A Function-Based Image Binarization based on Histogram

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1 International Research Journal of Applied and Basic Sciences 2015 Available online at ISSN X / Vol, 9 (3): Science Explorer Publications A Function-Based Image Binarization based on Histogram Hamid Sheikhveisi Payam e Noor University, Zahedan, Iran. Corresponding Author hamid.sheikhveisi@gmail.com ABSTRACT: A gray-level histogram of an image can be divided into four identical parts of gray-level value for better operations; our new approach is figured for the correct automatic binarization of digital images based on the presented theory. The algorithm follows a simple and accurate synthesis. A rectangular mixture function is employed to multiply by the input image; in this condition, the function is multiplied to the peak points of the image histogram, and in order to several peak points in the areas, to have a unity peak point, the global maximum theory is used. Finally achieved results are compared by ordinary methods: Otsu, Kapur, Rosin and Du algorithms. Experimental results show the good performance of the new approach toward the others. Keywords: Segmentation, Image binarization, Gray level image, Histogram, Rectangular function, Global maximum, Symmetry. INTRODUCTION Image segmentation is necessary to image processing and pattern recognition which leads to the high quality of the final result of analysis. Image segmentation is a process of separating an image into different regions. One of the particular types of segmentation is thresholding (R. C. Gonzalez et al., 2009); thresholding is a very low-level image segmentation method. It is widely used as a pre-processing step. One of the more significant steps in is finding a proper threshold value to segment an arbitrary object from its background. The next step is maybe defect detections, or any other operations. In more applications, image segmentation is included in the main step (K. S. Fu and J. K. Mui, 1981; N. R. Pal and S. K. Pal, 1993; P. K. Sahoo, 1988; M. Sezgin, B. Sankur, 2004). The main idea is that the intensity values of object pixels and the background pixels differ, such that object and background can be separated by selecting a proper threshold. A binary image is then obtained by assigning pixels with values less than threshold with zeros and the remaining pixels with ones. This type of thresholding is called bi-level threshold. We have also another type of thresholding that is proper for the composed or several distinct objects. In this type of thresholding, a multiple thresholding is applied to a better thresholding; this is called multi-level thresholding. Ideally, for a bi-level image, the histogram consists of two peak points; in this condition, the point between and at the bottommost point of these two peaks (valley), denotes the thresholding point. The optimum point is gotten into the bottommost one. In this situation, the pixels with less value than this will return to zero and the pixels that are equal to or bigger than it will return to one (M. Sezgin, B. Sankur, 2004). Let us consider image f of size M N with L gray levels in the range [0, L-1]. The gray level or the brightness of a pixel with coordinates ( i, is denoted by f ( i,. The threshold T is a value in the range of [0, L-1]. Now the thresholding technique determines an optimal value for T based on predefined measurements, so that: 1 for f ( i, T g( i, (1) 0 for f ( i, T Where g( i, is binarized image. An example for gray level image, gray level distribution histogram and the threshold are shown in fig.1.

