908502

8/22/2019 908502

1/16

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

AbstractThis 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 TermsAlpha-rooting, detection, frequency domain en-hancement, magnitude-reduction, sequency ordered transforms,visualization.

I. INTRODUCTION

IT 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 image

processing (analysis, detection, segmentation, and recognition).

Many methods have been proposed for image enhancement[11], [13], [14]. A survey of digital image enhancement

techniques can be found in [1], [34], [8], [26]. Most of those

methods are based on gray-level histogram modifications

[11], [12], while other methods are based on local contrast

transformation and edge analysis [14], [17], or the global

entropy transformation [25]. In all of these methods, there are

no general standards for image quality which could be used as

a design criteria for image enhancement algorithms.

At present, there is no general unifying theory of image

enhancement. Methods of image enhancement techniques

can be generally classified into two categories: spatial do-

main methods, which operate directly on pixels, including

Manuscript received August 12, 1999; revised November14, 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 with C ( p ; s ) .

region-based and rational morphology based, and frequency

domain methods. These methods operate on transforms of the

image, such as the Fourier, wavelet, and cosine transforms. The

basic advantages of transform image enhancement techniques

are 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 as

filtering, coding, recognition, and restoration analysis. Image

transforms give the spectral information about an image, by

decomposition of the image into spectral coefficients that

can be modified (linearly or nonlinearly), for the purposes of

enhancement and visualization. The resulting advantage is that

it is easy to view and manipulate the frequency composition of

the 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 as

alpha-rooting, modified unsharp masking, and filtering, which

are 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 which

need to be solved, because

1) such methods introducecertain artifacts (in [8] they called

these artifacts objectionable blocking effects);

2) such methods cannot simultaneously enhance all parts of

the image very well;

3) it is difficult to select optimal processing parameters,

and there is no efficient measure that can be served as a

building criterion for image enhancement.

Finding a solution to this problem is very important espe-

cially when the image enhancement procedure is used as a

preprocessing step for other image processing techniques suchas detection, recognition, and visualization. It is also important

when constructing an adaptive transform based image enhance-

ment technique. The research work presented here offers novel

frequency domain based image enhancement methods for ob-

ject detection and visualization. The new technique is based

on the so called sequency ordered [30] orthogonal transforms

such as Fourier, Hartley, cosine, and Hadamard transforms

and new enhancement operators. A new class of the fast

trigonometric systems is used for performing the transform

coefficients manipulation operations. A quantitative measure

10577149/01$10.00 2001 IEEE

Authorized licensed use limited to: Telecom ParisTech. Downloaded on July 26,2010 at 07:57:21 UTC from IEEE Xplore. Restrictions apply.
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

8/22/2019 908502

2/16

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 : 9 2 .

of image enhancement is introduced. The technique devel-

oped here has been successfully employed on NASAs Earth

Observing System satellite data products for the purpose of

anomaly detection and visualization. These satellites collect

a Tera-byte of data per day, and fast and efficient methods

are crucial for analyzing these data.

The paper is organized as follows: In Section I, the sequency-

ordered transformis briefly described, which will be used forthe

image enhancement. Then in Section II, we define the so-called

sequency ordered orthogonal transform, quantitative measure of

signal/image enhancement and, then, describe in general a trans-

form-based image enhancement algorithm. Our first technique


8/22/2019 908502

3/16

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 in

order to evaluate the enhancement algorithm. Zonal magnitude

reduction 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 remarks

are 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 implemented

with low computational complexity.

When analyzing signals and systems, it is useful to map data

from the time domain into another domain (in our case, the fre-

quency domain). The basic characteristics of a complex wave

are the amplitude and phase spectra. Specifying amplitude and

phase spectra is an important concept for complex waves. For

example, an amplitude spectrum contains information about the

energy content of a signal and the distribution of the energy

among the different frequencies, which is often used in many

applications. To achieve this, the real variable, , is generalizedtothe complex variable, , which thenismapped back via

inverse mapping. For example, the Fourier transform maps the

real line (time domain) into the complex plane, or real wave into

the complex one. This, however, requires a high complexity in

implementation, since it involves complex multiplications and

additions.

It is obvious to ask the question: Is it possible to construct a

discrete orthogonal system which maps a real signal to another

real signal while maintaining the advantages of a complex do-

main? The motivation for this question is that it is often easier

and efficient, especially from the standpoint of calculation, to

deal with real rather than complex numbers. If we accomplish

this task, we can obtain significant computational advantages in

signal processing, or more specifically, in the signal enhance-

ment.

