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The purpose of this study is to apply different thresholding in mammogram images, and then we will determine which technique is the best in thresholding (extraction) malignant and benign tumors from the rest breast tissues. The used technique is Otsu method, because it is one of the most effective methods for most real world views with regard to uniformity and shape measures. Also, we present all the thresholding methods that used the concept of between class variance. We found from the experimental results that all the used thresholding techniques work well in detection normal breast tissues. But in abnormal tissues (breast tumors), we found that only neighborhood valley emphasis method gave best detection of malignant tumors. Also, the results demonstrate that variance and intensity contrast technique is the best in extraction the micro calcifications which represent the first signs of breast cancer.

Normal cells of the human body grow and divide to generate new cells in order to meet the body needs. If these normal cells grow old or destroyed, they die. So the new cells take their place. Cancer occurs when these new cells are generated and the body does not need them; in addition, the old and destroyed cells do not die as they should, so these additional cells are constructed as a mass tissue known as a lump, growth or tumor [

One of the main lethal cancers is breast cancer [1,2]. It occurs in both males and females, but the breast cancer in men is scarce [1,3]. Around 25% of all cancers in woman are breast cancer, and approximately 20% of cancers causing death are breast cancers. It primarily sites in ducts (tubas that transfers milk to the nipple) and in the lobules (glands which make milk) in the breast by taking the form as micro-calcifications or masses [

This paper is organized as follows: Section 2 is a brief introduction of segmentation, and mention types of segmentation used in mammograms. It also defined the thresholding, and related works for thresholding used in mammogram images. Section 3 illustrated the formulation of the structure of an image. Section 4 describes Otsu method, and the techniques related to it. Section 5 is about the thresholding evaluation methods. Section 6 is a discussion for experimental results. Conclusions appear in Section 7.

Segmentation in image processing plays a central role in detection the region of interest from background. Its inputs are images and the outputs are the properties were obtained from those images [1,2]. Segmentation of intensity images (such as mammograms), contains four types of methods: thresholding techniques, boundary-based methods, region-based methods, and hybrid techniques that used both boundary and region criteria [

The thresholding in mammograms images is based on separated the histogram into background and breast tissues. Depending on the value of threshold all pixels less than the threshold are classified as background, and the reminder pixels are breast or vice versa [1-5]. As a related work there are many researchers used (global or local) thresholds to split the breast region from background; like in [

In general, the previous thresholding techniques have disadvantages including some need manual adjustment of thresholds, and others require local statistics to get the thresholds (local thresholds) [

To analyze and process any image we should know that an image is generated from a set of pixels denoted as n; for each image level there are a set of pixels denoted as n_{i}. Therefore, the total number of pixels is defined as:

Gray level histogram is normalized and regarded as a probability distribution:

The gray level of an image is [0… L−1]. where the gray level 0 is the darkest and the gray level L−1 is the lightest.

The probability of occurrence of the two classes can be denoted as the following:

(3)

The mean and variance of the foreground and background are denoted respectively as the following:

, (4)

, (5)

It worth to mention that in each image there is a specific thresholding algorithm used to get an optimal threshold, which separated the object from the background.

Otsu method is based on established the optimal threshold that (minimizing intra-class variance) or maximizing inter-class variance. The following equations will represent the within-class variance, and the between class variance respectively.

The final form of between-class variance can also be denoted as the following:

Otsu method is known as: It’s simple, effective, easier to apply and choosing the optimal threshold is automatically and stably [

The position of the optimal threshold is displayed in

The reason for formulating valley emphasis technique is that it can establish an optimal threshold for both bi-

modal and unimodal histogram. In other word, it can extract large and small objects from the background. This technique can be considered as a modified of Otsu method, which failed in detection small objects. Establishing the optimal threshold will be based on two factors:

• It should have minimum probability of occurrence (valley in the grey level histogram).

• Making between class variance is larger as much as possible like in Otsu method.

