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IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO. 3, MARCH 2001 367

Transform-Based Image Enhancement Algorithmswith Performance Measure

Sos S. Agaian, Member, IEEE, Karen Panetta, Senior Member, IEEE, and Artyom M. Grigoryan, Member, IEEE

Abstract—This paper presents a new class of the “frequencydomain”-based signal/image enhancement algorithms includingmagnitude reduction, log-magnitude reduction, iterative mag-nitude and a log-reduction zonal magnitude technique. Thesealgorithms are described and applied for detection and visual-ization of objects within an image. The new technique is basedon the so-called sequency ordered orthogonal transforms, whichinclude the well-known Fourier, Hartley, cosine, and Hadamardtransforms, as well as new enhancement parametric operators.A wide range of image characteristics can be obtained from asingle transform, by varying the parameters of the operators.We also introduce a quantifying method to measure signal/imageenhancement called EME. This helps choose the best parametersand transform for each enhancement. A number of experimentalresults are presented to illustrate the performance of the proposedalgorithms.

Index Terms—Alpha-rooting, detection, frequency domain en-hancement, magnitude-reduction, sequency ordered transforms,visualization.

I. INTRODUCTION

I T IS well-known that image enhancement is a problem-ori-ented procedure. The goal of the image enhancement is to

improve the visual appearance of the image, or to provide a“better” transform representation for future automated imageprocessing (analysis, detection, segmentation, and recognition).Many methods have been proposed for image enhancement[11], [13], [14]. A survey of digital image enhancementtechniques can be found in [1], [34], [8], [26]. Most of thosemethods are based on gray-level histogram modifications[11], [12], while other methods are based on local contrasttransformation and edge analysis [14], [17], or the “global”entropy transformation [25]. In all of these methods, there areno general standards for image quality which could be used asa design criteria for image enhancement algorithms.

At present, there is no general unifying theory of imageenhancement. Methods of image enhancement techniquescan be generally classified into two categories: spatial do-main methods, which operate directly on pixels, including

Manuscript received August 12, 1999; revised November 14, 2000. This workwas supported in part by NASA under Grant NAG8-1311. The associate editorcoordinating the review of this manuscript and approving it for publication wasDr. Henri Maitre.

S. S. Agaian is with the Division of Engineering, The University of Texas,San Antonio, TX 78249-0669 (e-mail: [email protected]).

K. Panetta is with the Department of Electrical Engineering and ComputerScience, Tufts University, Medford, MA 02155 (e-mail: [email protected]).

A. M. Grigoryan is with CAMDI Laboratory, Department of Electrical En-gineering, Texas A&M University, College Station, TX 77843-3128 (e-mail:[email protected]).

Publisher Item Identifier S 1057-7149(01)01662-1.

Fig. 1. Diagram of the image enhancement withC (p; s).

region-based and rational morphology based, and frequencydomain methods. These methods operate on transforms of theimage, such as the Fourier, wavelet, and cosine transforms. Thebasic advantages of transform image enhancement techniquesare 1) low complexity of computations and 2) the critical roleof the orthogonal transforms in digital signal/image processing,where they are used in different stages of processing such asfiltering, coding, recognition, and restoration analysis. Imagetransforms give the spectral information about an image, bydecomposition of the image into spectral coefficients thatcan be modified (linearly or nonlinearly), for the purposes ofenhancement and visualization. The resulting advantage is thatit is easy to view and manipulate the frequency composition ofthe image, without direct reliance on spatial information.

In [8], a comparative analysis of transform based image en-hancement techniques is given. It includes techniques such asalpha-rooting, modified unsharp masking, and filtering, whichare all motivated by the human visual response. The analysis ofthe existing transform based image enhancement techniques [1],[8], [13], [34]shows that there are the common problems whichneed to be solved, because

1) such methods introduce certain artifacts (in [8] they calledthese artifacts “objectionable blocking effects”);

2) such methods cannot simultaneously enhance all parts ofthe image very well;

3) it is difficult to select optimal processing parameters,and there is no efficient measure that can be served as abuilding criterion for image enhancement.

