(r, c) is de"ned as

k(r, c)"c g6p2(r, c)

, 0(c)1

where g6 is the global mean of image graylevel andc is a user de"ned parameter.

The histogram equalization technique may beadopted to enhance the local contrast of the image.In this method the intensity of each pixel is modi-"ed through a local histogram equalization overa small region of the image around that pixel[23}26].

However, this kind of transformation using onlylocal graylevel statistics cannot distinguish betweenconsistent variation in intensity over a region andthe variation in intensity due to presence of a fea-ture (bright or dark) within a region. So it maystretch contrast evenly in both the cases. As a re-sult, undesired contrast intensi"cation (in suppos-edly smooth region) takes place at some regions ofthe image, which may require further processingsuch as de-enhancement [23]. On the other hand, iflocal contrast is stretched based on the presence ofspatial features, then this problem can be avoidedcompletely. As mathematical morphology is an ap-propriate tool for dealing with spatial features orshapes, we intend to modify Eq. (1) in terms ofmathematical morphological operators.

S. Mukhopadhyay, B. Chanda / Signal Processing 80 (2000) 685}696 687

Fig. 1. Illustrating bright tophat transformation through graylevel opening: (a) original function, (b) function opened with circular disk,(c) superposition of the previous two and (d) features after tophat transform.

3. Multiscale mathematical morphology

Mathematical Morphology is a powerfultechnique in the "eld of image processing andcomputer vision. In morphology, the objects inan image are considered as set of points and opera-tions are de"ned between two sets: the objectand the structuring element (SE) [28,12]. The shapeand the size of SE is de"ned according to thepurpose of the associated application. Basic mor-phological operations are erosion and dilation.Other operation like opening (closing) is sequentialcombination of erosion (dilation) and dilation (ero-sion). We adopt, here, function- and set-processing(FSP) system [19]. FSP dilation of a graylevelimage g(r, c) by a two-dimensional point set B is

de"ned as

(g=B)(r, c)"maxMg(r!k, c!l) D (k, l)3BN. (2)Similarly, FSP erosion of f (x, y) by B is de"ned as

(g>B)(r, c)"minMg(r#k, c#l) D (k, l)3BN. (3)The shape of the structuring element B plays

a crucial role in extracting features or objects ofgiven shape from the image. However, for a cat-egorical extraction of features or objects from theimage based on shape and size we must incorporatea second attribute to the structuring element whichis its scale. A morphological operation with a scala-ble structuring element can extract features basednot only on shape but also on size. Also features ofidentical shape but of di!erent size are now treated


separately. Such a scheme of morphological opera-tions where a structuring element of varying scale isutilized is termed as multiscale morphology [28,19].Multiscale opening and closing are de"ned, respec-tively, as

(g"nB)(r, c)"((g>nB)=nB)(r, c), (4)

(gz nB)(r, c)"((g=nB)>nB)(r, c), (5)

where n is an integer representing the scale factor ofthe structuring element. If B is convex nB is ob-tained by dilating B recursively n!1 times withB itself as [19]

nB"B=B=B=2=Bhggiggj

n~1 5*.%4

. (6)

By convention nB"M(0,0)N when n"0.

3.1. Multiscale tophat transformation

The tophat transformation originally proposed in[21] provides an excellent tool for extracting bright(respectively, dark) features smaller than a givensize from an uneven background. It relies on thefact that by gray-scale opening, one can removefrom an image the brighter areas, i.e. features, thatcannot hold the structuring element. Subtractingthe opened image from the original one yields animage where the features that have been removedby opening clearly stand out. Similar thing is truefor closing operation also. That means using a clos-ing in stead of an opening and subtracting theoriginal image from the closed one helps us extractdark features from a brighter background. Let uscall it a black tophat transformation as opposed towhite tophat transformation in case of opening.Suppose the structuring element used in both open-ing and closing is a disk, or, more speci"cally,a discrete approximation of disk. Therefore, thebright tophat tranformation decomposes an imageinto two parts as given by

g(r, c)"(g"B)(r, c)hgigj

1!35 1

#[g(r, c)!(g"B)(r, c)]hgggigggj

1!35 2

(7)

where B is a disk in discrete domain. Fig. 1 showsan example of bright tophat transformation for anone-dimensional signal. Let us call part 1 of Eq. (7)the base image with respect to B(r, c). And let us call

part 2 of Eq. (7) the feature image at size of B as itcontains all the bright features of g(r, c) that aresmaller than the size of B.

An ordered sequence of morphological tophat"ltering through opening (closing) of the imagewith a disk structuring element at di!erent scalesextracts scale-speci"c bright(dark) features from theimage. These scale-speci"c features resulting fromthe multiscale tophat transformation of the imagecan be ampli"ed selectively to achieve local con-trast stretching. Based on this notion we proposea local contrast enhancement method as describedelaborately in the following section.

