1784 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 17, NO. 10, OCTOBER 2008
There are also other advantages of using compressed domain
representation. For example, due to the spectral separation, it
is possible to enhance features by treating different frequency
components differently. To this end, different algorithms have
been advanced for both color and grey level images in the block
DCT domain, such as alpha rooting , multicontrast en-
hancement , , by processing the AC coefﬁcients and its
modiﬁed form by processing both DC and AC coefﬁcients ,
etc. However, there are also some disadvantages in processing
images in the block DCT domain. As in most cases blocks
are independently processed, blocking artifacts may become
more visible in the processed data. Some times superﬂuous
edges may appear in the image boundaries due to the sharp
discontinuities of the distribution at its boundaries.
The display of a color image depends upon three fundamental
factors, namely i) its brightness, ii) contrast, and iii) colors.
Interestingly, all the previous work have considered either the
brightness (such as adjustment of dynamic ranges) or the con-
trast (such as image sharpening operations), and even in some
cases a combination of both attributes. But none of these al-
gorithms have considered the preservation of colors in the en-
hanced image. In this work we have considered all three at-
tributes while designing a simple computationally efﬁcient al-
The simplicity of the proposed algorithm lies in the fact that
the computation requires only scaling of the DCT coefﬁcients
mostly by a factor which remains constant in a block. In con-
trast, previous algorithms , , and , dealt with nonuni-
form scaling of DCT coefﬁcients in a block. For example, in
, the scale factors are computed for every coefﬁcient (both
the DC and AC coefﬁcients) by taking their roots. In , the
relative contrast between a pair of successive bands of AC coef-
ﬁcients is scaled by a factor, which remains constant for every
block. This eventually requires computation of different scale
factors for different bands of AC coefﬁcients. In , a similar
strategy has been incorporated. However, in this technique the
amount of scaling of the relative contrast between the successive
bands of AC coefﬁcients varies from one block to the other. It
also varies between the low-frequency bands and the high fre-
quency bands. On the other hand, the proposed algorithm not
only uses the same scale factor for both the DC and AC coef-
ﬁcients, but also scales the chromatic components as well with
the same factor (with the exception of their DC coefﬁcients as
discussed later). This simplicity, however, does not make the
scheme inferior to others. In fact in many respects, it has been
found to provide better performance metrics, as observed in our
The major objective for processing the data in the compressed
domain is to reduce the computational complexity and storage
requirements. Hence, these two requirements should be taken
into account in designing the pertinent algorithms. For many
spatial domain processing, an equivalent computation in the
DCT domain could be developed by using the properties of the
DCT such as its linear and orthogonal property, sub-band rela-
tionship , spatial relationship , and convolution-multi-
plication property .
II. MATHEMATICAL PRELIMINARIES
The Type II DCT is more commonly used in image compres-
sion algorithms. In the case of a 2-D image
it is given by
where is given by
The coefﬁcient is the DC coefﬁcient and the remaining
are the AC coefﬁcients for the block. The normalized transform
coefﬁcients are deﬁned as
Let and denote the mean and standard deviation of an
image. Contrast of an image is usually modeled
with the Weber law , where is the difference
in luminance between a stimulus and its surround, whereas is
the luminance of the surround . As provides a measure for
surrounding luminance and is strongly correlated with ,
we redeﬁne the contrast of an image as follows:
It may be emphasized here that the above deﬁnition is merely
intuitive by drawing analogy from the Weber Law as mentioned
before. It also reﬂects the local contrast measure and under the
present context, we apply it to the individual blocks.
In the following theorem, we state how the contrast of an
image is related to the scaling of its DCT coefﬁcients.
Theorem 1: Let be the scale factor for the normalized
DC coefﬁcient and be the scale factor for the normalized
AC coefﬁcients of an image of size . Let the DCT
coefﬁcients in the processed image be given by
The contrast of the processed image then becomes
times of the contrast of the original image.
