International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 38
ISSN 2229-5518
Novel Weighted Mean Separated Histogram Equalization for Contrast Enhancement of Underwater Images
Dr. S. A. Hariprasad, Arunlal. K. S, Vikhar Ahmed
Abstract— Underwater acoustic is growing interest because of its applications in scientific research and technology. Its applications such as mine detection, marine biology and military operations requires a high quality of images. In underwater environment, quality of image is degraded by scattering of light and absorption of light which results in low contrast, poor visibility, blurring of image. Histogram equalization (HE) is the conventional method of enhancing the contrast of an image, but HE creates unwanted visual artifacts, which lead to over enhancement of image, loss of image details and loss of natural look of image. Recursively Mean Separated Histogram Equalization (RMSHE) is one of the modifications to HE to overcome from the limitations of HE. This method will reduce the visual artifacts and enhance the contrast of image but still there is a loss of image details. In this paper a modified RMSHE referred as Weighted Mean Separated Histogram Equalization (W MSHE) is presented which will enhance the contrast of image along with reduction of visual artifacts. The method preserves image details and brightness. In this method Histogram is divided into four sub-Histograms based on weighted mean value and then apply clipping limit to each sub-Histogram followed by equalization of each sub-Histogram. Performance of the algorithm is measured in terms of Absolute Mean Brightness Error (AMBE), Entropy of image and difference in Standard Deviation (SD). It is found that with proposed method AMBE is improved by 52.57%, SD is improved by 39.64% as compared to RMSHE, and Entropy of image with proposed method is 6.6221 whereas Entropy with RMSHE is 6.4746.
Index Terms— Brightness Preservation, Clipped Histogram Equalization Contrast Enhancement, Entropy, Histogram Equalization, Image Detail Preservation, Pixel.
Underwater acoustic is having a greater focus because of its applications in scientific research and technology. Applications, such as mine detection like resources available for the extraction of gold, copper, silver, zinc, cobalt and manganese, underwater power and telecommunication cables, pipelines, marine biology like fishes, invertebrates, reptiles, sea grasses and fungi, and submarines for civil and military purpose. These applications require high quality of underwater images. Underwater images are essentially characterized by their poor visibility because light is exponentially attenuated as it travels in the water, and the scenes result poorly contrasted and hazy. Light attenuation limits the visibility distance at about twenty meters in clear water and five meters or less in turbid water.
The light attenuation process is caused by absorption and scattering, which influence the overall performance of underwater imaging systems. Forward scattering generally leads to blur of the image features. Absorption and scattering
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effects are not only due to the water itself but also due to the components such as a dissolved organic matter. The visibility range can be increased with artificial illumination of light on the object, but it produces non-uniform of light on the surface of the object and producing a bright spot in the center of the image with poorly illuminated area surrounding it. The amount of light is reduced when we go deeper, colors drop off depending on their wavelengths. The blue color travels across the longest in the water due to its shortest wavelength. Underwater image suffers from limited range visibility, low contrast, non-uniform lighting, blurring, and bright artifacts. A lot of work have been done to overcome from the problem of underwater images.
The conventional method for enhancing the contrast of an image is Histogram Equalization. This method will redistribute gray levels of entire histogram of an image and make brighter part more brighter and darker part darker. This method creates unwanted visual artifacts and significantly change the brightness of image, which lead to over enhancement of image, loss of image details and loss of natural look of image. Many researchers have tried to overcome from the limitations of conventional HE. Yu Wang, et al[1] have proposed ‘Image Enhancement Based on Equal Area Dualistic Sub-Image Histogram Equalization Method(DSIHE)’ in which histogram of an image is divide into two parts based on image median value followed by Histogram equalization of each part and it reduces the visual artifacts to some extent. Yeong Teag Kim [2] has proposed
‘Contrast Enhancement Using Brightness Preserving Bi- Histogram Equalization (BPBHE)’ in which histogram is
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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 39
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divided into two parts based on mean value of image followed by Histogram equalization of both parts, in this case more artifacts are reduced as compared to previous method. Soong- Der Chen, et al[3] have proposed ‘Minimum Mean Brightness Error Bi-Histogram Equalization in Contrast Enhancement (MMBEBHE)’ in which histogram is divided into two parts based on some threshold value followed by equalization of both parts and tried to reduce the difference between mean brightness of input image and enhanced image which results in brightness preservation. Chao Wang, et al[4] have proposed
‘Brightness Preserving Histogram Equalization with Maximum Entropy (BPHEME): A Variational Perspective’ in which each gray level is weighted with some threshold value followed by histogram equalization, in this process brightness and entropy of an image is preserved. M. Abdullah-Al- Wadud[5], et al have proposed ‘A Dynamic Histogram Equalization for Image Contrast Enhancement’ in which the
image histogram is partitioned based on local minima and
This paper is organized as. Section 2 will briefly explain Histogram Equalization and Recursively mean Separated Histogram Equalization, Section 3 will present the Proposed Method of Weighted Mean Separated Histogram Equalization. 4 Explains Image Enhancement parameters used in this work 5 The Results will be shown and Section 6 is our Conclusion and Future Work.
