Contrast Limited Fuzzy Adaptive Histogram Equalization for Enhancement of Brain Images V. Magudeeswaran, J. Fenshia Singh Department of ECE, PSNA College of Engineering and Technology, Dindigul, India Received 23 November 2016; accepted 3 February 2017 ABSTRACT: Contrast limited fuzzy adaptive histogram equalization (CLFAHE) is proposed to improve the contrast of MRI Brain images. The proposed method consists of three stages. First, the gray level intensities are transformed into membership plane and membership plane is modified with Contrast intensification operator. In the second stage, the contrast limited adaptive histogram equalization is applied to the modified membership plane to prevent excessive enhancement in contrast by preserving the original brightness. Finally, membership plane is mapped back to the gray level intensities. The performance of proposed method is evaluated and compared with the existing methods in terms of qualitative measures such as entropy, PSNR, AMBE, and FSIM. The proposed method provides enhanced results by giving better contrast enhancement and preserving the local information of the original image. VC 2017 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 27, 98 103, 2017; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ima.22214 Key words: contrast; entropy; histogram; brightness I. INTRODUCTION Enhancement of brain tissues in MRI Images plays an indispensable role in medical analysis. The main objective of image enhancement is to increase the contrast of the image. One of the most popular techniques used for enhancement of images is histogram equalization (HE). HE has the advantage that it is simple to implement and computationally fast. In this method based on the probability distribution of the input gray levels, the gray levels of the image are remapped. Another technique used for image enhancement is adaptive histogram equalization (AHE). This technique computes several histograms and uses them to redistribute the lightness values of the image. It improves the local contrast and enhances the definitions of edges in each region of an image. The main disadvantage of AHE method is the tendency to over-amplify noise in relatively homogeneous regions of an image. To overcome this drawback, a new technique called contrast limited adaptive histogram equalization (CLAHE) is used. It differs from ordinary adaptive histogram equalization in its contrast limiting. It can also be applied to global histogram equalization. Lidong et al. (2015) combined contrast limited adaptive histogram equalization and Correspondence to: J. Fenshia Singh; fenshiaj@gmail.com discrete wavelet transform and proposed a new method for image enhancement. HE technique significantly changes the brightness of an image. Hence the output image gets saturated. To overcome this limitation, several brightness preserving histogram equalization techniques have been proposed. At the beginning, Kim (1997) proposed a technique called brightness preserving bi-histogram equalization (BBHE). In this technique, the input image is split into two sub images based on the mean brightness. The sub images histograms are then independently equalized. The advantage of this method is that mean brightness can be achieved as the original mean brightness is retained. Then, equal area dualistic sub-image histogram equalization was introduced by Wan et al. (1999). Next, Zakiah et al. (2011) introduced a new technique called dualistic sub image histogram equalization (DSIHE). This method differs from BBHE such that it uses median of input image for histogram partition instead of mean brightness. An extension of this BBHE method called Minimum Mean Brightness Error Bi-Histogram Equalization (MMBEBHE) was proposed by Chen and Ramli (2003). This method finds the minimum mean brightness error between the original and enhanced image. Even though the mean brightness of the image is preserved using these techniques, they cannot be used to further expand the region of sub-histogram that is located next to the minimum or maximum value of the dynamic range. It also has some side effects like undesirable checkerboard effects, brightness change in images, etc. Recently Hum et al. (2014) introduced another form of bi-histogram equalization technique for multi objective image enhancement. Kang and Chen (2015) proposed a fast representation method based on double orientation histogram for local image descriptors. Abdullah-Al-Wadud et al. (2007) introduced a dynamic histogram equalization (DHE) technique to deal with this problem. In DHE, the original histogram is partitioned based on local minima. But brightness is not preserved in this method. Hence, Kong and Ibrahim (2008) proposed brightness preserving dynamic histogram equalization (BPDHE). In this method, the image histogram is partitioned based on local maxima of smoothed histogram. Another, technique called brightness preserving dynamic fuzzy histogram equalization (BPDFHE) has been proposed by Sheet et al. (2010). This is an enhanced version of BPDHE in which no remapping of histogram peaks takes place. Only redistribution of gray-level values between VC 2017 Wiley Periodicals, Inc.