Proof: From the deﬁnition of the DCT, it follows that the
mean of the image is given by
Similarly, from the Perseval’s Theorem, the standard deviation
of the image can be expressed as
MUKHERJEE AND MITRA: ENHANCEMENT OF COLOR IMAGES BY SCALING THE DCT COEFFICIENTS 1785
In fact, from (7), it can be seen that the sum of the squares
of the normalized AC coefﬁcients provide the variance of the
image. Hence, any change in the DC component does not have
any bearing on its standard deviation . So under scaling of
the DCT coefﬁcients by according to (5), the mean
and standard deviation of the processed image become
and , respectively. As a result the contrast of the pro-
cessed image becomes times of that of the original
In the block DCT space, the image is partitioned into a set
of blocks (in the JPEG standard, ). One of its
advantages of partitioning is that it captures the local statistics,
though in a predeﬁned manner. As one of our objectives for the
enhancement is to preserve the local contrast of the image, if we
keep in a block, the local contrast remains the
same as before.
However, the scaling of the component only does not
preserve the colors in the processed image. By preservation
of colors we mean that in the - - color space the color
vector of a pixel in the processed image has the same direction
as that in the original. For example in  this is carried out
in the - - space (in the spatial domain) by scaling the
and components with the same proportion of enhanced
values in pixels. Similar strategy is employed in the proposed
algorithm. However, one should take care of the nonlinearity in
the transformation of the - - color space to - - color
space. In the block DCT space this requires separate treatment
for the DC coefﬁcient and the AC coefﬁcients. The following
theorem summarizes these operations.
Theorem 2: Let and
denote the DCT coefﬁcients of
the and components, respectively. If the luminance
component of an image is uniformly scaled by a factor , the
colors of the processed image with and are preserved
by the following operations:
Proof: The - - color space is related to the - -
color space as follows:
assuming 8 bits for each color component.
Though the - - space is not linearly related to the -
- space, the color space - - , with and
, is linearly related to the - - space. Hence,
under uniform scaling by factor of all samples of and
, the magnitude of the color vectors in - - space is also
scaled by , while keeping its direction the same. Let the DCT of
and components be denoted by and , respectively.
They are related to the and the as follows:
From (11) and (12), (8) and (9) can be easily derived.
III. THE PROPOSED ALGORITHM
The proposed algorithm performs the color image enhance-
ment operation in three steps. First, it adjusts the background
illumination. The next step preserves the local contrast of the
image and the last one preserves the colors of the image. More-
over, in a block DCT space, the algorithm attempts to exploit the
advantage of having localized information from the DCT coefﬁ-
cients. The algorithm is designed in such a way that each block
(of size 8 8) for all the components could be handled indepen-
dently. This makes it more suitable for parallel implementation.
A. Adjustment of Local Background Illumination
In adjusting the local background illumination, the DC co-
efﬁcient of a block is used. The DC value gives the mean of
the brightness distribution of the block. This adjustment may be
performed by mapping the brightness values to a value in the
desired range. This function should be monotonic in the given
range. Let us denote the maximum brightness value of the image
as (which may be available from the header of the com-
pressed stream). Let the DCT coefﬁcients of a 8 8 block of the
luminance component be denoted by
. Then is the DC coefﬁcient and the rest are the AC
coefﬁcients. As before we denote the normalized DC and AC co-
efﬁcients by . In adjusting
the local brightness, this DC coefﬁcient is mapped to
by using a monotonically increasing function
in the interval of [0,1] as follows:
The function can be chosen in various ways. In our ex-
perimentations we have considered some of the previously used
functions for enhancement, namely, the twicing function (de-
noted here by ) , a function used in  (denoted here
by ) and the S-function  (denoted by ). Their func-
tional forms are given in (14)–(16), shown at the bottom of the
The reasons for choosing these functions are as follows: i)
they have been employed earlier in developing image enhance-
ment algorithms, and ii) there is no single function which has
been found to provide the best performance for every image. Our
objective here is to observe the performances of our proposed
algorithm with different choices of these mapping functions.