Finding a solution to this problem is very important espe-cially when the image enhancement procedure is used as apreprocessing step for other image processing techniques suchas detection, recognition, and visualization. It is also importantwhen constructing an adaptive transform based image enhance-ment technique. The research work presented here offers novelfrequency domain based image enhancement methods for ob-ject detection and visualization. The new technique is basedon the so called sequency ordered [30] orthogonal transformssuch as Fourier, Hartley, cosine, and Hadamard transformsand new enhancement operators. A new class of the fasttrigonometric systems is used for performing the transformcoefficients manipulation operations. A quantitative measure

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368 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO. 3, MARCH 2001

Fig. 2. (a) Linear combination of the clock and (b) moon images, which results in (c) an illegible image.

Fig. 3. Enhancement of the original image (a) via�-rooting based on the (b) Fourier, (c) Hadamard, and (d) cosine transforms when� = 0:92.

of image enhancement is introduced. The technique devel-oped here has been successfully employed on NASA’s EarthObserving System satellite data products for the purpose ofanomaly detection and visualization. These satellites collecta Tera-byte of data per day, and fast and efficient methodsare crucial for analyzing these data.

The paper is organized as follows: In Section I, the sequency-ordered transform is briefly described, which will be used for theimage enhancement. Then in Section II, we define the so-calledsequency ordered orthogonal transform, quantitative measure ofsignal/image enhancement and, then, describe in general a trans-form-based image enhancement algorithm. Our first technique


AGAIAN et al.: TRANSFORM-BASED IMAGE ENHANCEMENT ALGORITHMS WITH PERFORMANCE MEASURE 369

Fig. 4. The�-rooting by the 2-D cosine (from the top to bottom), Hadamard,Fourier, and Hartley transforms.

combines the magnitude and log-magnitude reductions for en-hancement. Section III focuses on a number of experiments inorder to evaluate the enhancement algorithm. Zonal magnitudereduction methods are given in Section IV, wherein the com-parative analysis of transforms based image enhancement algo-rithms (theoretical and experimental results) are provided. Fi-nally, in Section V, a discussion and some concluding remarksare given.

II. BACKGROUND

A. Sequency Ordered Systems

In this section, we review frequency ordered systems, de-scribe their properties, and introduce a new class of nonsinu-soidal sequency ordered systems. The latter can be implementedwith low computational complexity.

When analyzing signals and systems, it is useful to map datafrom the time domain into another domain (in our case, the fre-quency domain). The basic characteristics of a complex waveare the amplitude and phase spectra. Specifying amplitude andphase spectra is an important concept for complex waves. Forexample, an amplitude spectrum contains information about theenergy content of a signal and the distribution of the energyamong the different frequencies, which is often used in manyapplications. To achieve this, the real variable,, is generalizedto the complex variable, , which then is mapped back viainverse mapping. For example, the Fourier transform maps thereal line (time domain) into the complex plane, or real wave intothe complex one. This, however, requires a high complexity inimplementation, since it involves complex multiplications andadditions.

It is obvious to ask the question: Is it possible to construct adiscrete orthogonal system which maps a real signal to anotherreal signal while maintaining the advantages of a complex do-main? The motivation for this question is that it is often easierand efficient, especially from the standpoint of calculation, todeal with real rather than complex numbers. If we accomplish

this task, we can obtain significant computational advantages insignal processing, or more specifically, in the signal enhance-ment.

The one-dimensional (1-D) discrete Fourier transform (1-DDFT) is given by

(1)

The inverse 1-D discrete Fourier transform is defined as

(2)

The Heller’s identity allows to rewrite theFourier transform pairs as

(3)

Thus, the 1-D Fourier transform maps the time domain signalinto the frequency domain. The sum of the cosine products canbe defined as the “real” components of the spectrum, and thesum of the sine products can be defined as the “imaginary” com-ponents of the spectrum. To compute these components, one canuse the known algorithms of the fast Fourier transform [1], [34]or by using a new approach, an efficient manageable split al-gorithm [27] for computing the Fourier and other unitary trans-forms.

We now introduce a new system which has an inverse trans-form as well as the basic advantages of the complex domain.

Definition 1: The rate at which a function crosses thezero-axis is called itssequency(as an analog tofrequency).

