An Integrated Approach of Logarithmic Transformation and Histogram Equalization for Image Enhancement

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1 An Integrated Approach of Logarithmic Transformation and Histogram Equalization for Image Enhancement Saurabh Chaudhury 1, Sudhankar Raw 1, Abhradeep Biswas 1, Abhshek Gautam 1 1 Department of Electrical Engineering National Institute of Technology Silchar Assam , India { 1: saurabh1971@gmail.com} Abstract. Logarithmic Transformation and Histogram equalization (HE) are well known image enhancement techniques in spatial domain. These techniques are very popular for contrast enhancement because the methods are simple and effective. The basic idea of HE is to re-map the gray levels of an image. However, HE tends to introduce some annoying artifacts and unnatural enhancement. Here we propose an integration of the two techniques at pixel level, doing first the HE and then using logarithmic transformation for mapping purpose. Both the global HE and local HE are preformed on the input image pixels. The Histogram Equalization has been performed in the MATLAB environment. We have experimented the proposed techniques over a number of sample images and found to produce much better results compared to image enhancement using the inbuilt MATLAB function histeq. Keywords: Image processing, logarithmic transformation, Histogram Equalization, Contrast Enhancement, histeq 1 Introduction Image enhancement is among the simplest and most appealing areas of digital image processing. Basically, the idea behind enhancement techniques [1] is to bring out detail that is obscured, or simply to highlight certain features of interest in an image. It is important to keep in mind that enhancement is a very subjective area of image processing. Image enhancement can be carried out in two domainsspatial domain and frequency domain. Histogram and it equalization falls under spatial domain, so also the logarithmic transformation. Logarithmic transformation is a nonlinear basic gray level transformation function which maps a narrow range of low grey values to a wider range of output levels and thus enhancing the contrast levels and brightness of the image. A histogram on the other hand, is the es-

2 2 timation of the probability distribution of a particular type of data. An image histogram is a type of histogram which offers a graphical representation of the tonal distribution of the gray values in a digital image. For an 8-bit grayscale image there are 256 different possible intensities, and so the histogram will graphically display 256 numbers showing the distribution of pixels amongst those grayscale values. By viewing the image s histogram, we can analyze the frequency of appearance of the different gray levels (intensities) contained in the image. The histogram that shows only a fraction of the total range of gray levels in the image then the image has low contrast. Each color level (gray value) is represented as a point on x-axis and on y-axis is the number instance of a color level repeats in the image. Histogram may be viewed or plotted with Matlab imhist command. Sometimes all the important information in an image lies only in a small region of colors, hence it usually is difficult to extract information out of that image. There comes the need for histogram equalization. A good histogram is that which covers all the possible values in the gray scale used. This type of histogram suggests that the image has good contrast and that details in the image may be observed more easily. 1.1 Logarithmic Transformation Log transformations are one of the elementary image enhancement techniques of the spatial domain that can be effectively used for contrast enhancements of dark images. The log transform is essentially a gray level transform which means that the gray levels of image pixels are altered. This transformation maps a narrow range of low gray level values in the input image to a wider range of output levels. The opposite is true for higher input gray levels. Thus the dark input values are spread out into the higher gray level values which improve the overall contrast and brightness of the image. The general form of the log transformation can be mathematically represented as s = c log (1 + r) (1) where, s is the output grey level, r is the input grey level and c is a constant. It is assumed that r 0. Fig.1 shows such a transformation function. This transformation is used to expand the dark pixels in an image while compressing the higher-level pixel values as illustrated in Fig. 2 where the hidden diffraction pattern become prominent and clearly visible.

3 3 Fig. 1. Logarithmic Transformation Function Fig. 2. Diffraction Pattern Enhanced Through Log Transformation 1.2 Histogram Equalization (HE) Various enhancement schemes are used for enhancing an image which includes gray scale manipulation, filtering and Histogram Equalization (HE) [2,3,4,5,6]. Histogram equalization is one of the well known image enhancement technique. It has become a popular technique for contrast enhancement because this method is simple and effective. In the latter case, preserving the input brightness of the image is required to avoid the generation of non-existing artifacts in the output image. The basic idea of HE method is to re-map the gray levels of an image. HE tends to introduce some annoying artifacts and unnatural enhancement.

