IJCER (www.ijceronline.com) International Journal of computational Engineering research

International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5

A Modified SVD-DCT Method for Enhancement of Low Contrast Satellite
Images
G.Praveena1, M.Venkatasrinu2,
1
M.tech student, Department of Electronics and Communication Engineering, Madanapalle Institute of Technology and
Science (MITS), MADANAPALLE-517325,
2
Asst.professor, Department of Electronics and Communication Engineering, Madanapalle Institute of Technology and
Science (MITS),MADANAPALLE-517325

Abstract:
During the last decade, several techniques are proposed for contrast enhancement of a low-contrast satellite images. In this a
new technique has been proposed based on the Singular Value Decomposition (SVD) and Discrete Cosine Transform (DCT).
The proposed technique modified SVD-DCT converts the image into the SVD-DCT domain after normalizing the singular
value matrix. Then the modified image is reconstructed by using inverse DCT. In the enhancement procedure Adaptive
Histogram Equalization (AHE) has been used.. The perceptual and quantitative results of the proposed modified SVD-DCT
method clearly indicates increased efficiency and flexibility over the exiting methods such as Linear Contrast Stretching
technique, GHE technique, DWT-SVD technique, DWT technique, De-correlation Stretching technique, Gamma Correction
method based techniques.

Keywords: Adaptive Histogram Equalization (AHE), Contrast enhancement, Discrete Cosine Transform (DCT) and Singular
Value Decomposition (SVD).

1. Introduction
Satellite images are used in many applications such as geosciences studies, astronomy and geographical information
systems. One of the problem occurs in satellite images while capturing image with a huge amount of distance, is the dark light
and contrast of image.
Suppose, if an image has been taken in very dark or a very bright situation, the information may be lost in those areas
which are excessively and uniformly dark or bright. Satellite images are low contrast and dark images, which has complete
information but is not visible. The problem is how the contrast of an image can be improved from the input satellite images.
Image contrast enhancement is one of the most important issues in low-level image processing. Its purpose is to
improve the quality of low contrast images. There have been several techniques to overcome this issue for the contrast analysis
of satellite image such as General Histogram Equalization (GHE), Gamma correction and Linear contrast stretching. These
techniques are very simple and effective for the contrast enhancement. But these techniques are not efficient as the information
laid on the histogram of the image, which is totally lost.
The proposed technique based on the singular value decomposition (SVD) and discrete cosine transform (DCT) has
been proposed for enhancement of low-contrast satellite images. In the enhancement procedure Adaptive Histogram
Equalization (AHE) has been used.
The enhancement mapping cannot improve image contrast satisfactorily since the contrast of an object is interfered
by the whole image. Naturally, it is difficult to find enhance the whole image. AHE stretches the local contrast to improve the
visibility of satellite images, while preserving information as it is. For this purpose, we are using Adaptive Histogram
Equalization (AHE). Here unlike General Histogram Equalization (GHE), AHE operates on small data regions rather than the
entire image. It is therefore suitable for improving the local contrast of an image and bringing out more detail [1]. The result
shows that visibility improvement of specific objects is successfully enhanced using SVD-DCT method by incorporating
AHE.
2. Proposed Methodology
Satellite images are low contrast and dark images, which has complete information but is not visible. The problem is
how the contrast of an image can be improved from the input satellite images.
For this reason, we propose a new contrast enhancement. Basically two parts involve in the enhancement of the satellite
images. The first one is Singular Value Decomposition (SVD) and second one is Discrete Cosine Transform (DCT). The
result shows that visibility improvement of specific objects is successfully enhanced using SVD-DCT method by
incorporating AHE.