We now investigate the mapping systems, or transforms,which meet the following properties of a special sequency-or-dered system.

Definition 2: A special sequency-orderedfunction set is anyset of functions, which satisfies the following properties:

1) the transform can be represented in the form of

(4)

2) and are sequency-ordered functions.andrespectively can be considered as “real” and “imagi-

nary” components of the sums .It is easy to see that the known orthogonal transforms such

as the Hartley, cosine, sine, and Hadamard transforms are theparticular cases of the sequency-ordered systems.

Remark 1: If and ,, then the sequency-ordered system be-



Fig. 5. Enhanced images via the�-rooting based on the (a)–(c) Fourier transform and (d)–(f) Hadamard transform.

comes the discrete Hartley transform of a 1-D, discrete realfunction, , is defined as [3]

(5)

where . The Hartley transform is sim-ilar to the Fourier transform, but only generates real coefficientsrather than complex ones.

Remark 2: If , ,and , , then the se-quency-ordered system becomes the cosine transform. Really,the discrete cosine transform is determined by the basis func-tions

if

if

(6)

(7)

Remark 3: If and , if iseven, and , if is odd, then the sequency-or-dered system becomes the Cal–Sal Walsh–Hadamard transform(C-SWHT). Really, the C-SWHT is defined as

(8)

where, if ;

, if ;denotes the sequency.

The system is the set of the Walsh ordered functions,

(9)

(10)

Remark 4: A transform definition via a parametric class oftrigonometric systems is

(11)



(a)

(b)

Fig. 6. Enhancement byC (p; s) coefficient and Fourier transform. (a) Original image and (b) enhanced images.

where

(12)

for some constants , and .Properties of these kinds of systems, including the fast algo-

rithms, can be found in [6].Remark 5: A new class of non sinusoidal function transforms

is defined via a parametric class of trigonometric systems as

sgn sgn

(13)

for some constants , and .Similar to the Fourier transform, one can define the “magni-

tude” and “phase” of the real transform. The “phase” asso-ciated with is defined as

(14)

where and are respectively the sum of the “real” and“imaginary” components in (11). The “magnitude” is defined as

(15)

The “power”

(16)

and phase spectra can be recombined to reconstruct completelythe .

Given an image of sizes , we consider a two-dimensional (2-D) unitary transform

(17)

where is the set of basis functionsof the transform , and ,is a complete set of orthogonal functions. and arecoefficients of the transform.

It is clear that the “magnitude” of the sequency-ordered sys-tems are similar to the magnitude of the Fourier transform. Thisfact points to possibility of construction unified transform basedenhancement algorithms for all sequency-ordered systems.

In the next section, we will show that the above defined mag-nitude information provides useful information for object loca-tion.

B. General Transform-Based Image Enhancement Algorithm

Analyzing the existing transform-based enhancement algo-rithms ( -rooting and magnitude reduction methods [2], [8]), wefind a common algorithm, which encompasses all of these tech-niques. The actual procedure of the signal/image enhancementvia an invertible transform consists of the following three steps:

Step 1) perform the orthogonal transform;Step 2) multiply the transform coefficients, and ,

by some factor, ;Step 3) perform the inverse orthogonal transform.



(a) (b)

(c) (d)

Fig. 7. Measure of log-enhancement by Fourier, Hadamard, and cosine transforms. (a) Fourier enhancement, (b) differenceEME (�; �)�EME (�; �), (c)differenceEME (�; �) � EME (�; �), and (d) differenceEME (�; �) � EME (�; �).

The frequency ordered system-based method can be repre-sented as

(18)

where is an operator which could be applied on the com-bination of and (particularly, on the modules ofthe transform coefficients) or could be applied directly tothese coefficients. For instance, they could be , ,or , . Basically, we are interested in thecases, when is an operator of magnitude (see cases1–4, below) and when is performed separately on thecoefficients.