two consecutive peaks takes place. Jabeen et al. (2016) proposed a method for image contrast enhancement using weighted transformation function. A method for dark image enhancement was proposed by Ling et al. (2015). Su et al. (2013) used quantum-behaved particle swarm optimization with an adaptive strategy for image enhancement. A contrast limited fuzzy adaptive histogram equalization (CLFAHE) technique is proposed to overcome the unwanted overenhancement of images. The proposed CLFAHE method improves the contrast of the original image and preserves the image brightness. The rest of this article is organised as follows. The conventional Contrast Limited Adaptive Histogram Equalization (CLAHE) is discussed in Section II. In Section III, the Fuzzy image enhancement is discussed in detail. The proposed contrast limited fuzzy adaptive histogram equalization (CLFAHE) is explained in Section IV. The Image Quality Assessment (IQA) parameters are discussed in Section V. Simulation of the test images and qualitative comparison of the results are given in Section VI. The conclusion of this article is given in Section VII. II. CONTRAST LIMITED ADAPTIVE HISTOGRAM EQUALIZATION Contrast limited adaptive histogram equalization (CLAHE) differs from normal adaptive histogram equalization (AHE) in terms of contrast limiting. This feature can also be applied to global histogram equalization, giving rise to contrast limited histogram equalization (CLHE). This CLHE technique is rarely used in practice. In case of CLAHE, for each neighbourhood, the contrast limiting procedure has to be applied from which a transformation function is derived. This technique was developed mainly to prevent the over-amplification of noise created by AHE. The over-amplification of noise is prevented by limiting the contrast enhancement of AHE. The slope of the transformation function gives the contrast amplification of a given pixel. This is proportional to the slope of the neighbourhood cumulative distribution function (CDF). Therefore it is proportional to the value of the histogram at that pixel value. In CLAHE, the amplification is limited by clipping the histogram at a predefined value before computing the CDF. Thus the slope of the CDF and also the transformation function are limited. Clip limit is the value at which the histogram is clipped and it depends on the normalization of the histogram and also on the size of the neighbourhood region. Instead of discarding the part of the histogram that exceeds the clip limit, it is advantageous to redistribute it equally among all histogram bins. This results in an effective clip limit that is larger than the prescribed limit as the redistribution will push some bins over the clip limit again. The redistribution procedure can be repeated recursively until the excess is negligible, if it is undesirable. one can use the great diversity of fuzzy logic, fuzzy measure theory and fuzzy set theory to modify/aggregate the membership values, classify data or make decisions using fuzzy inference. The new membership values are retransformed in the gray-level plane to generate new histogram modified gray-levels, image segments, or classes of objects. In general low membership values are assigned to dark pixels and high membership values are assigned to bright pixels. General Structure of Fuzzy Image Processing is shown in Figure 1. IV. PROPOSED WORK The main aim of proposed method is to generate an image of higher contrast than the original image. This is achieved by giving the larger weight to the gray levels that are closer to the mean gray level of the image when compared to those that are farther from the mean. The proposed fuzzy image enhancement involves three stages namely image fuzzification, modification of membership values for image enhancement and image defuzzification. Gray level intensities are transformed to fuzzy plane whose value range between 0 and 1 in image fuzzification. An image f of size M 3 N and intensity level in the range (0, L 2 1) is considered as set of fuzzy singletons in the fuzzy set notation, each with a membership function denoting the degree of having some gray level. The fuzzy matrix F corresponding to this image can be expressed as F5 [ M i51 [N j51 l ij f ij 0 l ij 1 (02) where f ij is the intensity of (m, n)th pixel and its membership value. Using a specific membership function the original image f in the spatial domain will be converted to a fuzzy domain according to its region (i.e., dark or bright regions). Then, to reduce amount of fuzziness of F Contrast intensification is applied by increasing the values of above 0.5 and decreasing those below it. Another fuzzy set is generated due