The one-dimensional (1-D) discrete Fourier transform (1-D

DFT) is given by

(1)

The inverse 1-D discrete Fourier transform is defined as

(2)

The Hellers identity allows to rewrite the

Fourier transform pairs as

(3)

Thus, the 1-D Fourier transform maps the time domain signal

into the frequency domain. The sum of the cosine products can

be defined as the real components of the spectrum, and the

sum of the sine products can be defined as the imaginary com-

ponents of the spectrum. To compute these components, one can

use 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 the

zero-axis is called its sequency (as an analog to frequency).

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 any

set of functions, which satisfies the following properties:

1) the transform can be represented in the form of

(4)

2) and are sequency-ordered functions. and

respectively 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 the

particular cases of the sequency-ordered systems.

Remark 1: If and ,

, then the sequency-ordered system be-

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

8/22/2019 908502

4/16


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 real

function, , is defined as [3]

(5)

where . The Hartley transform is sim-

ilar to the Fourier transform, but only generates real coefficients

rather 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 is

even, and , if is odd, then the sequency-or-

dered system becomes the CalSal WalshHadamard 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 of

trigonometric systems is

(11)

http://-/?-http://-/?-

8/22/2019 908502

5/16


(a)

(b)

Fig. 6. Enhancement by C ( 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 nonsinusoidal 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 completely

the .

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 are

coefficients of the transform.

It is clear that the magnitude of the sequency-ordered sys-

tems are similar to the magnitude of the Fourier transform. This

fact points to possibility of construction unified transform based

enhancement 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 andmagnitude reductionmethods[2], [8]), we

find a common algorithm, which encompasses all of these tech-

niques. The actual procedure of the signal/image enhancement

via 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.


8/22/2019 908502

6/16


(a) (b)

(c) (d)

Fig. 7. Measure of log-enhancement by Fourier, Hadamard, and cosine transforms. (a) Fourier enhancement, (b) differenceE M E

(

;

)

0 E M E

(

;

)

, (c)difference E M E ( ; ) 0 E M E ( ; ) , and (d) difference E M E ( ; ) 0 E M E ( ; ) .

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 of

the transform coefficients) or could be applied directly to

these coefficients. For instance, they could be , ,

or , . Basically, we are interested in thecases, when is an operator of magnitude (see cases

14, below) and when is performed separately on the

coefficients.

Let bethetransformcoefficients and let the enhance-

ment operator be of the form , where the

latter is a real function of the magnitude of the coefficients, i.e.,

. must be real because we only

wish 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) c o n s t a n t (when the enhancement

preserves all constant information);

2) , (which is

the so-called modified -rooting [8]);

3) , , [2];

4) .

Denoting by the phase of the transform coeffi-

cient , we can write

(19)

where is the magnitude of the coefficients. Rather than

apply the enhancement operator directly on the transformcoefficients , we will investigate the operator which is

applied on the modules of the transform coefficients,

(20)

We assume the enhancement operator takes one

of the forms , , at every point

.

In practice, the coefficient is used in

for image enhancement. The optimal value of is image de-

pendent and should be adjusted interactively by the user [8]. For

simplicity of our reasonings, we will assume that in definition


8/22/2019 908502

7/16


Fig. 8. (a) Original image and (b)(d) 2-D Fourier transform enhancements when operating with C 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 . One

can ask: What are the optimal values of , , and ? Can one

choose , , and automatically? What is the best enhance-

ment frequency ordered system? What is the optimal size of the

transform, ?

Remark 6: The above approach can be used 1) on the whole

image, 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-pass

image . The high-pass image is enhanced by multiplication

by and then recombined with the low-pass image [see

also [26], [8], when using the coefficient ].

C. Performance Measure of Enhancement

In this section, we present a new quantitative measure of

image enhancement.

The improvement in images after enhancement is often very

difficult to measure. A processed image can be said to have been

enhanced 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 is

no universal measure which can specify both the objective and

subjective 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 and

Rangayan was defined by the mean gray values in two rectan-

gular windows centered on a current pixel. Baghdan andNegrate

[17] proposed another definition of the local contrast based onthe local edge information of the image, in order to improve

the first mentioned definition. In [17], the local contrast method

proposed by Beghdadi and Negrate has been adopted, in order

to define a performance measure of enhancement. Use of sta-

tistical measures of gray level distribution measures of local

contrast 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 has

greater consistency than the statistical measures, is based on the

contrast histogram.