Let be the transform coefficients and let the enhance-ment operator be of the form , where thelatter is a real function of the magnitude of the coefficients, i.e.,

. must be real because we onlywish to alter the magnitude information, not the phase informa-tion. In the framework of this constraint, we have several possi-bilities for , which can offer far greater flexibility:

1) constant (when the enhancementpreserves all constant information);

2) , (which isthe so-calledmodified -rooting [8]);

3) , , [2];4) .Denoting by the phase of the transform coeffi-

cient , we can write

(19)

where is themagnitudeof the coefficients. Rather thanapply the enhancement operator directly on the transformcoefficients , we will investigate the operator which isapplied on themodulesof the transform coefficients,

(20)

We assume the enhancement operator takes oneof the forms , , at every point

.In practice, the coefficient is used in

for image enhancement. The optimal value ofis image de-pendent and should be adjusted interactively by the user [8]. Forsimplicity of our reasonings, we will assume that in definition



Fig. 8. (a) Original image and (b)–(d) 2-D Fourier transform enhancements when operating withC coefficients for(�; �) equal respectively to (0.05, 0.05),(1.9, 0.05), (0.05, 0.9), and (1.9, 0.9).

of the coefficients we have . Onecan ask: What are the optimal values of, , and ? Can onechoose , , and automatically? What is the best enhance-ment frequency ordered system? What is the optimal size of thetransform, ?

Remark 6: The above approach can be used 1) on the wholeimage, or via blockwise processing with block sizes 8, 16, 32,and 64 and 2) on some low-pass or high-pass filtered image.As an example, one can see in Fig. 1 that an original imagecan be divided first into a low-pass image and high-passimage . The high-pass image is enhanced by multiplicationby and then recombined with the low-pass image [seealso [26], [8], when using the coefficient ].

C. Performance Measure of Enhancement

In this section, we present a new quantitative measure ofimage enhancement.

The improvement in images after enhancement is often verydifficult to measure. A processed image can be said to have beenenhanced over the original image if it allows the observer to

better perceive the desirable information in the imaging. In im-ages, the improved perception is difficult to qualify. There isno universal measure which can specify both the objective andsubjective validity of the enhancement method [16]. In practice,many definitions of the contrast measure are used [12], [16],[17]. For example, the local contrast proposed by Gordon andRangayan was defined by the mean gray values in two rectan-gular windows centered on a current pixel. Baghdan and Negrate[17] proposed another definition of the local contrast based onthe local edge information of the image, in order to improvethe first mentioned definition. In [17], the local contrast methodproposed by Beghdadi and Negrate has been adopted, in orderto define a performance measure of enhancement. Use of sta-tistical measures of gray level distribution measures of localcontrast enhancement (for example, mean, variance or entropy)have not been particularly meaningful for mammogram images.A number of images, which clearly illustrated an improved con-trast, showed no consistency, as a class, when using these sta-tistical measurements. A measure proposed in [12], which hasgreater consistency than the statistical measures, is based on thecontrast histogram.



(a)

(b)

(c) (d)

Fig. 9. Fourier enhancement via log-reduction when coefficientsC (p; s) are calculated for one fixed parameter. (a) Surface of the enhancement measure (� =0:8), (b) image of the enhancement measure, (c) surface of the enhancement (� = 0:8), and (d) surface of the enhancement measure (� = 0:9).

Intuitively, it seems reasonable to expert that a imageenhancement measure values at given pixels should dependstrongly on the values at pixels that are close by weeklyon those that are further away and also this measure has torelated with human visual system. In our definition, we use amodification of Weber’s and Fechner’s laws. In [31], Weberestablished a visual law, argued that the human visual detection

depends on the ratio, rather than difference, between the lightintensity value and . The Weberdefinition of contrast was used to measure the local contrast ofa single object. (One usually assumes a large background witha small test object, in which case the average luminance will beclose to the background luminance. If there are many objectsthis assumption do not hold.) Fechner’s law [32] proposed the



following relationship between the light intensity andbrightness:

(21)

where is a constant, and are the “absolutethreshold” and “upper threshold” of the human eye [33].Below, a new quantitative measure of image enhancement ispresented.

