International Journal of Scientific & Engineering Research, Volume 4, Issue 9, September-2013 1510

ISSN 2229-5518

Automatic Enhancement of Low Contrast

Images using SMRT

Jaya V L, R Gopikakumari

Abstract— Contrast enhancement has an important role in Image processing applications as it extracts useful information from an image. Enhancement of low contrast images is usually done in the spatial domain as a preprocessing step, followed by image processing methods in the transform domain. This paper proposes a simple, yet powerful image enhancement technique in transform domain for addressing low contrast and brightness problems in gray-scale and color images. It uses SMRT to automatically change the statistical parameters such as mean & standard deviation by controlling brightness and contrast.

Index Terms— Image Enhancement, Sequency based Mapped Real Transform(SMRT), Brightness, Contrast, Scaling factor, SDME, Histogram Equalization.

1 INTRODUCTION

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MAGE enhancement is usually a preprocessing step in many image processing applications. Its aim is to accentuate relevant image features that are difficult to visualize under normal viewing conditions and thereby facilitating more accu- rate image analysis [1]. Various reasons for poor image quality may be due to poor illumination, lack of dynamic range in image sensor or wrong settings of lens aperture at the time of image acquisition. Sometimes, radiographic image details are
lost due to machine limitations or noise artifacts.
Visual appearance of an image can be significantly im-
proved by brightness variation and contrast stretching.
Brightness of an image can be varied by changing its mean
without changing histogram. Contrast can be determined from
its dynamic range, defined as the difference between highest
and lowest intensity level present in the image. Contrast en-
hancement stretches the histogram to perceive more details,
normally not visible. Hence histogram stretching can be used
to enhance low contrast images.
Many techniques for increasing contrast have been pro-
posed in the past and these can be classified into two catego-
ries: spatial domain methods and transform domain methods.
Spatial domain techniques perform direct manipulation of
pixels in an image and can be carried out on the whole image
or on a local region selected on the basis of image statistics.
Such techniques include histogram processing, image averag-
ing, sharpening edges or contours and nonlinear filtering [2],
[3], [4], [5].
In transform domain techniques, transform such as DFT,
DCT, DWT of the image is computed first. The transform coef-
ficients are then manipulated appropriately and inverse trans-
form is found to obtain the enhanced image [6], [7], [8], [9].

————————————————

• Jaya V L is currently pursuing Ph.D in Division of Electronics Engi- neerig, School of Engineering,CUSAT, Cochin, Kerala, India PH-+91

9745108648. E-mail: vl_jaya@yahoo.com

• R Gopikakumari is currently Professor in Division of Electronics Engi-

neerig, School of Engineering,CUSAT, Cochin, Kerala, India PH-+91

9446129193. E-mail: gopika@cusat.ac.in
Most common and simple image enhancement technique is contrast stretching and can be achieved by processing its his- togram. It is usually done in the spatial domain by way of his- togram stretching, equalization or matching. Histogram equal- ization employs a monotonic, non-linear mapping that re- assigns the intensity values of pixels in the input image and produces an image with uniform histogram. Histogram stretching spreads the histogram to a larger range by applying a piecewise linear function while histogram matching produc- es an image with pre specified histogram.
Instead of processing the histogram directly, statistical pa- rameters such as mean and Standard Deviation (SD) can be used for modifying the image. Mean is a measure of average gray level intensity of the image and SD is a measure of the histogram stretch.
Most of the image enhancement techniques are performed in the spatial-domain. But for efficient storage and transmis- sion, images are being represented in the compressed format [10], [11] using transform domain. If all the image processing tasks are performed in the same transform domain, the pro- cessing will be computationally efficient. Hence, it is im- portant to develop image enhancement techniques in the transform domain.
This paper proposes a way to improve the contrast and
brightness of an image using transform domain techniques.
Statistical parameters such as mean and SD can be varied by
modifying SMRT coefficients to improve the brightness and
contrast. Hence a method is proposed, which automatically
adjusts the image brightness and contrast to optimum levels
by modifying the SMRT coefficients appropriately by utilizing
full dynamic range of the histogram. A comparison between
the proposed method and Histogram Equalization is also per-
formed.