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

8/22/2019 908502

8/16


(a)

(b)

(c) (d)

Fig. 9. Fourier enhancement via log-reduction when coefficients C ( 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 image

enhancement measure values at given pixels should depend

strongly on the values at pixels that are close by weekly

on those that are further away and also this measure has to

related with human visual system. In our definition, we use a

modification of Webers and Fechners laws. In [31], Weber

established a visual law, argued that the human visual detection

depends on the ratio, rather than difference, between the light

intensity value and . The Weber

definition of contrast was used to measure the local contrast of

a single object. (One usually assumes a large background with

a small test object, in which case the average luminance will be

close to the background luminance. If there are many objects

this assumption do not hold.) Fechners law [32] proposed the

http://-/?-http://-/?-http://-/?-http://-/?-

8/22/2019 908502

9/16


following relationship between the light intensity and

brightness:

(21)

where is a constant, and are the absolute

threshold and upper threshold of the human eye [33].Below, a new quantitative measure of image enhancement is

presented.

Let an image be split into blocks of

sizes , and let , , and are fixed enhancement parame-

ters (or, vector parameter). For a given class of orthogonal

transforms, we define a value as

follows:

(22)

(23)

where and respectively are the min-

imum and maximum of the image inside the block

, after processing the block by transform based enhance-

ment algorithm. The function is the sign function, ,

or , depending on the method of enhancement under

the consideration. The decision to add this function has been

done 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 a measure of enhancement, or

measure of improvement.

Definition 4: The best (optimal) transform relative to the

measure of enhancement is called a transform such that

. The image enhancement algorithm based

on this transform is called an optimal 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. The

best (optimal) -transform-based enhancement image vector

parameter is called a parameter such that

.

It should be noted that the window size can be also includedin 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 enhancement

algorithm, 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 order

to 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 present

the above mentioned iterative algorithm. For each of the cases,we present two classes of experiments. The first class shows

how to choose the best operator parameter (or, the best enhance-

ment algorithm) forthe given transform. Thesecond class shows

how to choose the best image enhancement transform for the

given image. A quantitative comparison of the methods is also

presented below.

In order to enhance our images before passing them through

a 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 the

magnitude information in the determination of edges, reducing

the magnitude produces better edge detection capabilities. This

method 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 the

edge elements).

The clock image was taken as the original, , and

then the moon image was superimposed with it. This results

in an illegible image, as shown in Fig. 2. The result, , is

an enhanced image, which can now be passed through a visual-

ization algorithm.

Case 1: Transform based enhancement algorithm via oper-

ator .

http://-/?-http://-/?-

8/22/2019 908502

10/16


Fig. 11. Two-dimensional Fourier enhancement of the image (a) via the operator O with coefficients C , (b), and C , (c), when = 0 : 8 , = 1 : 5 , and = 0 : 8 ,and the histograms (d)(f) of the images (a)(c), respectively.

Test 1.1Choosing the Best Operator Parameter: This case

is known as modified -rooting or root filtering [8]. When

equals to zero, only the phase is retained. When , the

amplitude of the large transform coefficients are reduced

relative to the amplitude of the small coefficients, and the

result is enhanced edges and details in the image. Since most of

the edge information is contained in the high-frequency region

of the spectrum, the edges are enhanced by this method. By

varying the -level of the reduced image, we are able to enhance

the quality of our images for the visualization. Fig. 3(a)(c),

illustrates the process of enhancement of the image when the

parameter and the Fourier, Hadamard, and cosinetransforms are used. As we see in the above examples, the

magnitude reduction using servedto sharpen the image

as well as even out the brightness throughout the image. The

results of the visualization algorithms will be more accurate

because they will be operating on these enhanced images.

They will also be less dependent on magnitude variations

based on magnification and blurring, therefore making it much

easier to set a thresholding constant, which need not change

from image to image.

Test 1.2Choosing the Best Image Enhancement Transform

for the Given Image: Let be identical to after

the normalization by a constant.