Let an image be split into blocks ofsizes , and let , , and are fixed enhancement parame-ters (or, vector parameter). For a given class of orthogonaltransforms, we define a value asfollows:

(22)

(23)

where and respectively are the min-imum and maximum of the image inside the block

, after processing the block bytransform based enhance-ment algorithm. The function is the sign function, ,or , depending on the method of enhancement underthe consideration. The decision to add this function has beendone after studying various examples of enhancement by trans-form methods using the different coefficients ,

. This will be demonstrated in the following sections.Definition 3: is called ameasure of enhancement, or

measure of improvement.Definition 4: The best (optimal) transform relative to the

measure of enhancement is called a transformsuch that. The image enhancement algorithm based

on this transform is called anoptimal image improvement trans-form-basedenhancement algorithm.

Selection of Parameters:Suppose the transform based en-hancement algorithm depends on the parameters, and ,or vector , i.e., .

Definition 5: Let be the best (optimal) transform. Thebest (optimal) -transform-based enhancement image vectorparameter is called a parameter such that

.It should be noted that the window size can be also included

in the vector as a parameter of optimal enhancement.In the next section, the following problems are investigated.

How to design the best transform-based image enhancementalgorithm, and how to design the best-transform-based en-hancement image vector parameter ?

III. EXPERIMENTAL RESULTS

In this section, we perform a number of experiments in orderto evaluate the enhancement algorithm for 1-D and 2-D signals.For more clarity/visibility, we demonstrate the experimental re-sults for 2-D signals such as the moon plus clock image.

(a)

(b)

Fig. 10. Hadamard enhancement via log-reduction when coefficientsC (p; s) are calculated for fixed� = 0:8. (a) Surface of the enhancementmeasure (� = 0:8) and (b) image of the enhancement measure.

In our test cases, we use three classes of algorithms, namely,the transform based enhancement algorithms via the operators

, , and respectively. We also presentthe above mentioned iterative algorithm. For each of the cases,we present two classes of experiments. The first class showshow to choose the best operator parameter (or, the best enhance-ment algorithm) for the given transform. The second class showshow to choose the best image enhancement transform for thegiven image. A quantitative comparison of the methods is alsopresented below.

In order to enhance our images before passing them througha visualization algorithm, we reduce the magnitude informa-tion of the image while leaving the phase information intact.Since the phase information is much more significant than themagnitude information in the determination of edges, reducingthe magnitude produces better edge detection capabilities. Thismethod also tends to reduce the low-frequency componentsrather than the high-frequency components (both the low-fre-quency components, which are associated with sharp edges,and high-frequency components, which are associated with theedge elements).

The “clock” image was taken as the original, , andthen the “moon” image was superimposed with it. This resultsin an illegible image, as shown in Fig. 2. The result, , isan enhanced image, which can now be passed through a visual-ization algorithm.

Case 1: Transform based enhancement algorithm via oper-ator .



Fig. 11. Two-dimensional Fourier enhancement of the image (a) via the operatorO with coefficientsC , (b), andC , (c), when� = 0:8,� = 1:5, and� = 0:8,and the histograms (d)–(f) of the images (a)–(c), respectively.

Test 1.1—Choosing the Best Operator Parameter:This caseis known as modified -rooting or root filtering [8]. Whenequals to zero, only the phase is retained. When , the“amplitude” of the large transform coefficients are reducedrelative to the “amplitude” of the small coefficients, and theresult is enhanced edges and details in the image. Since most ofthe edge information is contained in the high-frequency regionof the spectrum, the edges are enhanced by this method. Byvarying the -level of the reduced image, we are able to enhancethe quality of our images for the visualization. Fig. 3(a)–(c),illustrates the process of enhancement of the image when theparameter and the Fourier, Hadamard, and cosinetransforms are used. As we see in the above examples, themagnitude reduction using served to sharpen the imageas well as even out the brightness throughout the image. Theresults of the visualization algorithms will be more accuratebecause they will be operating on these enhanced images.They will also be less dependent on magnitude variationsbased on magnification and blurring, therefore making it mucheasier to set a thresholding constant, which need not changefrom image to image.

Test 1.2—Choosing the Best Image Enhancement Transformfor the Given Image:Let be identical to afterthe normalization by a constant.