2 SMRT

MRT coefficients, 𝑌(𝑝) of an image 𝑥 , 0 ≤ 𝑛 , 𝑛 ≤ 𝑁 − 1 is

1 2

expressed [12] as

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(𝑝) = � 𝑥

− � 𝑥

𝑌𝑘1 𝑘2

∀(𝑛1 ,𝑛2 )|𝑧=𝑝

𝑛1 ,𝑛2

∀(𝑛1 ,𝑛2 )|𝑧=𝑝+𝑀

𝑛1 ,𝑛2

Experimental studies show that the contrast and SD of an image can be changed by scaling ac SMRT coefficients while preserving the image mean. The histogram gets stretched or
for 0 ≤ 𝑘1 , 𝑘2 ≤ 𝑁 − 1, 0 ≤ 𝑝 ≤ 𝑀 − 1 & 𝑀 = 𝑁/2. (1)
where 𝑧 = ((𝑛1 𝑘1 + 𝑛2 𝑘2 ))𝑁
2-D MRT maps an 𝑁 × 𝑁 matrix into M matrices of the
same size. Thus MRT in the raw form will have 𝑁3 /2 coeffi-
cients and is highly redundant. Unique MRT (UMRT) [13], [14]
is developed to remove redundant elements present in MRT
representation and arranges the N2 unique coefficients in an
𝑁 × 𝑁 matrix. Using SMRT [15], the 𝑁2 unique MRT coeffi-
cients are arranged in the order of sequency along horizontal,
vertical and diagonal directions and are represented by matrix
S.
compressed when the scaling factor cac is greater or less than one and thereby modifying the image contrast. Fig.2 shows changes in contrast of the image and the corresponding histo- grams for different values of cac .

The first coefficient, S(0,0), of the SMRT matrix is found in
terms of the input image as sum of all image pixel values and
is called dc coefficient. This value gives an indication of the
image mean and holds most of the image energy. The remain-
ing (𝑁2-1) coefficients represent the intensity values of the
image pixels in various patterns and can be termed as ac coef-
ficients.

3 SMRT BASED IMAGE ENHANCEMENT

In this method, dc as well as ac SMRT coefficients of the image are scaled using scaling factors cdc and cac respectively. Exper- imental studies show that if cdc >1 the histogram shifts forward and if it is less than one, the histogram shifts backward with- out changing its shape. Hence, the brightness of the image can be increased as shown in Fig. 1 by scaling, S(0,0) without any change in contrast.

Fig.2. Images and their histograms (a)&(b) Original (c)&(d) ac SMRT coefficients scaled with cac=2 (e)&(f) ac SMRT coefficients scaled with cac=3

The brightness and contrast adjusted SMRT matrix can be expressed as
𝑆̃(𝑖, 𝑗) = � 𝑐𝑑𝑐 𝑆(𝑖, 𝑗), 𝑖𝑖 𝑖 = 𝑗 = 𝑜
𝑐𝑎𝑐 𝑆(𝑖, 𝑗), 𝑜𝑜ℎ𝑒𝑒𝑒𝑖𝑒𝑒
When cac is made higher and higher, the histogram stretch-
es and extends to both ends. When this value is much higher,
the histogram gets split and departs to the two ends. Finally it
becomes a black and white image.
For maximum enhancement, the image mean or center of
the image histogram can first be brought to the center of the
range of the histogram (for n bit image representation, 2(n-1) is
the center of range of the histogram) by scaling S(0,0). Once
brightness is adjusted, contrast can be maximized by scaling
ac SMRT coefficients

Fig.1. Images and their histograms (a)&(b) Original (c)&(d) dc SMRT coefficient scaled with cdc=2 (e)&(f) dc SMRT coefficient scaled with cdc=3

3.1 Brightness Variations using dc SMRT Coefficient Scaling of dc SMRT coefficient can be done in two ways. In the first method, the scaling is done so as to bring the mean of the

image to the center of histogram range. In the second method,
center of image histogram is shifted to the center of histogram
range.