4. Proposed method

4.1. Local contrast enhancement using morphology

As mentioned in the previous section, the brighttophat tranformation decomposes an image intotwo parts. This may be expressed in terms of grayscale morphological operators as

g(r, c)"(g"B)(r, c)hgigj

1!35 1

#[g(r, c)!(g"B)(r, c)]hgggigggj

1!35 2

(8)

where (g"B)(r, c) is openning of graylevel imageg(r, c) by a graylevel structuring element h(r, c) de-"ned as

h(r, c)"G0 if (r, c)3B,

!R otherwise,where B is a disk in discrete domain. Then thegraylevel structuring element h(r, c) at scale n, inthis case, may be de"ned as

h(r, c)"G0 if (r, c)3nB,

!R otherwise.

The feature image [i.e. part 2 of Eq. (8)] givesa measure of local contrast in the original imagedue to presence of bright features. Hence, combin-ing Eqs. (1) and (8) we suggest the following trans-formation for local contrast stretching:

g8 (r, c)"(g"B)(r, c)#k[g(r, c)!(g"B)(r, c)] (9)where k is again a global ampli"cation factor and isgreater than one. So this transformation makes


bright features brighter and, thus, improves thelocal contrast. Now suppose k"2. Eq. (9) becomes

g8 (r, c)"g(r, c)#[g(r, c)!(g"B)(r, c)]. (10)

Let us denote [g(r, c)!(g"B)(r, c)] by FoB(r, c), i.e.

features of size less than that of B obtained byopening (more speci"cally, by bright tophat trans-formation). Accordingly, we can rewrite Eq. (10) as

g8 (r, c)"g(r, c)#FoB(r, c). (11)

Similarly we denote the bright-feature image atscale n by Fo

nB(r, c) as it contains all the features of

g(r, c) that are smaller than nB. Hence, the valueFonB

(r, c) of bright-feature image at (r, c) givesa measure of local contrast in the original imagedue to presence of bright features at scale n. Notethat Fo

0B(r, c) is an all-zero image. Now, let us de"ne

don(r, c)"Fo

nB(r, c)!Fo

(n~1)B(r, c). (12)

It is evident that don(r, c) contains bright features of

g(r, c) that are larger than scale (n!1), but smallerthan scale n. Therefore, we obtain, using multiscaleapproach, local contrast stretching of bright fea-tures as

g8 (r, c)"g(r, c)#k1do1(r, c)

#k2do2(r, c)#k

3do3(r, c)#2 (13)

where k1k

2k

32, since we know that

smaller the size of a bright feature, more should beits intensity for detectibilty. Suppose the featuresupto the scale m are needed to be enhanced then

g8 (r, c)"g(r, c)# m+i/1

kidoi(r, c). (14)

Theoretically, m may correspond to SE as large asthe entire image; however, for all practical purposem is small. This is because large features, in general,contribute heavily to global histogram and thuscan in#uence global contrast stretching in theirfavor. Secondly, the probability that do

i(r, c) being

null image is more as i increases. So we ignoredoi(r, c) for im. Now taking k

i~1"k

i#1 for all

i and choosing km"1 we "nally have local contrast

stretching of bright features as

g8 (r, c)"g(r, c)# m+i/1

FoiB

(r, c). (15)

Selecting km"1 we can avoid multiplication op-

eration to compute enhanced image and, thus, thecomputational cost is reduced to some extent.

Proceeding in a similar way based on multi-scaledark tophat transformations we achieve local con-trast stretching of dark features as

g8 (r, c)"g(r, c)! m+i/1

FciB

(r, c). (16)

Hence, to obtain the modifed image, in which con-trast of both (bright and dark) types of features arestretched locally, we add Eqs. (15) and (16) anddivide the result by 2 to get

g8 (r, c)"g(r, c)#0.5 m+i/1

FoiB

(r, c)

!0.5 m+i/1

FciB

(r, c). (17)

The constant multiplier 0.5 is used for assigningequal or impartial weightages to both dark andbright features. For the sake of generalization, weslightly modify Eq. (17) as

g8 (r, c)"g(r, c)#0.5 m+i/n

FoiB

(r, c)

!0.5 m+i/n

FciB

(r, c) (18)

where all the features, either dark of bright, smallerthan scale n are assumed to be noise in the image.

4.2. Implementation

The implementation of Eq. (18) describing fea-ture based local contrast enhancement involvesconstruction of a number of morphological towersas elaborated below.

4.2.1. Construction of morphological towersThe image to be enhanced is made to undergo

a sequence of grayscale morphological opening op-erations with a disc structuring element and itshigher-order homothetics. The resulting sequenceof images are kept in a stack called the openingtower as shown in Fig. 2. An identical tower, calledclosing tower, is constructed with the sequence ofthe images resulting from multiscale closing of the


daasalbionNota adhesivaclausura

Fig. 2. Schematic diagram of di!erent morphological towers.

input image. Therefore the ith entry in the opening(closing) tower contains the image opened(closed)with the structuring element iB.