1786 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 17, NO. 10, OCTOBER 2008
There are also other advantages for using each of the above func-
tions. The ﬁrst one, , is simple to implement. It has no pa-
rameter, yet it is found to be quite effective in brightening the
dark regions across different types of images. The second one,
, is also relatively simpler (than the third one). It has a single
parameter which should be centered around 2. This function
works well both in the dark and bright regions. The last one,
, is the most complex one. It has four parameters,
and . However, it can effectively control the dark regions (be-
tween ) and bright regions (between ) separately (by
choosing different values of for dark region and for bright
region). It may be noted also that . Plots of these
functions are shown in Fig. 2.
The results obtained by applying these functions on the image
of Fig. 1(a) are shown in Fig. 3. It may be noted that though the
dark regions get brightened by these processes, the images lack
the sharpness or details of the original one. So to preserve the
local contrast we apply the following simple procedure.
B. Preservation of Local Contrast
Let us deﬁne the enhancement factor for a block during ad-
justment of its luminance as
where is the mapped DC coefﬁcient and is the
original DC coefﬁcient.
Since the DCT is a linear transform, multiplying all the coef-
ﬁcients of by results in the multiplication of the pixel values
in the block by the same factor. This also preserves the contrast
of the block. However, there is a risk of overﬂow of some of
the pixel values beyond the maximum allowable representation
(say ). This can be controlled by taking into account of the
standard deviation and mean of the brightness distribu-
tion of the block. Let us assume that the brightness values of
this distribution lie within , where is a constant.
In that case should lie within an interval as stated by the fol-
Theorem 3: If we assume that the values in a block lies within
, the scaled values will not exceed if
Proof: Due to the scaling of the DCT coefﬁcients by ,
the mean and standard deviation of the block become as and
, respectively. A pixel value of the scaled block should lie
within . This implies and the scaled value
Fig. 2. Plots of the mapping functions: (a) (x), (b) (x), and (c) (x)(m =
n = 0:5).
Fig. 3. Enhanced image by scaling DC coefﬁcients only using (a) (x), (b)
(x), and (c) (x).
will not exceed if . Hence,
MUKHERJEE AND MITRA: ENHANCEMENT OF COLOR IMAGES BY SCALING THE DCT COEFFICIENTS 1787
Fig. 4. Enhanced images by scaling both DC and AC coefﬁcients using
(a)(x), (b) (x), and (c) (x).
Fig. 5. Enhanced images by scaling all the components including Cb and Cr
using (a) (x), (b) (x), and (c) (x).
The resulting images after the application of these operations
are depicted in Fig. 4. It can be seen that the colors look less
saturated in the enhanced images and there is a scope for further
improvement on the display of colors. This task is performed in
the next and ﬁnal stage.
C. Preservation of Colors
As described earlier, we have performed a restricted scaling
operation according to (8) and (9) for preserving the colors. It
may be noted that the previous enhancement algorithms  did
not perform this operation . These techniques only change
the luminance component and keep the chrominance com-
ponents ( and , respectively) unaltered. Though in the
- - color space the chrominance components are decor-
related better than that in the - - color space, the increasing
values in the component usually tend to desaturate the colors.
Typically one may observe from the conversion matrix for going
from the - - space to the - - space, for and
increasing while keeping and unchanged re-
duces both the and factors. This is why we be-
lieve that the chromatic components should be also processed
for preserving the colors. The improvement of the quality of the
enhanced image is also quite apparent from Fig. 5.
In this case, there is also a chance that the enhanced values
of the chromatic components may fall outside the range of rep-
resentation (in the spatial domain) due to the scaling operation.
One may adopt also a similar strategy of limiting the enhance-
ment factor as described in the previous section. However, in
our experimentation with a different set of images, we have not
observed any such case and this operation has been ignored in
the proposed algorithm.