The enhancement measure of the original image shown inFig. 2 is 4.5, or , where is the identicaltransform. Fig. 4 shows four curves which describe the mea-sure of the enhancement, when applying the Fourier, Hadamard,cosine, and Hartley transforms. We see that on the whole in-terval, where varies, the maximal measure of enhancement isprovided mostly by the cosine and Hadamard transforms. Thecurves have two maximums, at points and ,where the maximum measure is provided by the Fourier trans-form (The best transform among the above transforms). The ex-perimental results show that the parametercorresponds to thebest visual estimation of enhancement. The enhancement by thetransforms are very close between these two extreme points.


Test 2.1—Choosing the Best Operator Parameter:Fig. 5 il-lustrates the enhanced images by varying parameter, whenusing the Fourier transform, (a)–(c), and the Hadamard, (d)–(f).The log-magnitude reduction using serves to enhancethe edges around regions in the image. Fig. 6 demonstrates thepractical application of the proposed method on the images ob-tained by NASA’s Earth Observing System satellites.

Test 2.2—Choosing the Best Image Enhancement Transformfor the Given Image:Fig. 7 illustrates the measure of the



Fig. 12. Two-dimensional Fourier transform enhancement of (a) the original image and (b)–(d) results of the enhancement, respectively, for the coefficientsC ,C , andC with � = 0:9, � = 1:5, and� = 0:8.

image enhancement by using different transforms and varyingparameters and respectively in the intervals and

. Fig. 7(a) shows the surface of the measure for the Fouriermethod and (c) and (d) show the differences between themeasures when the Fourier, Hadamard, and cosine transformsare used for enhancement. The results of the Fourier transformbased image enhancement are shown in Fig. 8, for the boundaryparameters. The large values oflead to the elimination of thehigher frequencies on the image spectrum, and the operator

works as the filter of low frequencies. Contrarily, the smallvalues of increase the image enhancement.

Test 2.3–Comparison:To illustrate the above method of en-hancement, consider Fig. 9. Fig. 9 depicts the surfaces of mea-sure , when one of the parameters is fixed.


Test 3.1—Choosing the Best Operator Param-eter: Combining the magnitude reduction and magnitudereduction methods in accomplishes both thesharpening and edge enhancements for a given image. In ourexperiments, we found with and to

Fig. 13. Curves of the Fourier enhancement (a), (b), and (c), by two zones,when using the coefficientsC , C , andC , respectively.



Fig. 14. Curve of the Fourier enhancement by (a) two zones and (b)–(d) results of enhancement when radius of the first zone is 32, 64, and 127, respectively.

be the optimal magnitude reduction operator on the image.Fig. 9 illustrates the surface of the enhancement measure for

and , when the Fourier transform basedenhancement image algorithm is used. Fig. 10 illustrates thesurface of the enhancement measure for , when thesimilar Hadamard transform algorithm is applied.

Test 3.2—Choosing the Best Image Enhancement Trans-form: We face the problem of selecting the optimal orthogonaltransform for our application. Since our goal is to achievemaximum accuracy in the detection of regions of interest aswell maximize computational speed, we must balance thesetwo factors and make a selection that is appropriate for ourapplication. Therefore, we analyzed the quality of the resultsand the execution time for each of these orthogonal transformalgorithms.

Test 3.3—Comparison:An enlarged example of the pro-posed optimal magnitude reduction is shown in Fig. 11(a),when using the Fourier transform (b) and comparing with

-rooting (c). The histograms (d)–(f) show how the rangeof intensities differ, when using the different coefficients forthe enhancement. The measure of enhancement is 9.84 and7.80 when using respectively the coefficients and for

enhancement of the image. Fig. 12 illustrates for comparisonthe outputs of the 2-D Fourier transform enhancement for allthree methods under consideration. One can see that the max-imum measure of enhancement and best visual estimate occurswhen using the coefficient . All further referencesto the magnitude reduction algorithm will be to this specificcombination of magnitude reductions.

It should be noted, that from standpoint of information theory,the probability distribution, which conveys the most informa-tion, is perfectly uniform [11]. Therefore, if we could obtain asuniform a histogram as possible, the image information couldbe maximized.