4.2.2. Construction of diwerence towersThe pixel values of opened image is less than or

equal to that of the original image. Subtractingthe opened image from the original one producesthe feature image made up of bright features speci-"c to the scale of the SE. Each entry of the open-ing tower is subtracted individually from theoriginal image and the resulting bright featureimages are then kept in corresponding entries inanother tower called the diwerence tower. Anidentical di!erence tower is constructed for thedark feature images obtained by subtracting theoriginal image from each entry of the closing tower.Therefore the ith entry in the di!erence tower foropening (closing) contains an image consisting ofbright (dark) features which are smaller than orequal to iB.

4.2.3. Construction of the enhanced imageFor reconstructing the "nal image we do the

following:

f We sum up all the entries in the di!erence towercorresponding to the opening operation. Thisresults in an image consisting of bright featuresof all possible scales of interest that are present inthe original image.

So(r, c)" n+i/1

FoiB

(r, c). (19)

The summation, here, denotes pixelwise sum ofn images.

f We perform the same operation on the di!erencetower corresponding to the closing operation.This results in an image consisting of dark fea-tures of all scales of interest that are present inthe original image.

Sc(r, c)" n+i/1

FciB

(r, c). (20)


Fig. 3. (a) Original image, (b) histogram of the original image, (c) linear global contrast stretching and (d) global histogram equalization.

Finally, the locally enhanced image is obtainedby combining three images as given by

g8 (r, c)"g(r, c)#0.5S01(r, c)!0.5S#-(r, c). (21)The and &! operations are applied be-

tween corresponding pixels of three di!erent im-ages. However, it should be noted that at somepixels the value of g8 (r, c) computed using Eq. (21)may exceed the allowed graylevel range. In thatcase the weights 0.5 may be replaced by a suchthat not more than 1% of total pixels are clipped.

The value of a can be selected between 0 and 0.5using binary search technique.

5. Experimental results and discussion

The proposed algorithm has been tested on a setof biomedical images and the results have beencompared with that of other methods [see Figs.3}6]. Here we present detailed study with threeexample images. The images contain MR scan of


daasalbionNota adhesivase puede usar ee planos convexos y se debe ser parametrizable el valor de m

Fig. 4. (a) Original image, (b) local contrast stretching using multiscale morphology, (c) local contrast stretching based on local statistics[24], (d) local histogram equalization [23] and (e) local contrast stretching following the algorithm due to Dorst [4].

human brain. Fig. 3 shows the original image alon-gwith its graylevel histogram and the results ofglobal enhancement techniques like linear contraststretching and histogram equalization of it. Theexamples reveal that the global techniques cannotimprove the contrast of the image satisfactorily.Results of the proposed algorithm are shown inFigs. 4}6 (b) where n"1 (as the images are as-sumed to be noise-free), m"6 and B is a 3]3 SE.This means largest SE used is 13]13. The value ofm can be made larger depending on demand orprecision. However, it should be noted that verylarge value of m will not give noticeable improve-ment in the output since the feature images of

progressively larger scales have gradually smallerweightages in enhancing the image. Moreover, verylarge value of m, in spite of incorporating generality inthe scheme, increases the computational time unnec-essarily. The resulting image is seen to have morecontrast than its original version. Results of otherlocal contrast enhancement algorithms such as localhistogram stretching [4], contrast ampli"cationbased on local statistics [24] and the local histogramequalization [23] are shown in Figs. 4c}e, respective-ly, so as to get some idea about their relative perfor-mance. In each case the size of the local window hasbeen "xed at 13]13. The ampli"cation factor in thealgorithm due to Dorst [4] has been "xed at 3. For



local contrast enhancement using local statistics dueto Narendra and Fitch [24], the values for the min-imum standard deviation and the scale factor chosenare 0.05 and 1, respectively. For local histogramequalization the threshold for the ratio of global meanto local variance is "xed at 0.5. However, from theresults, the enhancement of noise is found to be theleast in case of morphological enhancement proposedby the authors. The signi"cant local enhancementof the image without appreciable enhancement ofnoise proves the e$cacy of the proposed method.

6. Conclusion

In this paper we have given a scheme for localcontrast enhancement of graylevel images. The

method employs multiscale morphological "lter-ing in extracting the scale speci"c dark andbright features from the input image through theimplementation of a number of towers. Therecombination of all such features at the timeof reconstruction emphasizes the basic require-ment of local contrast enhancement which de-mands that features of progressively smaller scalesshould get more weights. The scheme has beenimplemented and executed on a set of gray-scaleimages. The results have been compared with thoseof few standard methods. The results due to theproposed method have been found reasonably sat-isfactory. However, the computational time andspace required are high compared to other methodswhich the authors would like to improvesubsequently.



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Multi Scale Morpho