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For the calculation of ANOVA, Five groups are considered. The statistical parameters are applied for ANOVA calculation[17]. The important calculations are:

Sum of Squares between groups(SSB) = 5.68E+07

Sum of Squares within the group(SSW) = 9.25E+06

F(4,45) = 69.1, p < 0.05 (P = significance factor)

Critical value = 2.61 (approximately according to F-distribution table for F(4,45)

F test value > critical value i.e, 69.1> 2.61.

Hence Proposed approach rejects the null hypothesis. Which mean that our approach is correct.

In the present approach,we mainly concentrated on pre-processing step in representing the presence of cancer through various techniques and also applying Statistical parameters to distinguish cancerous to the non cancerous images. Then verifying that our approach is correct with ANOVA calculation. The present approach can further be extended to implement in Xilinx to diagnoise the cancer based on statistical parameters. Also finding the number of cancer cells present. Carcinoma is the most life threatening disease of which Lung cancer and Breast cancer are of high risk.

This approach aims at diagnosing carcinoma at an earlier stage by considering innovative algorithms. In this approach, a mammogram image is considered. To this image, image segmentation technique is applied which separates fore-ground regions from the background regions. Later, Binarization technique is used to improve the contrast of the image in order to make it more suitable for finding the tumour cell location in the affected area. Median filter is used for removing noise in the image.

To the noise-free images some statistical parameters are calculated. They are mean, variance, Standard deviation, Mean Square error and entropy are calculated. These approaches are done in order to improve the performance in statistical approach. Results are processed using MATLAB software.

Segmentation, Binarization, Carcinoma, Mammogram, Mean, Variance, Standard Deviation, Entropy ANOVA.

Carcinoma is the most life threatening disease in which abnormal cells divide without any control and can even occupy the cells nearby. As per 2018 American cancer society statistics 268,670 breast cancers are estimated, out of which expected deaths are 63,690 and 234,030 Lung cancers are estimated, out of which expected deaths are 154,040.[1] Cancers are of five types[2]. They are Carcinoma, Sarcoma, Melanoma, Lymphoma, and Leukemia, out of which Carcinoma is the most leading cause of deaths. Now-a-days the most affected Carcinoma are Lung and Breast cancer. Carcinoma are the most commonly diagnosed disease that originate in Skin, Lungs, Breasts, Pancreas and other organs and glands. Sarcoma is a rare kind of cancer. Sarcomas are different from other common carcinomas because they happen in a different kinds of Tissues. Skin cancers include Melanoma, Basal cell carcinoma, Squamous cell carcinoma. Basal and Squamous cell are common and treatment is very effective. Lymphoma is a cancer that begins at the infection fighting cells of Immune systems called Lymphocytes(white blood cells). These occur at Spleen, Thymus, and Bone marrow. Leukemia is a disorder which is usually a children’s condition, but it actually affects mostly adults. It’s more in men than women. Of all types of carcinomas, Breast cancer and Lung cancer accounts for more number of deaths[3]. One of powerful tool is the breast mammogram for detecting breast cancer[4]. For Lung cancer we consider Lung microscopic images[5-6]. These diseases are associated with structural changes in the Breast. Mammogram images gives the information about shape, color, size and texture which are used for the improved diagnosis and treatment of a complex disease. Mammogram is cost effective when compared to MRI and other scans. By considering scanned images it facilitates in examining the disease effectively by considering certain image enhancements techniques[7].In this work, Breast Mammograms and Microscopic Lung images are considered for diagnosing Breast cancer and Lung cancer. To these images Pre-processing is performed. Pre-processing step consists of Image segmentation and image Binarization. In image segmentation, we consider Variance Thresholding method, Watershed technique, DWT and edge detection techniques[12]. These techniques are compared and performance analysis is done between the obtained results. Pre-processing step is followed by a filtering process to remove noise in the images. The filters used in this process Median filter, Mean filter and Gaussian filter. Mean filter computes the value of each output pixel by finding the average of neighborhood pixels of the input image. Median filter is a non linear filter used to remove the noise from the image preserving the edges of the image. Gaussian filter These results are compared for the betterment of the output. Then Intermediate information method is performed in which Mean, Variance, Entropy, Standard Deviation, Mean Square Error and Skewness are calculated. Correlation is performed between reference parameters and intermediate information parameters. Euclidean distance is calculated for the images. The parameters are trained for a set of known breast mammogram and MRI and lung microscopic images. The parameters obtained during training phase and test phase are used to identify the disease.