4 4 1.3 Adaptive Histogram This is an extension of traditional Histogram Equalization technique. It enhances the contrast of an image by transforming the values in the intensity image I. Unlike histeq, 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. 1.4 Histogram Equalization Techniques There are a number of different types of histogram equalization exist, such as, cumulative histogram equalization, normalized cumulative histogram equalization, and localized equalization. A detailed list of histogram equalization techniques and their advantages and disadvantages are explained in [7]. Histogram expansion is a simple technique that enhances the contrast levels of an image. But it has the disadvantage that if there are gray values that are physically far apart from each other in the image then this method fails. LAHE offers an excellent image enhancement technique in terms of contrast level but has the disadvantage that it is computationally very slow and requires a high number of operations per pixel. Par sectioning on the other hand is easy to implement and better suits in hardware level, whereas, odd sectioning offers a good image contrast but has problems with histograms which cover almost the full gray scale. An advanced contrast enhancement using partially overlapped sub-block histogram equalization has been presented in [6]. This technique uses a low pass filter (as a mask) to get a non-overlapped sub-block histogram equalization which can produce high contrast associated with local histogram but can take advantage of simplicity of global equalization. In [8] a method to evaluate the performance of an enhancement technique is presented which they termed as EME on contrast. A modified histogram equalization is presented in [9] to avoid certain details which wash out after enhancement due to quantum jump of cumulative distribution function in histogram. Contrast enhancement using recursive mean-separate histogram equalization for scalable brightness preservation has been presented in [10]. A multi-histogram equalization technique has been presented in [11] which decomposes the image into several sub-images and then apply the classical HE process to each one. This way it performs a less intensive image contrast enhancement and the output image presents a more natural look. Contrast enhancement for digital image using histogram equalization [12] on the other hand takes gray scale image enhancement by multi-histogram equalization whereas for color images it applies a hue preserving HE for image enhancement.

5 5 Image histogram and histogram equalization find applications not only in image enhancement but also in other higher level processing such as in thresholding, adaptive thresholding [13], image segmentation [14] and super-resolution, image quality and image restoration. A histogram based thresholding approach might be to create a histogram of the image pixel intensities and use the valley point as the threshold. The histogram approach assumes that there is some average values for both the background and object pixels, but that the actual pixel values have some variation around these average values. The paper is organized as follows. Section 2 illustrates the proposed algorithms, the integrated global histogram equalization and local histogram equalization respectively which include the mapping function to be the logarithmic transformation and techniques behind such processing. In section 3 we present our observation on the results of exhaustive experimentation of the proposed techniques on some sample images and finally section 4 concludes the paper. 2 Proposed Algorithms The image enhancement, specifically, the contrast enhancement using Histogram Equalization technique with log transformation as the mapping function has been proposed here. Two algorithms have proposed- Global Histogram Equalization and Local Histogram Equalization. The algorithms and flowchart of which are discussed in the following subsections and are implemented using MATLAB. 2.1 Integrated Global Histogram Equalization with Log Transformation The following flowchart depicts the different steps that were followed during the Global Histogram Equalization.