Consider an image X with gray levels ‘k’ varies from k = 0, 1,
2, 3, ------------------L-1, ‘L’ is total number of gray levels
Let f(k) be frequency of occurrence of gray level ‘k’.
Probability of occurrence of gray levels in an image is known
as Probability Density Function (PDF) which is given by ‘p(k)’
of gray level ‘k’ is
assigns specific gray level ranges for each partition before equalizing them separately. These partitions further go through a repartitioning test to ensure the absence of any
𝑓(𝑘)
𝑝(𝑘) =
𝑁
𝑘 = 0, 1, 2, − − −𝐿 − 1 (1)
dominating portions. This method enhance the contrast well without introducing severe visual artifacts. Mary Kim et, al[8]
Cumulative Density Function (CDF) of gray level ‘k’ is given
by
have proposed ‘Recursively Separated and Weighted
Histogram Equalization for Brightness Preservation and
𝐿−1
𝐶𝐷𝐹(𝑘) = � 𝑝(𝑘)
(2)
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Contrast Enhancement’ in which histogram is separated based
on either mean value of image or median value of image followed by applying weighted threshold to each sub- Histogram followed by equalization of each sub-Histogram. This method will enhance the contrast with reduction of artifacts. . K.S. Sim et al [9] have proposed ‘Recursive sub- image histogram equalization applied to gray scale images (RSIHE)’ in which the histogram is divided recursively into four parts based on mean and median values on image followed by histogram equalization on each sub-histogram, this method will reduce the visual artifacts to greater extent but still some of the image details will be lost. Chen HeeOoi, et al[12] have presented ‘Bi-Histogram Equalization with a Plateau Limit for Digital Image Enhancement’ in which histogram is first divided into two sub-Histograms followed by applying plateau limits or threshold limits, which can be computed by average frequency of occurrence of gray levels in each of the sub-Histograms, after that histogram equalization is applied to each sub-Histogram, this method will reduces the artifacts to greater extent preserves entropy and enhance contrast of image. Haidi Ibrahim, et al[13] have proposed
‘Image Enhancement with Noise Suppression Ability using Histogram Manipulations’ in which histogram is inverted first followed by histogram equalization to reduce visual artifacts and to enhance contrast. Pei-Chen Wu et al[18] have proposed
‘A Weighting Mean-Separated Sub-Histogram Equalization for Contrast Enhancement’ in which histogram is divided into six parts based on weighted mean value followed by equalization of each part, this method will greatly preserves the brightness of image by reducing visual artifacts and enhance the contrast of image.
𝑘=0
Now using CDF, Transfer Function is computed which maps
input image into output image for entire range of gray levels. Transfer Function is given by
𝐹(𝑘) = (𝐿 − 1) ∗ 𝐶𝐷𝐹(𝑘) + 𝑙𝑜𝑤𝑒𝑟 𝑔𝑟𝑎𝑦 𝑙𝑒𝑣𝑒𝑙 (3)
Now output image Y (i, j) can be obtained by using above
transfer function as
𝑌(𝑖, 𝑗) = 𝐹�𝑋(𝑖, 𝑗)� (4)
Histogram Equalization will enhance the contrast of an image
but it increases the contrast of higher gray level regions and compresses the contrast in lower gray level regions, when the object of interest in an image only occupies a small portion of the image, this object will not be successfully enhanced by histogram equalization. Limitations of conventional Histogram Equalization are:
a) Creation of visual artifacts
b) Significant change in brightness of output image. c) Over enhancement
d) Unnatural look of image e) Washed out appearance
This is another approach of enhancing the contrast of an image with Brightness preservation [8], in which Histogram is divided into several segments and each of the segments is
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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 40
ISSN 2229-5518
equalized separately using Histogram equalization technique. Division of Histogram into several parts will reduce the unwanted artifacts (overshooting and undershooting of pixel values) to a greater extent. In this method histogram is
p(k)be Probability Density Function of gray level ‘k’.
N = Total Number of Pixels.