D. Suppressing Blocking Artifacts
The major problem in developing algorithms in the block
DCT domain is the blocking artifacts that may be visible as a
result of the independent processing of the blocks. One possible
solution is to make use of the information from neighboring
blocks for reducing or removing these artifacts as adopted in
 and  and elsewhere. However, this comes at the cost
of more computation and more buffer requirements. A simpler
Fig. 6. Enhanced images with blocking artifact removal by decomposition and
composition of DCT blocks using (a) (x), (b) (x), and (c) (x).
strategy is to suppress some of the coefﬁcients in the ﬁrst row
and column for removing such artifacts . However, we have
found these approaches not very effective. Sometimes applica-
tion of these techniques have resulted in the occurrence of spu-
rious horizontal or vertical edges in the enhanced images. In
our proposed technique, we have tried to address this problem
from a different perspective. We have observed that blocking ar-
tifacts are more visible in the regions where brightness values
vary signiﬁcantly, specially near the edges of sharp transitions
of luminance values. For suppressing these artifacts, therefore,
it would be necessary to keep the variations of the DC coefﬁ-
cients smooth or continuous. To this end, the mapping function
has been found to perform better than the others. In fact, the
strategy for adjusting its parameter depending on the ratio
of high and low spectral energies has been adopted in . Later
these values are further smoothed by taking the average of pa-
rameter values in the neighboring blocks. However, to keep the
computations limited within a block for achieving better par-
allelism, we have taken a different approach. We have decom-
posed the DCT blocks into smaller blocks, if necessary, and per-
formed computations on them. Later these smaller blocks are
merged into the original block size. In this case, we have identi-
ﬁed the blocks having signiﬁcant variations by examining their
standard deviations . If the is beyond a threshold (denoted
here as ), we decompose a 8 8 block into four 4 4
sub-blocks. Then the same enhancement algorithm is applied to
each sub-block. Finally, the four enhanced sub-blocks are com-
bined again to a 8 8 block. There exist efﬁcient algorithms for
these composition and decomposition operations with a mar-
ginal increase in the computational overhead , . These
additional operations also do not increase any buffer require-
ment. The results obtained after application of this technique
are shown in Fig. 6.
E. The Algorithm
The overall algorithm is summarized below. As each block
is independently processed, in the description processing with a
single block is narrated. In our description we have also consid-
ered a block of general size .
Algorithm Color Enhancement by Scaling (CES)
Input: : DCTs of three components of a block.
Input Parameters: (the mapping function), ,
1. Compute and using (6) and (7).
1788 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 17, NO. 10, OCTOBER 2008
Fig. 7. Few more examples of original and enhanced images using the tech-
nique reported in . (a) Image18, (b) enhanced image18, (c) image22, (d) en-
hanced image22, (e) image24, (f) enhanced image24.
2. If ,
2a. Decompose into DCT sub-blocks,
2b. For each block apply similar computations as described
in Steps 3 through 5, and
2c. Combine 4 of these blocks into a single
DCT block and return.
3. Compute the enhancement factor as follows:
3b. , and
4. Scale the coefﬁcients:
4a. , and
4b. Apply (11) and (12) on and for preserving colors.
End Color Enhancement by Scaling (CES)
It may be noted that the step-2 of the above algorithm may be
applied recursively. This would deﬁnitely improve the quality of
the results by further removing the blocking artifacts. In the lim-
iting case, the operation will be equivalent to the application of
mapping function [refer to (13)] to individual pixels. It is clear
that these would increase the computation and the improvement
would be mostly marginal, as it is expected that smaller blocks
are having lower variance values. Under the present context, as
the block size is 8 8 only, we have applied one level of decom-
position and composition (until the size of 4 4) if required.
This also keeps the algorithm simple by avoiding recursion or
IV. COMPARISON METRICS
We have compared the performance of the proposed enhance-
ment technique with several other compressed domain methods.