to this contrast intensification operator on the fuzzy set F. The membership function of which is expressed as 8 < Tðl ij Þ5 2 ðl ijþ 2 0 l ij 0:5 (03) : 12ð2 ð12ðl ij Þ 2 Þ 0:5 l ij 1 III. FUZZY IMAGE ENHANCEMENT Nowadays, fuzzy set theory is applied to develop new techniques for image noise removal, contrast improvement of image, etc. Mapping of image gray level intensities into a fuzzy plane using a membership function and modifying those member functions for contrast enhancement and finally mapping the fuzzy plane back to image gray level intensities results in fuzzy image enhancement. Fuzzy image processing has three stages: Image fuzzification ðuþ, suitable operation ðcþ on membership values and image de-fuzzificationðwþ. The output Y of the system for an input X is given by the processing chain Y5WðCUX ð ð ÞÞÞ (01) The main difference when compared to other methodologies is that the input data X will be processed in the so-called membership plane where Figure 1. General structure of fuzzy image processing. [Color figure can be viewed at wileyonlinelibrary.com] Vol. 27, 98 103 (2017) 99
We concentrate on contrast enhancement to enhance the image. This is achieved by making bright pixel brighter and dark pixel darker. The pixel which have middle intensity value are not changed much. Once the image is converted into the fuzzy domain the membership function is then modified according to its respective region to enhance the image. Then the contrast limited adaptive histogram equalization is applied to the fuzzy plane of image F as follows ~F5½i c max 2i c min ŠF k ði c in Þ1i c min (04) Where i c_min and i c_max be the minimum and maximum permissible intensity levels and the optimal value of this clip limit is also set. F k (i c_in ) be the cumulative distribution function (CDF) for input image i c_in which is given as F k ði c in Þ5 Xk f i ði j Þ (05) where, the probability density function is given by f i ði k Þ5 n k (06) N Here N is the total number of pixels and n k is the number of pixels with intensity level i k. Finally, the modified membership functions are defuzzified using their respective inverse membership functions. j50 Gðx; yþ5t 21 ð ~Fðx; yþþ5 [ M x51 [N y51 ~Fðx; yþðl21þ (07) where, G(x, y) denotes the (x, y)th pixels gray level in the enhanced image. The inverse transformation of T is denoted as T 21.Itmeans that the membership values are re-transformed into the gray-level plane. V. IMAGE QUALITY ASSESSMENT Image quality assessment (IQA) mainly aims to measure the quality of the image using computational models. In our evaluation, IQA indices like entropy, FSIM, PSNR, and AMBE are used. Entropy is used to measure the content of an image. Higher value of entropy indicates an image with richer details and more information are brought out from the image. Wei et al. (2015) proposed a method which deals with the maximization of entropy. Entropy is defined as, Entropy52 X pðxþlog 2 pðxþ (08) The feature similarity (FSIM) index computation consists of two stages. The local similarity map is computed in the first stage and then the similarity map is pooled into a single similarity core in the second stage. The feature similarity measure between f 1 (x) and f 2 (x) are separated into two components, each for phase congruency (PC) or gradient magnitude (GM). FSIM is defined as, where, P x2x FSIM5 S LðxÞ:PC m ðxþ P x2x PC mðxþ (09) PC m ðxþ5 max m PC 1ðxÞ; PC 2 ðxþ (10) Figure 2. (a) Original image, (b) histogram equalised image, (c) AHE image, (d) CLAHE image, (e) BHE image (f) Proposed CLFAHE image. 100 Vol. 27, 98 103 (2017)
Figure 3. Image and histogram of (a) Original image, (b) Histogram equalised image, (c) AHE image, (d) CLAHE image, (e) BHE image (f)proposed CLFAHE image. X stands for whole image spatial domain Similarity SLðxÞ5½S PC ðxþš a ½S G ðxþš b (11) S PC ðxþ5 2PC 1ðxÞ:PC 2 ðxþ1t 1 2PC 2 1 ðxþ1pc2 2 ðxþ1t 1 S G ðxþ5 2G 1ðxÞ:G 2 ðxþ1t 2 G 2 1 ðxþ1g2 2 ðxþ1t 2 (12) (13) where T 1 is a positive constant used to increase the stability of S PC, T 2 is a positive constant which depends on the dynamic range of GM values. Zhang et al. (2011) has given a brief description about FSIM. Peak signal-to-noise ratio (PSNR) is the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the output signal. PSNR is most easily defined via the mean squared error (MSE). Given a noise free m 3 n monochrome image I and its noisy approximation K, MSE is defined as: MSE5 1 mn X m21 X n21 i50 j50 ½Iði; jþ2kði; jþš 2 (14) The PSNR (in db) is defined as: MAXI 2 PSNR510log 10 MSE Here, MAX I is the maximum possible pixel value of the image. (15) Table I. Comparison of entropy values Image 1 4.26 5.90 6.04 5.46 5.97 Image 2 4.43 5.91 5.90 5.18 6.03 Image 3 4.32 5.85 5.90 5.10 5.96 Image 4 4.55 6.03 6.07 5.28 6.00 Image 5 4.50 6.03 6.09 5.36 6.10 Image 6 5.45 7.08 7.02 6.86 7.12 Image 7 5.14 6.93 6.91 6.55 6.89 Image 8 4.60 6.17 6.34 5.50 6.22 Image 9 4.27 5.89 6.08 4.80 5.98 Image 10 2.96 4.13 4.21 3.55 4.09 Vol. 27, 98 103 (2017) 101