The enhancement measure of the original image shown in

Fig. 2 is 4.5, or , where is the identical

transform. 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 is

provided mostly by the cosine and Hadamard transforms. The

curves 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 theparameter corresponds to the

best visual estimation of enhancement. The enhancement by thetransforms are very close between these two extreme points.


ator .

Test 2.1Choosing the Best Operator Parameter: Fig. 5 il-

lustrates the enhanced images by varying parameter , when

using the Fourier transform, (a)(c), and the Hadamard, (d)(f).

The log-magnitude reduction using serves to enhance

the edges around regions in the image. Fig. 6 demonstrates the

practical application of the proposed method on the images ob-

tained by NASAs Earth Observing System satellites.

Test 2.2Choosing the Best Image Enhancement Transform

for the Given Image: Fig. 7 illustrates the measure of the

http://-/?-http://-/?-

8/22/2019 908502

11/16


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

image enhancement by using different transforms and varying

parameters and respectively in the intervals and

. Fig. 7(a) shows the surface of the measure for the Fourier

method and (c) and (d) show the differences between the

measures when the Fourier, Hadamard, and cosine transforms

are used for enhancement. The results of the Fourier transform

based image enhancement are shown in Fig. 8, for the boundary

parameters. The large values of lead to the elimination of the

higher frequencies on the image spectrum, and the operatorworks as the filter of low frequencies. Contrarily, the small

values of increase the image enhancement.

Test 2.3Comparison: 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.


ator .

Test 3.1Choosing the Best Operator Param-

eter: Combining the magnitude reduction and magnitude

reduction methods in accomplishes both the

sharpening and edge enhancements for a given image. In our

experiments, we found with and toFig. 13. Curves of the Fourier enhancement (a), (b), and (c), by two zones,when using the coefficients C , C , and C , respectively.


8/22/2019 908502

12/16


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 based

enhancement image algorithm is used. Fig. 10 illustrates the

surface of the enhancement measure for , when the

similar Hadamard transform algorithm is applied.

Test 3.2Choosing the Best Image Enhancement Trans-

form: We face the problem of selecting the optimal orthogonal

transform for our application. Since our goal is to achieve

maximum accuracy in the detection of regions of interest aswell maximize computational speed, we must balance these

two factors and make a selection that is appropriate for our

application. Therefore, we analyzed the quality of the results

and the execution time for each of these orthogonal transform

algorithms.

Test 3.3Comparison: 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 range

of intensities differ, when using the different coefficients for

the enhancement. The measure of enhancement is 9.84 and

7.80 when using respectively the coefficients and for

enhancement of the image. Fig. 12 illustrates for comparison

the outputs of the 2-D Fourier transform enhancement for all

three methods under consideration. One can see that the max-

imum measure of enhancement and best visual estimate occurs

when using the coefficient . All further references

to the magnitude reduction algorithm will be to this specific

combination 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 could

be 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 of

the 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 experimented

with it using various magnitude reduction coefficients, in order

http://-/?-http://-/?-

8/22/2019 908502

13/16


Fig. 15. Two-dimensional Fourier enhancement for two zones ( = 1 6 ).

to find the optimal values for this configuration. The goal is to

find 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 TRANSFORM BASED 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, we

propose varying the transform based image enhancement within

radially concentric zones. The motivation of using zones comes

from the fact that: a very short transform coefficient length

corresponds to the homogenous image blocks, a medium

transform coefficient length corresponds to the texture, and a

long transform coefficient length corresponds to the highly

active image blocks. By using this method, we achieve much

more flexibility and control over the magnitude reductions

in different regions within the frequency domain. By using

increasingly greater reductions in higher frequencies, we

manage to attenuate the high-frequency noise component of the

image. At the same time, we also maintain the edge enhancing

effects of the magnitude reduction algorithm.We now demonstrate zonal transform based image enhance-

ment via a few examples. For this, we describe the transform

based image enhancement algorithm (including iterative algo-

rithm) with two and three zones. It should be noted that, in the

case considered above, we have used one zone.

In order to accomplish this method, we first have to find

the maximum and minimum values within the frequency do-

main data. Then, using these maximum and minimum points as

end-markers, we divide the frequency domain into regions based

on each points magnitude distance from themaximum 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 four

pairs of and values, as well as three values of the distance

to specify our magnitude reductions. These values can be deter-

mined by means of the enhancement measure.