To this end, we considered how the compressed domain tech-
niques perform compared to that of a very good spatial domain
enhancement technique. For the latter we chose the scheme pro-
posed in  which is based on a multiscale retinex processing. It
essentially involves multiscale Gaussian ﬁltering and point-wise
center-surround subtraction in the logarithmic scale. Finally, the
pixel values are remapped to their original scale, followed by
an empirical adjustment of color components. The processing
is performed in the - - color space and is computation-
ally quite expensive. However, the algorithm appears to pro-
vide excellent enhancement results as can be seen in the web-
site http://dragon.larc.nasa.govt/retinex/pao/news. Fig. 7 shows
some of the images from this website.
For perceptual quality evaluation purposes, we have consid-
ered these spatial-domain processed images as the reference
images and have used the metric proposed in . For future
reference we call this metric the Wang–Bovic-Quality-Metric
(WBQM) and its deﬁnition is given below. Let and be two
distributions. The WBQM between these two distributions is de-
where is the covariance between and and are
the standard deviations of and respectively, and as well
as are their respective means. It may be noted that this mea-
sure takes into account of the correlation between the two dis-
tributions and also their proximity in terms of brightness and
contrast. The WBQM values should lie in the interval .
Processed images with WBQM values closer to 1 are more sim-
ilar in quality according to our visual perception. We have mea-
sured WBQM measures independently for each component in
the - - space and called them as -WBQM, Cb-WBQM
and Cr-WBQM, respectively.
Wang et al.  have also suggested another no reference
metric for judging the image quality reconstructed from the
block DCT space to take into account visible blocking and blur-
ring artifacts. In , this metric has been used. In our com-
parison also, we have used the same one and call it the JPEG-
Quality-Metric (JPQM). The computation of this metric is de-
scribed in . We have used the MATLAB code available
at their web-site http://anchovy.ece.utexas.edu/z˜wang/research/
nr_jpeg_quality/index.html to compute these values. Inciden-
tally, in , same parameter set has been used for getting the
JPQM values. It may be noted that for an image with good vi-
sual quality, the JPQM value should be close to 10.
MUKHERJEE AND MITRA: ENHANCEMENT OF COLOR IMAGES BY SCALING THE DCT COEFFICIENTS 1789
Finally, we are also interested to observe the quality in terms
of color enhancement. In this regard, we have used a no-ref-
erence metric called colorfulness metric (CM) as suggested by
Susstrunk and Winkler . The deﬁnition for this metric in the
- - color space is as given below.
Let the red, green and blue components of an Image be
denoted by , and , respectively. Let and
. Then the colorfulness of the image is
where and are standard deviations of and , respec-
tively. Similarly, and are their means. In our compar-
ison, however, we have used the ratio of CMs between the en-
hanced image and its original for observing the color enhance-
ment factor CEF.
We have compared the performance of the proposed approach
with that of three existing DCT domain color enhancement tech-
niques, namely alpha-rooting , multicontrast enhancement
 technique, and multicontrast enhancement coupled with
dynamic range compression . In alpha rooting a DCT co-
efﬁcient is modiﬁed as given by the following equation:
In our experimentation, the value of has been kept as 0.98.
This value has been chosen empirically after observing the per-
formance of this technique with different values of .
For multicontrast enhancement, the spectral energy for each
diagonal band such that is expressed as the average
of the absolute value of the DCT coefﬁcients in the band. The
algorithm computes a contrast measure as
the ratio of the cumulative energy sums till the th band for the
enhanced and original image. Then the coefﬁcients at each band
are scaled by the factor . In our experimentation, has been
taken as 1.95.