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3.1.1 Modification of image mean
Average value or mean, 𝜇 of an image can be found from dc
SMRT coefficient as

𝑆(0,0)

rl and rh . A scaling factor which stretches the histogram to its ends gives the maximum contrast. The shift in maximum pixel value, rhshift , for 0.1 increase in scaling factor is calculated. The ac scaling factor is determined as

𝜇 =
𝑁2
(3)

2𝑛−(𝑟ℎ+𝑟𝑠ℎ𝑖𝑓𝑡)

When cdc is changed regularly, regular changes in image mean
is observed without any change in SD. The lower(rl ) and up- per(rh ) values of the histogram also change in a linear manner. A plot of scaling factor versus mean, rl and rh values for lena
image is shown in Fig.3.
𝑐𝑎𝑐 =

10∗𝑟ℎ𝑠ℎ𝑖𝑓𝑡

+ 1 (8)

Fig.4. Plot of SD, rl and rh for changes in ac scaling factor

Fig.3. Plot of mean, rl and rh for changes in dc scaling factor

The scaling factor to bring the mean of the image histogram to 2(n-1) can be found from

𝑆̃(0,0)−𝑆(0,0)

3 EXTENSION TO COLOR IMAGES

Most of the electronic equipments acquire and display color images and hence enhancement of color images is also im- portant. Classical approaches generally apply equalization of the red, green, and blue planes in the RGB images. However, this approach has an inherent problem of changing the hue of
Thus,
𝑒𝑠ℎ𝑖𝑓𝑡 = 2(𝑛−1) − 𝜇 =

𝑟𝑠ℎ𝑖𝑓𝑡∗𝑁2

𝑁2

(4)
the output image. So image enhancement is performed in YCbCr color space and scaling is applied only to the lumi- nance (Y) component keeping Cb and Cr constant. Finally the image is converted back to RGB space. This method produces better perceptible results as compared to scaling the R, G, and
𝑐𝑑𝑐 =

𝑆(0,0)

+ 1 (5)
B planes separately.

3.1.2. Shift of image histogram center

The Centre of image histogram, rc can be found from rl and rh
values of the image as given below
𝑒𝑙 + 𝑒ℎ

4 QUANTITATIVE EVALUATION OF ENHANCED IMAGES

𝑒𝑐 =

(6)
2
Assessment of images after enhancement is often difficult.
The shift in histogram to shift the image histogram center to
2(n-1) is
𝑒𝑠ℎ𝑖𝑓𝑡 = 2(𝑛−1) − 𝑒𝑐 (7)
and cdc can be found from equation(5).
Several measures are available in the literature. An enhance-
ment measure using the concept of the second derivative is
proposed by Panetta et. al. in [16], [17]. It is called Second De-
rivative like Measure of Enhancement (SDME) and is defined
as
So by scaling S(0,0) alone, the image mean and hence

𝑘1

𝑘2

𝐼𝑙,𝑚 − 2𝐼𝑙,𝑚 + 𝐼𝑙,𝑚
brightness can be varied without changing SD.
1

𝑆𝑆𝑀𝑆 = −
� � 20 𝑙𝑛 � 𝑚𝑎𝑥

𝑐𝑒𝑛

𝑚𝑖𝑛

𝑙,𝑚 + 2𝐼𝑙,𝑚 + 𝐼𝑙,𝑚 �

(9)

3.2 Contrast Variations using ac SMRT Coefficient

𝑘1 𝑘2

𝑚=1 𝑙=1

𝐼𝑚𝑎𝑥

𝑐𝑒𝑛

𝑚𝑖𝑛

After fixing the image mean, histogram can be stretched suita-
bly by scaling ac SMRT coefficients. Fig.4 shows a linear rela-
where an image is divided into 𝑘1 × 𝑘2 blocks

𝑙,𝑚 , 𝐼𝑙,𝑚 and 𝐼𝑙,𝑚 refers to the maximum, minimum and cen-

tionship between the scaling factor cac and the parameters SD,
𝐼𝑚𝑎𝑥

𝑚𝑖𝑛

𝑐𝑒𝑛

tral pixel values in each block of the image. The block size

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should be an odd number. Higher the value of SDME, better is the enhancement.