A. Iterative Transform Based Image Enhancement Algorithm

We now discuss briefly an algorithm via the magnitude re-duction approach. Naturally, one wonders if it is possible to fur-ther enhance the image. Since the proposed magnitude reduc-tion method works well at enhancing the edge information ofthe image, a second pass through the magnitude reduction al-gorithm might serve to further enhance the image. We have im-plemented this iterative enhancement method and experimentedwith it using various magnitude reduction coefficients, in order



Fig. 15. Two-dimensional Fourier enhancement for two zones (� = 16).

to find the optimal values for this configuration. The goal is tofind the optimal iteration parameters. We propose the followingalgorithm for iterative transform based image enhancement:

1) perform the orthogonal transform;2) multiply the transform coefficients by some factors

3) repeat step 2 for several iterations, while varying coeffi-cients

4) perform the inverse orthogonal transform.

IV. ZONAL TRANSFORMBASED ENHANCEMENT METHODS

The classical transform based image enhancement tech-niques are performed uniformly over the entire frequencyspectrum. As an expansion of these kinds of techniques, wepropose varying the transform based image enhancement withinradially concentric zones. The motivation of using zones comesfrom the fact that: a very “short” transform coefficient lengthcorresponds to the homogenous image blocks, a “medium”transform coefficient length corresponds to the texture, and a“long” transform coefficient length corresponds to the highlyactive image blocks. By using this method, we achieve muchmore flexibility and control over the magnitude reductionsin different regions within the frequency domain. By usingincreasingly greater reductions in higher frequencies, wemanage to attenuate the high-frequency noise component of the

image. At the same time, we also maintain the edge enhancingeffects of the magnitude reduction algorithm.

We now demonstrate zonal transform based image enhance-ment via a few examples. For this, we describe the transformbased image enhancement algorithm (including iterative algo-rithm) with two and three zones. It should be noted that, in thecase considered above, we have used one zone.

In order to accomplish this method, we first have to findthe maximum and minimum values within the frequency do-main data. Then, using these maximum and minimum points asend-markers, we divide the frequency domain into regions basedon each point’s magnitude distance from the maximum and min-imum. We set distance dividers between the maximum and min-imum points, which divide the frequency domain into regions.Each region has the specified magnitude reduction value,, andlog-magnitude reduction value,. We next determine the fourpairs of and values, as well as three values of the distanceto specify our magnitude reductions. These values can be deter-mined by means of the enhancement measure.

Case 4: Transform based image enhancement algorithmswith two zones, and .

a) The enhancement operator can be defined by

if

if(24)



Fig. 16. Two-dimensional Hadamard enhancement for two zones (� = 16).

Remark 7: The zone has to be very small and coefficienthas to be near to zero or zero. b) The enhancement

operator can be defined by

if

if ,(25)

where is a constant (which can be the mean of all ,), , where is the size of the

input signal, , , and are constants (and ).As examples, Fig. 13 illustrates the curves of the enhance-

ment measure for images, by using two zones and the Fouriertransform based enhancement method for the different operators

, a), , b), and , c), for the parameters, , and . The varying parameter for

the curves is the radiusof the first zone by which the area ofthe Fourier spectrum is divided; the second zone is the rest ofthe area. Fig. 13 shows that when radius of the zone increases,the measure of image enhancement grows faster when using thecoefficient , than .

Fig. 14 illustrates the example of the image enhancement bytwo zones with varying radius-parameter. As can be observedfrom the experimental results, the proposed algorithm effec-tively enhances the overall contrast and sharpness of the test im-

ages. A lot of details, that could not been seen in the test image,have been clearly revealed.

c) The enhancement operator can be defined by

if

if ,(26)

wheremagnitude of the transform image;,thresholding operator;very small constant (or, zero).

is defined as , whereand are real functions and is a coefficient (or, a zero-

frequency component). For instance, ,when and .

Figs. 15 and 16 illustrate the examples of the image enhance-ment by using the Fourier and Hadamard transforms and twozones. The threshold is and parameter takes values0.5, 0.6, 0.7, 0.8, and 1.

Case 5: Transform Based Image Enhancement Algorithmswith Three Zones.

The enhancement operator can be defined by

if

if

if

(27)



This is a typical contrast stretching transform, which has to beapplied in the frequency domain (see [13, pp. 235–237]).