Mean value of image is compute as:
𝐿−1
divided into four segments based on mean values. Fig 2.1
shows division of histogram into four sub-Histograms.
∑ 𝑘∗𝑝(𝑘)
∑𝐿−1 𝑝(𝑘)
(7)
Fig 2.1: Dividing Histogram of image into four sub-Histograms
In Fig 2.1 shows the entire range X= {0, 1, 2, 3, ……….. L-
Histogram of image is now divided into two sub-Histograms
XLand XU.
XLwill have gray levels {𝐾0 , 𝐾1 , 𝐾2 , … … … . . 𝐾𝑚 }
𝑋𝑈 will have gray levels {𝐾𝑚+1 , 𝐾𝑚+2 , 𝐾𝑚+3 , … … … . . 𝐿 − 1}
Further mean values of XLand XU are computed in the same
way and XL and XU are divided. After that each sub-Histogram
is clipped by a threshold limit. The histogram in these ranges
will be clipped in order to avoid intensity saturation in the output image. Frequency of occurrence of gray in four sub-
Histograms are denoted by ℎ𝑎 ,ℎ𝑏 , ℎ𝑐 and ℎ𝑑 .
Threshold limits can be computed as follows
1} of the Histogram is divided into four parts. Mean value Xm
𝑇 = 1
∑𝑋𝑚𝑙 ℎ (𝑘)
can be calculated by using the Relation:
∑𝐿−1 𝑥∗𝑃𝐷𝐹(𝑥)
1
𝑇2 =
𝑋𝑚𝑙 +1
1
𝑘=0
𝑎
∑𝑋𝑚 ℎ (𝑘)
(8)
(9)
𝑋𝑚 =
𝑥=0
(5)
𝑋𝑚−1−𝑋𝑚𝑙
𝑘=𝑋𝑚𝑙 +1
∑𝐿−1 𝑃𝐷𝐹(𝑥)
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Where ‘x’ is gray level and PDF(x) is probability of
occurrence of gray level ‘x’. and Xm is mean value. Now using
Xm divide Histogram into two parts, again considering two
𝑇3 =
1
𝑋𝑚𝑢 −1−𝑋𝑚
1
∑𝑋𝑚𝑢
𝑘=𝑋𝑚
𝐿−1
+1 ℎ𝑐 (𝑘)
(10)
sub-Histograms as separate Histogram find their mean values and divide two sub-Histograms into four sub-Histograms.
𝑇4 = 𝐿−1−𝑋
∑𝑘=𝑋𝑚𝑢+1 ℎ𝑑 (𝑘)
(11)
Histogram Equalization is carried out separately on each of
the sub-Histograms. In this entire process contrast of an image is enhanced and unwanted artifacts will be suppressed, hence brightness is preserved.
Frequency of occurrence of gray levels in each sub-Histogram
is clipped by threshold limits. Fig 3.1 shows applying
threshold limits
𝑇1 𝑖𝑓 ℎ𝑎 (𝑘) ≥ 𝑇1
ℎ (𝑘) = �
ℎ𝑎 (𝑘) 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
( 12)
In this proposed method Histogram Specification is
𝑇 𝑖𝑓 ℎ (𝑘) ≥ 𝑇
carried out. In which an image Histogram is specified so as to
get a desired enhanced image. Process involves dividing Histogram into four sub-Histograms based on weighted mean values, computing threshold limits by taking average of frequency of gray levels in each sub-Histogram followed by applying threshold limits to each sub-Histogram and carrying out Histogram equalization on each part separately. In this process visual artifacts are reduced, contrast enhancement is
ℎ2 (𝑘) = � 2 𝑏 2
ℎ𝑏 (𝑘) 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
ℎ (𝑘) = � 𝑇3 𝑖𝑓 ℎ𝑐 (𝑘) ≥ 𝑇3
3 ℎ𝑐 (𝑘) 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
ℎ (𝑘) = � 𝑇4 𝑖𝑓 ℎ𝑑 (𝑘) ≥ 𝑇4
4 ℎ𝑑 (𝑘) 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
(13)
(14)
(15)
controlled and image details are preserved which results in an output image rich in details having good quality and natural look.
Let X = {K0 , K1 , K2, K3 , … … … … … L − 1} be gray levels of test
image and h(k) is frequency of occurrence of gray level k.