The contrast enhancement operation of  is almost sim-
ilar to that reported in . In , the norm has been used,
while in , the norm has been used for deﬁning relative
contrast among the spatial frequency bands. Besides in , the
technique is further reﬁned by varying the parameter of dy-
namic range compression for each block depending on its spec-
tral content. The parameter is also smoothed by taking average
of its values used in the neighboring blocks. In our experimenta-
tion, we have used the same set of parameter values (
and ), as used in . Further, following the
similar implementation in , during application of multicon-
trast enhancement on the bands of AC coefﬁcients, we have kept
the scaling parameter  as 1 for low frequency bands and as
the enhancement factor (equivalent to in the Theorem 1 of this
paper) for high frequency bands. In , a preprocessing step of
noise removal and a postprocessing operation of smoothing the
DC coefﬁcients are also carried out for further improvement of
the result. In our implementation, we have not considered these
LIST OF TECHNIQUES CONSIDERED FOR COMPARATIVE STUDY
steps, as both these steps could be applied to other algorithms
for similar improvement.
We have implemented our proposed algorithms CES with dif-
ferent choices of the mapping functions. As we would like to ob-
serve the effect of employing blocking artifact removals (Step
2 of the algorithm CES), the algorithms for both the variations
(with and without the computation described in the Step 2) have
been implemented. The names of different techniques and the
parameter set used in experimentations are listed in Table I.
A. Enhanced Images: A Few Examples
In this section, we present the results of different approaches
used for processing the set of images shown in Fig. 7. The
processed images are shown in Figs. 8, 10, and 12, respectively.
For observing the enhancement near edges, portions of the
enhanced images near typical edges, are shown in enlarged
forms in Figs. 9, 11, and 13, respectively. Further, the per-
formance metrics of different techniques are also tabulated in
Tables II–IV. In the tables, the maximum performance mea-
sures are shown as bold numbers. It has been found that the
alpha rooting technique leads to an image that is almost similar
to its original, and, hence, its JPQM measures are higher than
other schemes. But its other performance indices are quite
poor. Though the MCEDRC performs quite well in terms of
JPQM, its measures related to colors (CEF, Cb-WBQM, and
Cr-WBQM) are signiﬁcantly poorer than those obtained by the
CES techniques. Among CES techniques, TW-CES has per-
formed the best in our examples, though its performance related
to suppression of the blocking artifacts is usually poorer. It
should be noted also that adoption of blocking artifact removal
(Step 2 of the algorithm CES) has signiﬁcantly improved the
JPQM measures. This is also reﬂected by the improvement of
the visual quality of the enhanced images.
1) Iterative Processing: It should be noted that the proposed
approach can also be applied iteratively for additional enhance-
ment if necessary. However, it has been generally observed that
additional iterations increase the appearances of blocking and
blurring artifacts in the processed images. But for a few of the
images more than one iterations has improved the visual quality.
Typical examples of applying TW-CES-BLK on the image 22
1790 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 17, NO. 10, OCTOBER 2008
Fig. 8. Enhancement of image18.
Fig. 9. Zoomed portion of the enhanced image18.
with two or more iterations are shown in Fig. 14. It can be ob-
served that an increase in the number of iterations has led to a
steady decrease of the JPQM values (refer Table V). However,
with two iterations there is a signiﬁcant improvement of the CEF
B. Average Performances at Different Compression Levels
We have experimented with a set of color images (image1
to image24 except the image21 which is not a color image).
These images have been compressed using JPEG at different
compression quality factors, namely 100, 75, 50 and 30. At
each compression level, we have listed the average performance
metrics of different techniques in Tables VI–IX, respectively.
From these tables it should be noted that the TW-CES-BLK
provide the best performance indices though it is relatively poor
in reducing the blocking artifacts compared to that obtained
using other mapping functions. The other two variations of
Fig. 10. Enhancement of image22.
Fig. 11. Zoomed portion of enhanced image22.
CES (DRC-CES-BLK and SF-CES-BLK) are quite good in
suppressing the blocking artifacts. It is also interesting to note
that the performance measures related to colorfulness and
similarity with the reference images do not vary signiﬁcantly
at varying levels of compression. However, as expected, the
blocking artifacts are more and more visible with increasing
levels of compression.
C. Computational Complexity
We have also compared the computational complexity in
terms of number of additions, multiplications (or divisions) and
exponentiation operations per pixel for the different techniques.