6 6 Fig. 3. Flow-chart Showing Global Histogram Equalization Technique Consider a discrete grayscale image{x} and let n i be the number of occurrences of gray level i. The probability of an occurrence of a pixel of level in the image is p x (i) = p(x=i) = n i /n, 0 I < L (3) L being the total number of gray levels in the image, n being the total number of pixels in the image, and p x (i)being in fact the image's histogram for pixel value i, normalized to [0,1]. The cumulative distribution function is defined corresponding j=i to p x as cdf x (i)= j=0 p(j) where p is a function of x which is also the image's accumulated normalized histogram. We would like to create a transformation of the form y = T(x) to produce a new image {y}, such that its CDF will be linearized across the value range, i.e. cdf x (i) = ik for some constant K. The properties of the CDF allow us to perform such a transform. For logarithmic transformation this can be defined as y= T(x)= log {1+cdf(x)} (4) We notice here that T maps the gray levels in the image into the range [0,1] in a logarithmic way such that a large range of input gray levels can be confined to a narrow range of output gray levels. In order to map the values back into their original range, the following simple transformation needs to be applied on the result: y = y.{max{x}-min{x}}+ min{x}. 2.2 Integrated Local Histogram Equalization with Log Transformation The following flowchart as shown Fig. 4 depicts the algorithmic steps that have been implemented in the proposed approach for local histogram equalization.

7 7 The input image is loaded and the histogram obtained by using the function imhist [15]. A window of our own chosen size is initialized. CDF values for the pixels in the image are computed. The middle values for each window is computed and the CDF value calculated. The pixels in the original image are replaced by the new CDF values which depend on the value of the CDF of the middle element. Img(i,j) = round (cdf(ele)/(m*n)*255) The histogram of the equalized image is obtained. Histograms of new and original images are compared. Print the graphic results. Fig. 4. Flow-chart Showing the Proposed Algorithm on Local Histogram Equalization 3 Observations and Results In this work we have chosen three different types of images. Each image has its own characteristic features and differs from each other in terms of their detail, contrast levels, background and the amount of noise. Fig. 5 (a) shows the image of human lungs. The Matlab equalized image and the proposed global and local histogram equalized images are shown in Fig. 5 (b), (c) and (d) respectively. The original black & white image is of high contrast and difficult to diagnose whether any damage has taken place or not. MATLAB equalized on the other hand gives a dark image with a lot of noise content in the image and clearly not suitable for medical diagnosis. However, integrated logarithmic-global histogram equalized image implementing the proposed algorithm, clearly enhance the quality of image in terms of the contrast levels, in noise contents and easy for diagnosis. Locally

8 8 equalized image with log transformation, although, it is better than Matlab equalized image but definitely, not better than global one. Fig. 8 shows the histograms of the lung image. The original image has got high contrasts and so the pixels are distributed more towards the higher levels. Whereas, both the MATLAB equalized and the integrated global equalized image show a constricted intensity distribution, thus bringing out the detail more clearer and is best in case of integrated global equalized image. The integrated local equalized image is definitely not better in quality than the integrated global equalization. The image of Fig. 6 (a) is a MRI view of the human brain showing the left and right brain and other cortical regions. Here, we observe that the original image has poor contrast levels and the intensity distribution is not uniform as can be observed from the histograms in Fig. 9. We cannot categorize the image into a bright foreground and a dark background. The MATLAB equalized image has a better contrast but the various parts in the cross section cannot be easily distinguished. Moreover it introduces undesirable noises in the image. Proposed algorithms using integrated global equalization show a significant change in the contrast levels and the details of the image are much clearer, easy for diagnostics and without introducing any noise. Local equalization is also carried out for the same image. However, the contrast is not as good as integrated global one but definitely better than the Matlab equalized image. In fact the integrated global histogram equalization method scores above all other techniques referred here. In case of satellite image of Fig. 7, both the MATLAB equalized image and the global histogram equalized image are better contrast image than the original low contrast image obtained from the satellite. The integrated global equalized image differs from the MATLAB equalized image in the regions in the lower left of the landscape as it brings out better contrast than the MATLAB image which can be depicted from the histogram of Fig. 10. On the other hand, locally equalized image exposes much more details than the global histogram equalized one throughout the image. The image has exposed details like trees and fields in the right half of the image, stones and other objects in dark regions. Also the higher intensity distributions at the edges are brought down to a lower value because of log transformation along with local equalization which is not expected in local equalization only (where the gray levels of the boundary pixels get over-amplified). 4 Conclusion In this paper we have presented two algorithms for histogram equalization namely, the integrated global and local HE wherein we have used the logarithmic transformation for mapping the image. We have observed that for most of the medical images integrated global HE works well compared to integrated local HE. This is because of the fact that in such images, there is a little variation in contrast levels of different details in the image. Moreover, the technique is simple and takes less time for computation. However, in case of satellite captured image, as there are