Issn 2250-3005(online) September| 2012 Page 1615


2.1 Adaptive Histogram Equalization:
Adaptive histogram equalization (AHE) is a computer image processing technique used to improve contrast in
images. It differs from ordinary histogram equalization in the respect that the adaptive method computes several histograms,
each corresponding to a distinct section of the image, and uses them to redistribute the lightness values of the image. It is
therefore suitable for improving the local contrast of an image and bringing out more detail.
Ordinary histogram equalization uses the same transformation derived from the image histogram to transform all
pixels. This works well when the distribution of pixel values is similar throughout the image. However, when the image
contains regions that are significantly lighter or darker than most of the image, the contrast in those regions will not be
sufficiently enhanced.
Adaptive histogram equalization (AHE) improves on this by transforming each pixel with a transformation function
derived from a neighborhood region.
Adaptive histogram equalization is an extension to traditional Histogram Equalization technique. It enhances the
contrast of images by transforming the values in the intensity image using contrast-limited adaptive histogram equalization
(CLAHE).Unlike Histogram equalization, it operates on small data regions (tiles), rather than the entire image. Each tile's
contrast is enhanced, so that the histogram of the output region approximately matches the specified histogram. The
neighboring tiles are then combined using bilinear interpolation in order to eliminate artificially induced boundaries. The
contrast, especially in homogeneous areas, can be limited in order to avoid amplifying the noise which might be present in the
image.
Adaptive histogram equalization of an original image and its histogram as shown in below figure 2.1
1200

1000

800

600

400

200

0

0 50 100 150 200 250

2.1.1: original 2.1.2: histogram
3000

2000

1000

0
0 50 100 150 200 250

2.1.3: Adaptive equalized image 2.1.4: histogram equalization

Fig 2.1: Adaptive equalized image and its histogram

2.2 singular Value Decomposition (SVD)
SVD is based on a theorem from linear algebra which says that a rectangular matrix A, which is a product of three
matrices that is (i) an orthogonal matrix UA, (ii) a diagonal matrix ΣA and (iii) the transpose of an orthogonal matrix VA. The
singular-value-based image equalization (SVE) technique is based on equalizing the singular value matrix obtained by singular
value decomposition (SVD). SVD of an image, can be interpreted as a matrix, is written as follows:
…………………………………….. (1)

Where UA and VA are orthogonal square matrices and ΣA matrix contains singular values on its main diagonal [1].
Basic enhancement occurs due to scaling of singular values of the DCT coefficients. The singular value matrix
represents the intensity information of input image and any change on the singular values change the intensity of the input
image.
The main advantage of using SVD for image equalization, ΣA contains the intensity information of the image.
In the case of singular value decomposition the ratio of the highest singular value of the generated normalized matrix,
with mean zero and variance of one, over a particular image can be calculated using the equation as:
………………… (2)

By using this coefficient to regenerate an equalized image using:
………………….. (3)



Where E equalized A is used to denote the equalized image. The equalization of an image is used to remove the
problem of the illumination.
2.3 Discrete Cosine Transform (DCT)
The DCT transforms or converts a signal from spatial domain into a frequency domain. DCT is real-valued and
provides a better approximation of a signal with few coefficients. This approach reduces the size of the normal equations by
discarding higher frequency DCT coefficients.
Important structural information is present in the low frequency DCT coefficients. Hence, separating the high-frequency
DCT coefficient and applying the illumination enhancement in the low–frequency DCT coefficient, it will collect and cover
the edge information from satellite images. The enhanced image is reconstructed by using inverse DCT and it will be sharper
with good contrast [1].
In the proposed technique, initially the input satellite image „A‟ for processed by AHE to generate . After getting this,
both of these images are transformed by DCT into the lower frequency DCT coefficient and higher–frequency DCT
coefficient. Then, the correction coefficient for the singular value matrix can be calculated by using:

………………………… (4)

Where is the lower-frequency coefficient singular matrix of the satellite input image, and is the
lower-frequency coefficient singular matrix of the satellite output image of the Adaptive Histogram Equalization (AHE).
The new satellite image (D) is determined by:
= …………………………. (5)
………………………. (6)
is the lower DCT frequency component of the original image that is reconstructed by applying the inverse operation
(IDCT) to produce equalized image is
………………………… (7)
The performance of this method is measured in terms of following significant parameters:

…………. (8)

…………(9)
Mean (μ) is the average of all intensity value. It denotes average brightness of the image, where as standard deviation is the
deviation of the intensity values about mean. It denotes average contrast of the image. Here I(x, y) is the intensity value of the
pixel (x, y), and (M, N) are the dimension of the Image.