The valley-emphasis equation is as in [

In this technique the smallest probability of occurrence h (t) value; means the largest the weight (1 − h (t)). The largest weight confirms that the chosen threshold is in the valley between two peaks for (bimodal histogram) as seen in

To give more reliable segmentation result; a neighbourhood valley emphasis technique is presented. It developed the prior technique by computing the grey values for both the valley point and its neighborhood. So that, selection the optimal threshold will be based on maximum weight of the valley and its neighborhood.

If the image has one dimensional histogram h(i); the neighborhood grey value h(i) of the grey level i is denoted as :

Equation (10) refers to the sum of probability of occurrence for the neighborhood valley point; within the range n = 2m + 1. Where n is denoted as neighborhood length; usually it is odd number.

The neighborhood valley emphasis technique is de-

noted as the following:

The optimal threshold which increasing between class variance will be denoted as the following:

Equation (11) represents the smallest probability of occurrence of the valley point and its neighborhood; in contrast, to Equation (9) that has only minimum probability of occurrence of the valley point.

This technique is suitable for processing images with big diversity between the object variance and background variance [

A presented technique used both within-class variance and the intensity contrast at the same time.

This technique succeeded in extraction an object from complex background distribution in an image. It is idea based on attempt to make the within class variance is smallest, and the intensity contrast is largest simultaneously. In addition, there is a parameter λ that represents the important factor in the formula. It’s a weight that balanced the contribution for the (within class variance and intensity contrast).

The proposed formula is defined as the following:

where (t), (t) are the mean intensities of the object and background. Refers to the square root of within-class variance; the is formulated from the following equation (14).

In Equation (14), the first term refers to the probability of class occurrence and the standard deviation (variance) of the first class, while the second term refers to the probability of class occurrence and the standard deviation (variance) of the second class.

The optimal threshold will dichotomize the image into object and background to get best segmentation result [

The presented technique is used for segmented images that have large variance discrepancy between the object and background. It computes both the variance sum and variances discrepancy to get effective segmentation outcomes.

The introduced technique is formulated as the following:

where

and

or

.

σ_{D}(t) Is a measurement of the two classes. σ_{0}^{1}(t), σ_{0}^{2}(t) are the standard deviation (variances) for the two classes. α is a main factor that determines the contributions of variance sum and variance discrepancy.

The optimal threshold will tend to make the effect of class variance sum is smallest, and increase the focus of variance discrepancy at the same time [

The quality of thresholding technique is a critical issue; it various depending on the type of the thresholding technique and the kind of image. In order to analyze the performance of the thresholding techniques, there are different evaluation methods used to measure their robustness and efficiency. In our study we used two evaluation methods Region Non-Uniformity (NU) and Inter-Region Contrast (GC) [

This method measures the ability to distinguish between the background and object in the thresholded image. A good thresholded image should contain higher intra region uniformity, which is related to the similarity attribute about region element In the following NU Equation (17): σ^{2}(t) denotes to the variance of the whole image, while σ_{0}^{2}(t) denotes to the variance of the object (foreground). w_{0}(t) denotes to the probability of occurrence of the object. NU equal to zero denotes to well thresholded image, but NU = 1 denotes to incorrect thresholded image [

This method is very important in measure the contrast degree in the thresholded image. A good thresholded image should have higher contrast across adjacent regions. In the following GC Equation (18) the object average gray-level is known as μ_{0}(t), and the background average gray-level is known as μ_{b}(t) [

In the following examples we applied the thresholding techniques on negative mammogram images in order to bring the part of interest from bright region (second mode) to dark region (first mode) and then determine the threshold values. It is worth to mention that the radiologist diagnosis the first

In the first example

Most early breast cancer can be diagnosed by detecting micro calcifications in the mammogram image.

average = 0.169415. On the other hand, the smallest inter region contrast GC = 0.319315 is presented from variance discrepancy method.