9 9 different levels of contrasts among different objects, and hence the integrated local HE works well as it can be observed from the image of Fig. 7 (d). References [1] Maini Raman and Agarwal Himanshu: A Comprehensive Review of Image Enhancement Techniques, Journal of Computing, Vol. 2, Issue 3, ISSN , March [2] Garg Rajesh, Mittal Bhawna and Garg Sheetal: Histogram Equalization Techniques For Image Enhancement. H.I.T., Sonepat, Haryana, India [3] Mark Eramian and David Mould: Histogram Equalization using Neighborhood Metrics. Department of Computer Science, 110 Science Place, Saskatoon, SK, Canada, S7N 5C9,Canada, S7N 5C9 [4] Mokhtar N.R, Harun Nor Hazlyna, Mashor M. Y., Roseline H., Mustafa Nazahah, Adollah R., Adilah H. and Nasir N.F.Mohd: Image Enhancement Techniques Using Local, Global, Bright, Dark and Partial Contrast Stretching For Acute Leukemia Images. In: Proc. of the World Congress on Engineering 2009 Vol I [5] Robert Krutsch and David Tenorio: Histogram Equalization: Technical Report, Microcontroller Solutions Group, Guadalajara [6] Kim Joung-Youn, Kim Lee-Sup and Hwang Seung-Ho: An Advanced Contrast Enhancement Using Partially Overlapped Sub-Block Histogram Equalization, IEEE Trans. on Circuits and Systems for Video Technology, Vol. 11, No. 4, APRIL [7] Freescale : [8] Krishan Kant Lavania, Shivali and Rajiv Kumar, A Comparative Study of Image Enhancement using Histogram Approach, International Journal of Computer Applications, Vol. 32, No. 5, Oct [9] M.M. Naushad Ali and M. Abdullah- Al-Waded, Image Enhancement using a Modified Histogram Equalization, Springer-Verlag Berlin Heidelberg 2012, pp [10] S D Chen, A R Ramli, Contrast enhancement using recursive mean-separate histogram equalization for scalable brightness preservation, IEEE Trans. on Consumer Electronics, Vol 49, No. 4, No [11] David Menotti, Laurent Najman, Jacques Facon and Arnaldo de A. Araujo, Multi- Histogram Equalization Methods for Contrast Enhancement and Brightness Preserving, IEEE Trans. On Consumer Electronics, Vol. 53, No. 3, August [12] David Menotti, Arnaldo de A. Araujo, Giselle L. Pappa,, Laurent Najman and Jacques Facon, Contrast Enhancement in Digital Imaging using Histogram Equalization, VII Workshop of Theses, 2008-esiee.fr [13] Gonzalvez and Woods: Digital Image Processing, Pearson Education Inc. 2002, India Reprint. ISBN [14] Shapiro, Linda G. & Stockman, George C. (2002). "Computer Vision". Prentice Hall. ISBN [15] Sabih D. Khan. Image Processing in Matlab: An Introductory Approach. Khwarzimic Science Society.

10 10 Fig. 5. (a) Image of Human Lungs. (b - d) are the Images after Matlab, Integrated Global HE, Local HE Fig. 6. (a) Human Brain (b-d) are Matlab Equalized, Integrated Global-Logarithmic and Local-Logarithmic Equalized Brain Image

11 11 Fig. 7. (a) Satellite Captured Image, (b to d) are The Images after Matlab, Integrated Global-Logarithmic and Local-Logarithmic Equalization Fig. 8. (a) Histogram of Lung Image and (b-d) Equalized Histograms

12 12 Fig. 9. (a) Histogram of Brain Image and (b-d) Equalized Histograms Fig. 10. (a) Histogram of Satellite Image and (b-d) Equalized Histograms