6 RESULTS AND DISCUSSION

Histogram Equalization (HE) is one of the most common methods used for image enhancement. It may increase the contrast of background noise, while decreasing the usable sig- nal. This technique may produce images with over enhance- ment. It tends to introduce some annoying artifacts and un- natural enhancement.
In Fig.5, (a) shows a low contrast image, (c) its histogram equalized image and (e) enhanced image using the proposed method while (b), (d) & (f) show the respective histograms. Similarly, Fig.6 and Fig.7 show the enhancement for two other low contrast images. Analysis of the results shows that the proposed enhancement method works well for low contrast images. Generally for medical images, histogram stretches to both the ends and hence there is no scope for further en- hancement by contrast stretching. But there may be certain objects of interest that is hidden as a low contrast sub image. In such cases, this method can be used to enhance the image locally.

mammogram and a low contrast sub image are shown in Fig.8. Histogram equalized and the enhanced image using the proposed method is shown in Fig.9.

Fig.6. Images and their histograms (a)&(b) Original(lena image) (c)&(d) Enhanced using HE (e)&(f) Enhanced using proposed method( cdc=1.16 and cac=1.38)

Fig.5. Images and their histograms (a)&(b) Original(woman image) (c)&(d) Enhanced using HE (e)&(f) Enhanced using proposed method( cdc=2.66 and cac=4.15)

Sometimes mammograms are not well defined and detec- tion of micro calcifications is important in the early detection of breast cancer. Computer aided analysis of mammograms depends on regions of interest (ROI) that are normally low in contrast. A contrast stretching and brightness improvement may bring the ROI better for analysis and easy diagnosis. A

IJSER © 2

Fig.7. Images and their histograms (a)&(b) Original(lena image) (c)&(d) Enhanced using HE (e)&(f) Enhanced using proposed method( cdc=1.18 and cac=2.01)

http://www.ijs

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TABLE 1

COMPARISON OF SDME OF VARIOUS IMAGES FOR HE AND PRO- POSED METHOD

Images	SDME
Images	Original Image	HE	Proposed
Lena	23.57	57.49	99.91
Woman	27.32	47.96	144.74
Moon	14.60	53.32	161.81
Mammogram	92.91	61.88	223.26

brightness for monochrome and color images and this method can give good performance for low contrast images.

Fig.8. Mammogram image and low contrast subimage

Fig.10. Application to color images (a) original image (b) using RGB

space (c) using YCbCr

Fig.9. Mammogram images and their histograms (a)&(b) Original (c)&(d) Enhanced using HE (e)&(f) Enhanced using proposed method( cdc=0.60 and cac=8.34)

The improvement of the brightness, contrast and visual quality of images can be verified using SDME measure and the values obtained for the images under consideration are shown in Table.1. It shows that the proposed method is supe- rior to histogram equalization method.
Application of the above method to chrominance compo- nent of the YCbCr space and RGB components of the RGB space of color images are shown in Fig.10.
The enhanced images show that the proposed automatic contrast enhancement method gives better contrast and

6 CONCLUSION

An important aspect of image processing is the flexibility in developing a linear, automatic, simple, yet powerful en- hancement techniques based on statistical measures to have a close, predictable correspondence with image appearance. In this paper, a simple, automatic, brightness and contrast en- hancement method that uses transform based contrast stretch- ing is presented. By controlling dc SMRT coefficient, any low contrast image can be brightened or darkened. Dynamic range can be changed and thereby contrast can be improved by scal- ing ac SMRT coefficients. The performance of this method is compared with classical Histogram Equalization technique and quantitatively assessed using SDME. Experimental results show that the proposed method outperforms the HE quantita- tively and qualitatively.

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