2 Background Object Figure. 1. Histogram of a gray level image In the last three decades several methods have been proposed, which set the thresholds according to a certain criterion, an overview can be found in (M. Sezgin, B. Sankur, 2004). Typically, there are two approaches for thresholding methods; local and global. In global thresholding, a same threshold value is used across the whole image. While in local thresholding, an image is separated into many sub-regions (H.D. Cheng, Y.H. Chen, 1996). Local thresholding investigates the relationship between brightness of neighborhood pixels to adapt the threshold in order to the intensity statistic of different. One of the principal drawbacks of local threshold is finding more than one threshold value in some conditions; the other is the more elapsed time toward global thresholding. Some factors affect the certain value of gray level and make the threshold get complicated; poor contrast, inconsistency between sizes of object and background, non-uniformity in the background, and correlated noise are some of these cases. Since, the prosperity of thresholding depends on the proper selection of threshold value. In order to the properties the thresholding techniques are employing, sezgin has categorized them into six groups as below (M. Sezgin, B. Sankur, 2004): Histogram shape-based methods where the histogram of the image is viewed as a mixture of two Gaussian distributions associated to the object and back ground classed; Zhi thresholding (Zhi-Kai Huang, Kwok-Wing Chau, 2008) or sezan thresholding (M.I. Sezan, 1985) are two examples of this method. Clustering-based methods where the gray level pixels are clustered in two classes as background and foreground objects, or alternatively modelled as a mixture of two Gaussians; iterative thresholding (T. W. Ridler, and S. Calvard, 1979), Otsu thresholding (N. Otsu, 1979), minimum error thresholding (J. Kittler and J. Illingworth, 1986), fuzzy clustering thresholding (D.Mangamma, 2011). Entropy-based methods use the difference in entropy between the foreground and background regions, such as Kapur thresholding (J.N. Kapur, 1985) and Peng method (Peng-Yeng Yin, 2002). Object attribute-based methods find a measure of similarity (fuzzy shape similarity, edge coincidence, etc.) between the gray level and threshold image; such as edge field matching threshold (L.Herts and R. W. Schafer, 1988) and topological stable-state thresholding (A. Pikaz and A. Averbuch, 1996). Spatial Methods used higher order probability distribution and/or correlation between pixels such as Brink thresholding (Brink, A.D., 2002). Local Methods like san threshold have not good results in order to described drawbacks (Berrin A., 2008). The proposed method is perfectly independent from thresholding approaches. It defines the binarized image by multiplying the maximum gray level of the image with the complex rectangular image whereas other binarization methods just select the proper value for histogram thresholding. Proposed Approach The main idea of the proposed approach derived from the gray scale histogram processing; indeed if we have the maximum value of the intensity histogram (we called it mvih), the histogram diagram is divided to 4 areas. Fig.2 shows an illustration of defined separated. From fig.2, Area I contains the maximum values of the histogram, while Area IV has the minimum values. Results from the last literatures showed that if we find two proper peaks and also the suitable valley between them, a good result can be achieved for thresholding purposes. 419

3 Figure. 2. Histogram dividing. For this approach, mixture rectangular functions are considered to multiply by the input image. Our idea in this approach is in to find a 0 and/or 1 (binary) function to multiply by the input image for attaining a binary output image. The presented mixture function is a rectangular function; the rectangle function Π (x) is a function which is 0 outside the interval [-1/2, 1/2] and unity inside it. It is also called the gate function, pulse function, or window function, and is defined as (Weisstein, Eric W., 2011): 1 0 for x ( x ) for x (2) for x 2 Total procedure for the proposed method is as below: Step 1) Image acquisition Step 2) intensity level converting (we consider that the input image is RGB) The separate values of the three color channels (R, G, and B) are combined to produce an intensity image (gray) using a commonly accepted transformation as below: Intensity R G B (3) If the input image is an intensity level image, step 2 will be neglected. Step 3) Find the histogram (probability distribution function) of the gray level image; the histogram of a digital image with L total possible intensity levels in the interval [0, L-1] is defined as the discrete function: h[ r k ] n k (4) where r k is the k th intensity level in the range [0, L-1] and n k is the number of pixels in the image whose intensity image is r k. The value of L-1 is also differing for various classes (255 for unit8, 1 for double, etc.). Step 4) Divide the input histogram to 4 identical areas; fig.3 obviously shows the same dividing between 4 areas. Step 5) Find the Maximum Points (Peaks) of each area; peak value of whole 4 areas has been found as c 1, c 2, c 3 and c 4. Red points in fig.3 shows the peak values found by the implemented approach. As it can be seen from fig.3, some problems are made by this method; each 4 areas have more than 1 peak point. Indeed, local maxima points of each area are extracted. For attaining just 1 peak point for each area, we need to find the global maxima. A function has a global (or absolute) maximum point at x if f(x ) f(x) for all x. A global maximum of f(x) in [0, L-1] is basically the greatest value of f(x) in [0, L-1]. Global maxima in [0, L-1] will always occur either at the critical points of f(x) within [0, L-1] or at the end points of the interval (Thomas, 2010). Three main steps to find the global maxima are as: Find out all the critical points of f(x) in [0, L-1]. Let l 1, l 2 l n be the different critical points. Find the value of the function at these critical points and also at the end points of the domain. Let the values of the function at critical points be f (l 1 ), f (l 2 )..f (l n ). 420