These are expressed in the form of , where
denotes the number of additions, denotes the number
of multiplications (or divisions) and denotes the number
of exponentiation operations for every pixel in the original
image. In estimating the number of operations, we have also
MUKHERJEE AND MITRA: ENHANCEMENT OF COLOR IMAGES BY SCALING THE DCT COEFFICIENTS 1791
Fig. 12. Enhancement of image24.
Fig. 13. Zoomed portion of enhanced image24.
ignored normalization operations on the coefﬁcients such as
division by the block length (8) or maximum intensity value
PERFORMANCE MEASURES FOR DIFFERENT TECHNIQUES ON
PERFORMANCE MEASURES FOR DIFFERENT TECHNIQUES ON
PERFORMANCE MEASURES FOR DIFFERENT TECHNIQUES ON
Fig. 14. Enhanced images after number of iterations: (a) 2, (b) 3, and (c) 4.
PERFORMANCE MEASURES ON ITERATIVE APPLICATIONS OF TW-CES-BLK ON
(may be taken as 255 in most cases). For different algorithms,
the accounting for different operations are described in the
1) Alpha Rooting (Ar): The computation according to
(20) requires 1 multiplication and 1 exponentiation operation.
1792 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 17, NO. 10, OCTOBER 2008
AVERAGE PERFORMANCE MEASURES WITHOUT COMPRESSION
AVERAGE PERFORMANCE MEASURES WITH JPEG COMPRESSION
AT QUALITY 75
AVERAGE PERFORMANCE MEASURES WITH JPEG COMPRESSION
AT QUALITY 50
AVERAGE PERFORMANCE MEASURES WITH JPEG COMPRESSION
AT QUALITY 30
Hence, the computational complexity can be expressed as
2) Multicontrast Enhancement (MCE): Computation of the
cumulative energies for both enhanced and original blocks, re-
quires 126 additions (ignoring the cost of absolute operations).
For computing , 14 divisions are required and
ﬁnally the scaling of the AC coefﬁcients requires two multipli-
cations each. The total number of operations for each block is
COMPUTATIONAL COMPLEXITIES OF DIFFERENT TECHNIQUES
thus 140 multiplications and 126 additions. Hence, the number
of operation per pixel becomes .
3) Multicontrast Enhancement With Dynamic Range Com-
pression (MCEDRC): As this technique uses norm, the com-
putation of cumulative energies becomes more expensive than
the previous technique. In this case, the number of operations
is 128 Multiplications and 126 Additions. In addition, the dy-
namic range compression requires the computation of the func-
tion with 2 exponentiation and 2 addition operations. Con-
sidering all other factors similar to the previous one, the per pixel
operation can be expressed as . Here, we
have ignored the computational overhead of the dynamic adjust-
ment of the parameter (refer Table I) for reducing the blocking
4) Contrast Enhancement by Scaling (CES): In this algo-
rithm, the scaling of the coefﬁcients by a constant for each com-
ponent is the major computational task. This would require 192
multiplications and four additions. The additions are necessary
for translating (and retranslating back) the DC coefﬁcients of
the Cb and Cr components. Computation of the scaling factor
depends on the type of functions used. In addition, there is an
overhead of computing the standard deviation and the mean
of the block, which requires 63 multiplications, 62 additions
and one exponential operation (square root).
The per pixel operations of different techniques are summa-
rized in the Table X.
For removing the blocking artifacts, the composition and
decomposition operations both require operations
for each component . This implies additional overhead for
such blocks would be roughly operations. However,
the number of blocks requiring such decomposition should be
small. It may be noted that the multiscale-retinex technique
in the spatial domain  requires much higher computation.
Typically, Gaussian smoothing with scale requires a convo-
lution with a mask of size . Exploiting the symmetry
of the Gaussian mask, this computation can be performed
with multiplications and number of additions.