After applying threshold limits to each sub-Histogram,
conventional Histogram Equalization is carried out on each sub-Histogram separately. Output enhanced image Y (i , j) can be obtained from input image K(i , j) as:
𝑌(𝑖, 𝑗) = 𝐹�𝐾(𝑖, 𝑗)� (16)
𝑃𝐷𝐹(𝑘) = ℎ(𝑘)
𝑁
(6)
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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 41
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Fig 3.1: Dividing Histogram into 4 parts and applying clip limit to each sub- histogram
This is defined as difference in mean brightness of input image and mean brightness output image. When image is over enhanced, unwanted artifact will be created, brightness of the output image changes drastically and image will lose its natural appearance. That is lesser the value of AMBE better the equality of image.
Let Ex be mean brightness of input image and Ey be mean brightness of output image. AMBE can be given by
equation as in [18]
𝑆𝐷 = √𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒
𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 𝐸𝑛ℎ𝑎𝑛𝑐𝑒𝑚𝑒𝑛𝑡 = 𝑆𝐷𝑜𝑢𝑡𝑝𝑢𝑡 − 𝑆𝐷𝑖𝑛𝑝𝑢𝑡 (19)
E is mean brightness of image. p(x) is PDF.
(a) (b)
(c) (d)
Fig 5.1 (a) Original image (b) Output of HE (c) Output of RSMHE (d) Output of Proposed Method
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𝐴𝑀𝐵𝐸 = |𝐸𝑋 − 𝐸𝑌 | (17)
𝐸𝑥 = ∑𝐿−1 𝑥 ∗ 𝑝(𝑥)
𝐸𝑦 = ∑𝐿−1 𝑦 ∗ 𝑝(𝑦)
Where p(x) and p(y) are Probability Density Function of Input
and output image gray levels respectively.
This is defined as measure of richness of details present in an image. When contrast of an image is enhanced, details of an image may be lost. So entropy of an image should be same after enhancement or difference between Entropy of an image before enhancement and after enhancement should be very less. Entropy is given by
𝐿 −1
(Above image is taken from the website:
www.photostockplus.com)
TABLE 5.1 COMPARISION OF DIFFERENT PARAMETERS ON HE , RMSHE AND PROPOSED METHOD
AMBE | Entropy | Difference in SD | |
HE | 35.90 | 6.4606 | 45.25 |
RMSHE | 2.0346 | 6.4746 | 21.92 |
Proposed | 0.965 | 6.6221 | 13.23 |
From table 5.1 it can be noticed that an image of Entropy 6.6360 is taken and HE will perform equalization on entire histogram and creats visual artifacts which results in over enhancement and resultant image will have a unnatural appearance. RMSHE has reduced the visual artifacts to
𝐸𝑛𝑡𝑟𝑜𝑝𝑦 = � 𝑝(𝑘) ∗ 𝑙𝑜𝑔2 𝑝(𝑘)
𝑘=0
(18)
maximum extent and results in less difference between brightness of input image and processed image , hence output image of RMSHE has natural appearance. Proposed mathod
Where p(k) is Probability Density Function of gray level ‘k.
Standard Deviation gives the contrast of image. Difference in Standard Deviation between input image and output image measures the contrast enhancement of an image. If an image is over enhanced the difference will be high. So for desired enhancement difference should be less. Variance, SD and contrast enhancement is given by.
𝐿−1
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = �(𝑥 − 𝐸)2 ∗ 𝑝(𝑥)
𝑥=0
has successfully reduced the artifacts and has preserved the details of image hence output image of proposed method is having natural look and rich in details.
Contrast of underwater images vary due to scattering, attenuation and absorption of light. In this work an underwater image of Entropy 6.6360 is taken and conventional Histogram Equalization and different modified Histogram
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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 42
ISSN 2229-5518
Equalization algorithms are implemented and their results are compared.
• Conventional Histogram Equalization results high value of AMBE of 35.90, high difference in SD of
45.25and reduced entropy of 6.4606 due to, creation of visual artifacts and loss of image details leading to over enhancement, which results in unnatural appearance of output image.
• RMSHE Successfully reduced the visual artifacts but still there is a loss in details of output image. AMBE is improved to 2.0346 and difference in SD is improved to
21.92, Entropy improved to 6.4746.
• Proposed method is Modified RMSHE which will successfully reduce AMBE value to 0.965 by reducing visual artifacts to greater extent and also reduce the difference in SD to 13.23, along with this it preserves the image details hence entropy of output image is
6.6221which is nearly equal to entropy of input image. Though the proposed method will enhances the image but still there are traces of artifacts in the output image. In ideal case value of AMBE should be zero for no artifacts but in this method value of AMBE is not zero which indicates the presence of traces of artifacts. These artifacts can be removed by further dividing the histogram recursively into several
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