Case 4: Transform based image enhancement algorithms

with two zones, and .

a) The enhancement operator can be defined by

if

if(24)


8/22/2019 908502

14/16


Fig. 16. Two-dimensional Hadamard enhancement for two zones ( = 1 6 ).

Remark 7: The zone has to be very small and coefficient

has to be near to zero or zero. b) The enhancementoperator 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 radius of the first zone by which the area of

the Fourier spectrum is divided; the second zone is the rest of

the area. Fig. 13 shows that when radius of the zone increases,

the measure of image enhancement grows faster when using the

coefficient , than .

Fig. 14 illustrates the example of the image enhancement by

two zones with varying radius-parameter . As can be observed

from 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)

where

magnitude of the transform image;,

thresholding operator;

very small constant (or, zero).

is defined as , where

and 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 two

zones. The threshold is and parameter takes values

0.5, 0.6, 0.7, 0.8, and 1.

Case 5: Transform Based Image Enhancement Algorithms

with Three Zones.

The enhancement operator can be defined by

if

if

if

(27)


8/22/2019 908502

15/16


This is a typical contrast stretching transform, which has to be

applied in the frequency domain (see [13, pp. 235237]).

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 magnitude

techniques) have been described and applied for detection and

visualization on objects within an image. The new techniques

are 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 reduction

techniques and developed an entirely novel method. The

wide range of characteristics can be obtained from a single

transform by varying enhancement parameters. A quantitative

measure of signal/image enhancement was presented, which

demonstrated the optimal method to automatically choose thebest parameters and transform. The proposed algorithms are

simple to apply and design, which makes them practical. A

number of experimental results were given which illustrate the

performance of these algorithms. The comparative analysis

of transforms based image enhancement algorithms has been

described, too. Lastly, the comparison of the Fourier transform

and Walsh, cosine and Hartley transforms was given. We find

that for a negligible tradeoff of accuracy, one can use the Walsh

transform to achieve significantly higher performance enhance-

ment. For our purposes, where speed is a major concern, the

proposed method turns out to be a dramatic improvement over

existing methods. We have also proposed the zonal transform

based image enhancement algorithms.

REFERENCES

[1] S. S. Agaian, Advances and Problems of Fast Orthogonal Transform forSignal/Image Processing Applications, pp. 146215, 1990.

[2] R. Kogan, S. S. Agaian, and K. P. Lentz, Visualization using rationalmorphology and zonalmagnitude-reduction, Proc. SPIE, vol. 3304, pp.153163, 1998.

[3] R. P. Millane, Analytic properties of the Hartley transform and theirapplications, Proc. IEEE, vol. 82, pp. 413428, Mar. 1994.

[4] D. F. Elliot and K. R. Rao, Fast Transforms: Algorithms, Analyses, Ap-plications. New York: Academic, 1983.

[5] K. G. Beauchamp, Walsh Functions and Their Applications. NewYork: Academic, 1975.

[6] K. O. Egiazarian, S. S. Agaian, and J. Astola, On a parametric familyof discrete trigonometric transforms, Proc. SPIE, 1996.

[7] J. H. McClellan, Artifacts in alpha-rooting of images, in Proc. IEEEInt. Conf. Acoustics, Speech, Signal Processing, Apr. 1980, pp. 449452.

[8] S. Aghagolzadeh and O. K. Ersoy, Transform image enhancement,Opt. Eng., vol. 31, pp. 614626, Mar. 1992.

[9] R. Rajcsy and Liberman, Texture grandiuts as a depth one, Comput.Graph. Image Process., vol. 5, pp. 5257, 1976.

[10] D. L. Donoho, De-noising by soft-thresholding, IEEE Trans. Inform.Theory, vol. 41, pp. 613627, May 1995.

[11] A. Rosenfeld and A. C. Kak, Digital Picture Processing. New York:Academic, 1982, vol. 1.

[12] W. M. Morrow, R. B. Paranjape, R. M. Rangayyan, and J. E. L. De-sautels, Region-based contrast enhancement of mammograms, IEEETrans. Med. Imag., vol. 11, pp. 392406, Sept. 1992.

[13] A.Jain, Fundamentals of Digital Image Processing. Englewood Cliffs,NJ: Prentice-Hall, 1989.

[14] T. L. Ji, M. K. Sundareshan, and H. Roehrig, Adaptive image con-trast enhancement basedon human visual properties,IEEE Trans. Med.