In , the enhancement is performed with convolutions with
three Gaussian masks with scales 15, 80, and 250, respectively.
Besides, there are other operations such as subtraction in
the logarithmic scale and color restoration of pixels. These
are carried out for all color components in the R-G-B space.
Hence, the per pixel computation requirement is given by
VI. CONCLUDING REMARKS
In this paper, we have presented a simple approach for
enhancing color images in the block DCT domain by scaling
MUKHERJEE AND MITRA: ENHANCEMENT OF COLOR IMAGES BY SCALING THE DCT COEFFICIENTS 1793
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Jayanta Mukherjee (M’90–SM’04) received the
B.Tech., M.Tech., and Ph.D. degrees in electronics
and electrical communication engineering from the
Indian Institute of Technology (IIT), Kharagpur, in
1985, 1987, and 1990, respectively.
He joined the faculty of the Department of Elec-
tronics and Electrical Communication Engineering,
IIT, Kharagpur, in 1990, and later transferred to the
Department of Computer Science and Engineering
where he is presently a Professor. He served as the
head of the Computer and Informatics Center at IIT,
Kharagpur, from September 2004 to July 2007. He was a Humboldt Research
Fellow at the Technical University of Munich in Germany for one year in 2002.
He also has held short-term visiting positions at the University of California,
Santa Barbara, University of Southern California, Los Angeles, and the National
University of Singapore. His research interests are in image processing, pattern
recognition, computer graphics, multimedia systems, and medical informatics.
He has published over 100 papers in journals and conference proceedings in
Dr. Mukherjee received the Young Scientist Award from the Indian National
Science Academy in 1992.
1794 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 17, NO. 10, OCTOBER 2008
Sanjit K. Mitra (S’59–M’63–F’74–LF’00) received
his M.S. and Ph.D. degrees in electrical engineering
from the University of California, Berkeley, in 1960
and 1962, respectively.
He is presently with the Ming Hsieh Department
of Electrical Engineering, University of Southern
California, Los Angeles, as the Stephen and Etta
Varra Professor. He has published over 700 papers
in the areas of analog and digital signal processing,
and image processing. He has also authored and
co-authored twelve books, and holds ﬁve patents.
Dr. Mitra is the recipient of the 1973 F. E. Terman Award and the 1985 ATT
Foundation Award of the American Society of Engineering Education, the 1989
Education Award, and the 2000 Mac Van Valkenburg Society Award of the IEEE
Circuits AND Systems Society, the Distinguished Senior U.S. Scientist Award
from the Alexander von Humboldt Foundation of Germany in 1989, the 1996
Technical Achievement Award and the 2001 Society Award of the IEEE Signal
Processing Society, the IEEE Millennium Medal in 2000, the McGraw-Hill/
Jacob Millman Award of the IEEE Education Society in 2001, the 2002 Tech-
nical Achievement Award of the European Association for Signal Processing
(EURASIP) and the 2005 SPIE Technology Achievement Award of the Interna-
tional Soceity for Optical Engineers, the University Medal of the Slovak Tech-
nical University, Bratislava, Slovakia, in 2005, and the 2006 IEEE J. H. Mul-
ligan, Jr. Education Medal. He is the co-recipient of the 2000 Blumlein-Browne-
Willans Premium of the the Institution of Electrical Engineers (London) and the
2001 IEEE Transactions on Circuits AND Systems for Video Technology Best
Paper Award. He has received Honorary Doctorate degrees from the Tampere
University of Technology, Finland, the Technical University of Bucharest, Ro-
mania, and the Technical University of Iasi, Romania. He is a member of the
U.S. National Academy of Engineering, the Norwegian Academy of Technolog-
ical Sciences, an Academician of the Academy of Finland, and a corresponding
member of the Croatian Academy of Sciences and Arts, and the Academy of
Engineering, Mexico. He is a Foreign Fellow of the Indian National Academy
of Engineering and the National Academy of Sciences, India. He is a Fellow of
the AAAS and SPIE.