V. CONCLUSION

A new class of “frequency domain” based signal/image en-hancement algorithms (magnitude reduction, log-magnitude re-duction, iterative magnitude, and log-reduction zonal magnitudetechniques) have been described and applied for detection andvisualization on objects within an image. The new techniquesare based on the so-called “sequency” ordered orthogonal trans-forms, which include the well-known fast orthogonal Fourier,Hartley, cosine, and Hadamard transforms, as well as new en-hancement parametric operators.

We have improved upon the current magnitude reductiontechniques and developed an entirely novel method. Thewide range of characteristics can be obtained from a singletransform by varying enhancement parameters. A quantitativemeasure of signal/image enhancement was presented, whichdemonstrated the optimal method to automatically choose thebest parameters and transform. The proposed algorithms aresimple to apply and design, which makes them practical. Anumber of experimental results were given which illustrate theperformance of these algorithms. The comparative analysisof transforms based image enhancement algorithms has beendescribed, too. Lastly, the comparison of the Fourier transformand Walsh, cosine and Hartley transforms was given. We findthat for a negligible tradeoff of accuracy, one can use the Walshtransform to achieve significantly higher performance enhance-ment. For our purposes, where speed is a major concern, theproposed method turns out to be a dramatic improvement overexisting methods. We have also proposed the zonal transformbased image enhancement algorithms.

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Sos S. Agaian(M’85) received the M.S. degree inmathematics and mechanics from Yerevan State Uni-versity, Armenia, the Ph.D. degree in mathematicsand physics from Steklov Institute of Mathematics,Academy of Sciences, Moscow, Russia, and theDoctor of Industrial Sciences degree from ComputerCenter, Academy of Sciences, USSR in 1985. Healso received the Full Professor Diploma from theSupreme Attestation Board, USSR, in 1986.

He was a Visiting Professor with the Department ofElectrical Engineering and Computer Science, Tufts

University, Medford, MA, from 1993 to 1997. He was Senior Scientist withAWARE, Inc., from 1996 to 1997. He erved as a Chairman of the Departmentof Digital Signal Processing, National Academy of Sciences of Armenia, from1979 to 1993. In 1997, he joined the Division of Engineering, University ofTexas, San Antonio, where he is currently an Associate Professor. He is the au-thor of three books and 11 inventions and has written more than 185 papers onorthogonal and logical transforms, with application on compression, filtering,and recognition. His current research interests include signal and image pro-cessing, computer vision, visual communication, and applied mathematics.



Karen Panetta (SM’95) received the B.S. degreein computer engineering from Boston University,Boston, MA, and the M.S. and Ph.D. degrees inelectrical engineering from Northeastern University,Boston.

She is an Assistant Professor of electrical engi-neering and computer science at Tufts University,Medford, MA. Her research interests include visual-ization of complex data sets, fault simulation, largesystem simulation, and behavioral modeling. Sheis currently a NASA JOVE Fellow for the NASA

Langley Research Center. Her research has been supported by Compaq, Intel,Analog Devices and, most recently, the NSF CAREER award. She holds twopatents in developing discrete-event simulation methodologies and algorithms.

Dr. Panetta is Faculty Advisor for the student chapter of IEEE at Tufts Uni-versity and a Member of ACM and the Society for Computer Simulation.

Artyom M. Grigoryan (S’78–M’99) received the M.S degrees in mathematicsfrom Yerevan State University, Armenia, in 1978, imaging science fromMoscow Institute of Physics and Technology, Moscow, Russia, in 1980,and electrical engineering from Texas A&M University, College Station, in1999, and the Ph.D. degree in mathematics and physics from Yerevan StateUniversity, Armenia, in 1990.

From 1990 to 1996, he was a Senior Researcher with the Department of Signaland Image Processing, Institute for Problems of Informatics and Automation,and Yerevan State University, Academy Science of Armenia. In 1996, he joinedthe Department of Electrical Engineering, Texas A&M University, where he iscurrently a Research Engineer. He holds one patent in the development of theautomated 3-D fluorescentin situhybridization spot counting on tissue microar-rays. He is author of 40 papers and specializes in the design of robust nonlinearand linear optimal filters, linear filtration, theory of fast one-dimensional andmultidimensional unitary transforms, and processing the fluorescent images.


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