4 l 1 l 2 l 3 l n Figure. 3. Areas Dividing and finding the peak points for each area; red stars are the peak value of each area. Find M1 =Max {f (0), f (l 1 ), f (l 2 ) f (l n ), f (L-1)}. Now M1is the maximum value of f(x) in [0, L-1]. Step 6) Generate 4 rectangular functions by the center of peak points. f ( x) h (( x ci )/ b) (5) where h is height, c is the center, and b is the full-width. h is one in this work, and c is the peak point of areas; b is calculated as L/32.5 after some trial and errors. Step 7) Multiply the generated function by the intensity image to get the output binary image. y ( x) I( x) (6) where I and y are pixels in the input (intensity) and output (binary) image, respectively. Fig. 4 shows the result of the algorithm for an image. Figure. 4. Multiply of rectangular function and the input image. Experimental results We tested the proposed real-time thresholding technique on a Pentium 4 processor at core 2 duo1.60ghz under Matlab environment (Mathworks, 2010). An experimental test images have been prepared by complex different dataset to cover a variety of situations and conditions. Some examples of our thresholding result are shown below. 421

5 (A) (B) (C) 422

6 Figure. 5. (A) Original image with different sizes, (B) Histogram (Probability Distribution) of the input image, (C) Binarized image. The experiment result of proposed approach is then compared by Otsu, Kapur method (J.N. Kapur et al., 1985) and local relative entropy threshold (LRE), joint relative entropy threshold (JRE) and global relative entropy threshold (GRE) (Y. Du, 2004); we are also used Rosin method (Venkatesh, S. and P. Rosin., 1995), but in order to improper results, it is neglected in evaluation section. To evaluate the performance of the proposed algorithm toward the other conditional methods, six performance metrics are defined: TP Sensitivity TP FN TN Specificity TN FP TP Positive. Pr edictivevalue. TP FP TN Negative. Pr edictivevalue. TN FN TP FP Index. of. Suspicion TP FN TP Diagnostic. Accuracy TP FP FN (7) (8) (9) (10) (11) (12) where TP is the number of true positives, FN the number of false negatives, TN the number of true negatives, and FP the number of false positives. A positive is a part that is classified as object; true classification is defined by an expert. The sensitivity and specificity measure the percentages of accurate classifications for the object and background cases, respectively. The positive predictive value is the proportion of object classified as object that is really object, and inversely for the negative predictive value. The index of suspicion gives the degree of awareness of the likelihood of an object to be an object. An index higher than 100% represents an over-diagnosis while an index lower than 100% represents under-diagnosis. The diagnosis 423

7 accuracy shows the loss of accuracy due to misclassified elements. Table 1 shows the different classification accuracy indices for three combinations of segmentations: Proposed method, Otsu, Kapur, LRE, JRE and GRE. Table.1. Segmentation symmetry values for image binarization Symmetry Features Proposed Otsu[22] Kapur [23] LRE [24] JRE [24] GRE[24] Sensitivity (%) Specificity (%) Positive predictive value (%) Negative predictive value (%) Index of suspicion (%) Diagnostic accuracy (%) ` (D) (E) (F) (G) (H) (I) Figure. 6. Results of thresholding of images from the difference dataset with various algorithms; (A) Input image, (B) Histogram of the image, (C) Otsu, (D) Kapur, (E) Rosin, (F) LRE, (G) JRE and (H) GRE thresholding. 424

8 (D) (E) (F) (G) (H) (I) Figure. 7. Results of thresholding of images from the difference dataset with various algorithms; (A) Input image, (B) Histogram of the image, (C) Otsu, (D) Kapur, (E) Rosin, (F) LRE, (G) JRE and (H) GRE thresholding. (D) (E) (F) (G) (H) (I) Figure. 8. Results of thresholding of images from the difference dataset with various algorithms; (A) Input image, (B) Histogram of the image, (C) Otsu, (D) Kapur, (E) Rosin, (F) LRE, (G) JRE and (H) GRE thresholding. CONCLUSIONS In this paper, a novel gray level binarization algorithm is proposed using the rectangular function. In order to the fact that the histogram of image can be used to depict the statistical character of probability density function, the peak points of histogram is used to find the proper point of binarization. A rectangular function is used to achieve the proper function which gets 1 for some defined peak points and inverse, gets zero for less value points respectively. As an example of the application of the methodology, tests were performed on a random selection of different dataset providing a quantitative and thorough evaluation of six different 425

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