Imag., vol. 13, pp. 573586, Dec. 1994.[15] N. Netravali and Presada, Adaptive quantization of picture signals

using spatial masking, Proc. IEEE, vol. 65, no. 4, pp. 536548, 1977.[16] J. K. Kim, J. M. Park, K. S. Song, and H.W. Park, Adaptive mammo-

graphic image enhancement using first derivative and local statistics,IEEE Trans. Med. Imag., vol. 16, pp. 495502, Oct. 1997.

[17] A. Beghcladiand A. L. Negrate, Contrast enhancement techniquebased

on local detection of edges, Comput. Vis., Graph., Image Process., vol.46, pp. 162274, 1989.[18] D.-C. Chang and W.-R. Wu, Image contrast enhancement based on a

histogramtransformationof localstandarddeviation,IEEE Trans. Med.Imag., vol. 17, pp. 518531, Aug. 1998.

[19] G. X. Ritter and J. N. Wilson, Handbook of Computer Vision Algorithmsin Image Algebra. Boca Raton, FL: CRC Press, 1996.

[20] J. B. Zimmerman, S. M. Pizer, E. V. Staab, J. R. Perry, W. McCartney,and B. C. Brenton, An evaluation of the effectiveness of adaptivehistogram equalization for contrast enhancement, IEEE Trans. Med.

Imag., vol. 7, pp. 304312, Dec. 1988.[21] R. Gonzalez and Wintz, Digital Image Processing, 2nd ed. Reading,

MA: Addison-Wesley, 1987.[22] D. Ballard and C. Brown, Computer Vision. Englewood Cliffs, NJ:

Prentice-Hall, 1982.[23] J. Harris, Constant variance enhancement: A digital processing tech-

nique, Appl. Opt., vol. 16, pp. 12681271, May 1977.

[24] P. Natendra and Rithch, Real-time adaptive contrast enhancement,IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-3, pp. 655661,Nov. 1981.

[25] A. Khellaf, A. Beghdadi, and H. Dupoiset, Entropic contrast enhance-ment, IEEE Trans. Med. Imag., vol. 10, pp. 589592, Dec. 1991.

[26] D. Wang and A. H. Vagnucci, Digital image enhancement, Comput.Vis., Graph., Image Process., vol. 24, pp. 363381, 1981.

[27] A.M. Grigoryanand S. S. Agaian, Split manageable efficient algorithmfor Fourier and Hadamard transforms, IEEE Trans. Signal Processing,vol. 48, pp. 172183, Jan. 2000.

[28] J. A. Saghri, P. S. Cheatham, and H. Habibi, Image quality measurebased on a human visual system model, Opt. Eng., vol. 28, no. 7, 1989.

[29] H. S. How and D. R. Tretter, Frequency characterization of the discretecosine transform, Proc. SPIE, vol. 1349, pp. 3142, 1990.

[30] H. F. Harmuth, Applications of Walsh function in communications,IEEE Spectrum, pp. 8242, 1969.

[31] I. E. Gordon, Theory of Visual Perception. New York: Wiley, 1989.

[32] G. T. Fechner, Elements of Psychophysics. New York: Rinehart &Winston, 1960, vol. 1.[33] L. E. Krueger, Reconciling Fechner and Stevens: Toward an unified

psychophysical law, Behav. Brain Sci., vol. 12, pp. 251320, 1989.[34] S. S. Agaian, Advances and Problems of Fast Orthogonal Transform

for Signal/Image Processing Applications. Moscow, Russia: Nauka,1991, pp. 99145.

Sos S. Agaian (M85) received the M.S. degree inmathematics and mechanics from Yerevan State Uni-versity, Armenia, the Ph.D. degree in mathematics

and 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 wasa VisitingProfessorwith theDepartment 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.

http://-/?-http://-/?-

8/22/2019 908502

16/16


Karen Panetta (SM95) 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, large

system simulation, and behavioral modeling. Sheis currently a NASA JOVE Fellow for the NASALangley 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 (S78M99) 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 1990to 1996,he wasa SeniorResearcherwith theDepartment ofSignaland Image Processing, Institute for Problems of Informatics and Automation,and Yerevan State University, Academy Science of Armenia. In 1996, he joined

the 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 fluorescent in situ hybridization 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.

Date post:	08-Aug-2018
Category:	Documents
Upload:	jimakosjp
View:	215 times
Download:	0 times

908502

Documents