2.4. Flow Chart:
The following flowchart shows the proposed scheme:

Fig 2.2 Flow chart of the proposed methodology



3. Results
The performance of this method is measured in terms of following significant parameters:

…………. (8)

………… (9)
Mean (μ) is the average of all intensity value. It denotes average brightness of the image, where as standard deviation is
the deviation of the intensity values about mean. It denotes average contrast of the image. Here I(x, y) is the intensity value of
the pixel (x, y), and (M, N) are the dimension of the Image [3].
The results for the enhancement of satellite images are given. The proposed method is compared with other existing
methods such as Linear Contrast Stretching technique, GHE technique, DWT-SVD technique, DWT technique, De-correlation
Stretching technique, and Gamma Correction method shown in figure3.1. The visual and quantitative result shows that the
proposed method has increased efficiency and flexibility.
The resultant images for the enhancement of satellite images are given below fig 3.1, the following resultant images
of DCT-SVD gives the better contrast as well as high image quality. The images are:
Input image Equalized Satellite Image of LCS Histogram Equalized image Equalized Satellite Image of dwt-svd Equalized stellite image of dct-svd

5000
3000 3000
1000
4000 1000

3000 2000 2000

2000 500 500
1000 1000
1000

0 0 0 0 0
0 100 200 0 100 200 0 100 200 0 0.5 1 0 0.5 1

Equalized Satellite Image of dwt Equalized Satellite Image of decorrstretch Equalized Satellite Image of GammaEqualized Satellite Image of LL freq using dwt Equalized Satellite Image of DCT

Fig 3.1: Various resultant images using existing techniques and proposed technique

The quality of the visual results indicates that the proposed technique is sharper and brighter than existing technique
as compared. After obtaining mean and standard deviation, it is found that the proposed algorithm gives better results in
comparison with the existing techniques. Mean (μ) represent the intensity of the image and the standard deviation represent (σ)
the contrast present in the images. The proposed DCT method represents the better contrast as well as better brightness with
appropriate contrast. However, the estimated mean (μ) and standard deviation (σ) in Fig 3.1 of the proposed method covers a
good range of gray level and this is the cause of the better illumination. Therefore the observation of the proposed DCT gives
the better result. In order to exhibit the superiority of the proposed methodology three different images have been taken for
analysis. The singular values denote luminance of each image layer after decomposition using DCT methodology.
The Mean (μ) & standard deviation ( ) values are given below for analysis of this result. Here we can observe that
the proposed method DCT-SVD gives better contrast as well as better brightness.

Table1: Comparison of the results between different proposed methodology and already existing techniques.



4. Conclusion
In this paper, a new technique has been proposed based on the Singular Value Decomposition (SVD) and Discrete
Cosine Transform (DCT) that means SVD-DCT domain for enhancement of low-contrast satellite images. The basic
enhancement occurs due to scaling of singular values of the DCT coefficients. Performance of this technique has been
compared with existing contrast enhancement techniques like histogram equalization, gamma correction and DWT-SVD based
techniques.
From the above experimental results, it can be concluded that the proposed algorithm is effective in naturally
enhancing low contrast images and the visibility improvement of specific objects compared to other existing methods. The
results show that the proposed technique gives better performance in terms of contrast (variance) as well as brightness (mean)
of the enhanced image as compared to the other existing techniques. Thus, this technique can be considered suitable for
enhancement of low contrast satellite image.

5. Future Scope
Image enhancement of low contrast satellite images using discrete cosine transform and singular value decomposition
can be implemented by using Adaptive histogram equalization is extended to color images. In case of grayscale images, DCT-
SVD can be replaced by contrast stretching method and de-correlation stretch methods.

References
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