Image Segmentation: The main aim of Image segmentation is to change the representation of the image into a purposeful image that is more suitable and easy to examine. Image segmentation is an important facet of digital image processing. Image Segmentation is used to locate the boundaries and curves. Image segmentation can be defined as a process of assigning pixels to homogeneous and disjoint regions which form a partition of the image that share some visual characteristics in the breast mammogram and lung microscopic image. The gray intensity of a muscle region is similar to that of the breast tumor cells and sometimes the muscles texture may also be similar to some abnormalities. A gray level image consists of two main features, namely region and edge. Segmentation algorithms generally are based on one of the two basic properties of intensity values.

- Discontinuity: to partition an image based on sharp changes in intensity
- Similarity: to partition an image into regions that is similar according to a set of predefined criteria.

In the first category, the approach is to partition an image based on abrupt changes in intensity, such as edges in an image[14]. The approach in the second category is based on partitioning image into regions that are similar according to a set of predefined criteria. Thresholding, Region growing and Region splitting and Merging are examples of the methods in this class. A mammogram has two distinctive regions exposed breast region and the unexposed non-breast region. The main feature on a mammogram is the breast contour, also known as Breast boundary. The breast contour can be obtained by partitioning the mammogram into breast and non breast regions. The extracted breast contour should adequately modeled.

Thus this approach provides the following goals:

- Specifies the locations of suspicious areas to suggest the radiologists during the diagnosis.
- Classifying the abnormalities of the breast as benign or malignant.
- Spotting prominent regions in mammograms such that conspicuous regions corresponding to distinctive areas that may include the breast boundary, the pectoral muscle, masses and some other dense tissue regions.

In this paper Thresholding is performing using Variance thresholding and Watershed algorithms.

Image Binarization: After the images are segmented,they are then converted to binary form. Binary images are easier to process and analyse than gray levels. The basic principle of converting an image into binary is to decide a threshold value, and then the pixels whose value are more than the threshold are converted to white pixels, and the pixels whose value are less than or equal to the threshold are converted to black pixels. If the threshold value is too large, results shows that fore ground regions are incorrectly assigned as background regions. If the threshold value is too small, results shows that background regions are incorrectly assigned as fore ground regions[14].

Average Information Method: This technique is based on averaging of the intensity level for every pixel position in an image. Every scanned image contains two sections that is steady indicator part and random noise component part[15]. In the averaging process, signal part remains constant but noise part changes from frame to frame. Signal part has impact on summation when contrast on noise section[16]. The parameters under Average information Method are:

- Mean: It calculates the Mean of the gray levels in the image. Mean depends on first moments of the data. Fist moment is represented as in eq
- Variance: It explains about the distribution of gray levels over the image. If the value of variance is high, the gray levels are spreaded extensively. It explains about the probability of distribution, which describes how far the value lies away from the mean. The second moment is given as in eq
- Entropy: It indicates average information of the image. Low entropy means no uncertainty of the image .The algorithm for this work is realized through MATLAB software. The steps for the algorithm are as follows:

Step 1: microscopic lung images and breast images are taken as an input image.

Step2: pre-processing step is performed which consists of image segmentation using variance thresholding and watershed approach. Image enhancement is done by using edge detection algorithms.

Step 4: Implementation of statistical parameters like mean and variance, Mean Square Error, entropy and Skewness values on both lung and breast images.

Step 5: calculating the statistical range for each parameter.

Step 6: Based on the Mean, variance, Mean Square Error, entropy and Skewness values graphs are plotted which differentiate non cancerous from the cancerous.

Step 7: Accuracy is calculated for each parameter and plotted on the graph.

In this paper, we consider both Breast and Lung cancerous image samples and pre-processed using Matlab software. Statistical parameters are performed for these image samples. Statistical parameters include calculating Mean,Variance, Standard Deviation, Entropy, Mean Square Error and Skewness. Performing these statistical parameters on 100 samples, Cancerous and non Cancerous values can be differentiated. Range is calculated for each parameter of Cancerous image. If the value of particular image lies in that range, then it is treated as cancerous. In the same way Range is calculated for non-Cancerous images.

Now analyse the individual parameter response for both Cancerous and non Cancerous. This will help us to better understand the impact of that particular parameter on both Cancerous and non Cancerous images. Graphical analysis of 16 samples of cancerous and 8 samples of non Cancerous are shown for each parameter in figure 5 to 10. From the Figures below we can say that lesser the overlap of the points for cancerous and non-cancerous images, better is the utility of the parameter for Cancer detection. Nearly all parameters have shown good response

According to the graphs obtained, clearly shows that the range for Cancerous and non Cancerous are different. From these graphs one can observe that higher values posses Cancer than that of the images with no Cancer. These parameters indicates certain variation or growth in particular part which may be Breast or a Lung. In terms of image processing, Standard Deviation shows how much variation or dispersion exists from expected value. Skewness is the measure of asymmetry of probability distribution of real valued random variable. Negative value indicate data is skewed left, which means left side is elongated to the right side

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