Table II. Comparison of FSIM values Image 1 0.91 0.91 0.88 0.91 0.95 Image 2 0.75 0.85 0.83 0.78 0.94 Image 3 0.72 0.86 0.85 0.80 0.96 Image 4 0.74 0.83 0.82 0.78 0.96 Image 5 0.73 0.85 0.86 0.83 0.96 Image 6 0.94 0.89 0.88 0.93 0.94 Image 7 0.95 0.90 0.89 0.94 0.94 Image 8 0.68 0.89 0.88 0.90 0.94 Image 9 0.77 0.84 0.84 0.75 0.96 Image 10 0.82 0.94 0.87 0.88 0.96 Table IV. Comparison of AMBE values Image 1 60.28 0.71 1.30 29.77 0.16 Image 2 86.20 20.51 29.45 33.89 5.28 Image 3 93.96 16.55 30.84 34.17 7.01 Image 4 89.67 23.71 34.14 33.42 6.57 Image 5 90.89 20.68 33.55 30.80 4.42 Image 6 30.87 8.35 5.15 20.52 0.43 Image 7 38.76 2.62 1.08 23.42 0.84 Image 8 88.25 19.44 32.50 22.77 2.58 Image 9 109.79 21.98 38.85 36.60 8.31 Image 10 131.82 14.29 25.40 27.07 3.95 Absolute mean brightness error (AMBE) is used to rate the performance in preserving the original brightness. It is defined as the absolute difference between the mean of the input and the output images. It is calculated as, AMBE5jEðXÞ2EðYÞj (16) X and Y denotes the input and output image, respectively, and E (.) denotes the expected value, i.e., the statistical mean. Lower AMBE indicates the better brightness preservation of the image. VI. RESULTS AND DISCUSSION In this section, comparison between proposed methods and several other conventional methods such as histogram equalization (HE), adaptive histogram equalization (AHE), contrast limited adaptive histogram equalization (CLAHE), and bi-histogram equalization (BHE) are presented. Entropy, FSIM, PSNR, and AMBE are used to evaluate the effectiveness of the proposed method. The proposed method was tested with several gray scale images and has been compared with other conventional methods mentioned above. Figure 2 shows the resulting MRI brain images obtained by the various existing methods and proposed method. Figure 2a shows the original input image. Histogram Equalized image is shown in Fig. 2b. Figure 2c shows the Adaptive Histogram Equalized image with contrast improvement. Figure 2d shows the resultant image of Contrast Limited Adaptive Histogram Equalization. Bihistogram equalized image is shown in Fig. 2e. Figure 2f shows the output image of the proposed method. Figure 3 shows the resulting MRI brain images and their histograms obtained by the various existing methods and proposed method. From Fig. 3 it is clear that the histogram of the input image and the histogram of proposed CLFAHE output image are more or less same. When compared to other histograms, the histogram of the proposed Table III. Comparison of PSNR values Image 1 11.41 22.21 18.24 15.86 22.52 Image 2 9.11 18.26 17.49 15.73 23.43 Image 3 8.22 19.40 17.16 15.59 23.21 Image 4 8.67 17.32 16.32 15.49 24.57 Image 5 8.51 18.12 16.59 16.73 22.59 Image 6 18.05 18.61 18.35 20.72 20.63 Image 7 15.90 18.42 17.25 19.17 20.45 Image 8 8.71 19.11 16.69 20.02 22.19 Image 9 6.93 17.60 15.49 13.66 25.03 Image 10 5.66 20.27 19.10 17.52 25.24 method is evenly distributed from 0 to 256. This is also considered as an advantage of the proposed method. The qualities of test images which are enhanced using above mentioned techniques are then measured in terms of entropy, FSIM, PSNR, and AMBE and are given in Tables (I IV). The entropy results from Table I shows that the proposed method improves the contrast of the image in a better way, which is numerically indicated by greater or more or less equal values as compared to the other conventional methods. By analysing the FSIM values in Table II, it is found that the proposed method has produced values that are closer to 1. This indicates the similarity between the original and enhanced image. Table III shows the PSNR values obtained from different images. By analysing these values, it is found that the proposed method produces greater PSNR values as compared to other conventional methods. The AMBE values are analysed using Table IV. From the table it can be concluded that the absolute mean brightness error is much reduced when compared to other conventional methods. Thus the proposed method has been found effective in enhancing contrast of images in comparison to few existing methods based on qualitative and quantitative analysis. VII. CONCLUSION In this work, a simple contrast limited fuzzy adaptive histogram equalization is presented for image contrast enhancement. 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