Dynamic graph cut based segmentation of mammogram
 S. Pitchumani Angayarkanni^{1}Email author,
 Nadira Banu Kamal^{2} and
 Ranjit Jeba Thangaiya^{3}
Received: 22 July 2015
Accepted: 23 July 2015
Published: 12 October 2015
Abstract
This work presents the dynamic graph cut based Otsu’s method to segment the masses in mammogram images. Major concern that threatens human life is cancer. Breast cancer is the most common type of disease among women in India and abroad. Breast cancer increases the mortality rate in India especially in women since it is considered to be the second largest form of disease which leads to death. Mammography is the best method for diagnosing early stage of cancer. The computer aided diagnosis lacks accuracy and it is time consuming. The main approach which makes the detection of cancerous masses accurate is segmentation process. This paper is a presentation of the dynamic graph cut based approach for effective segmentation of region of interest (ROI). The sensitivity, the specificity, the positive prediction value and the negative prediction value of the proposed algorithm are determined and compared with the existing algorithms. Both qualitative and quantitative methods are used to detect the accuracy of the proposed system. The sensitivity, the specificity, the positive prediction value and the negative prediction value of the proposed algorithm accounts to 98.88, 98.89, 93 and 97.5% which rates very high when compared to the existing algorithms.
Keywords
Fuzzification Graph cut Otsu’s method and ROCIntroduction
The population based cancer registry evidently shows from the various statistics, that the incidence of breast cancer is rapidly rising, amounting to a significant percentage of all cancers in women. Breast cancer is the commonest cancer in urban areas in India and accounts for about 25–33% of all cancers in women. Over 50% of the breast cancer patients in India, being in stages 3 and 4 will definitely face the survival problem (Hassanien and Ali 2011). The survival rate can be increased only through early diagnosis. Image processing technique together with data mining is used for extraction and analysis of the ROI. Tumor can be classified into three categories normal, benign and malignant. A normal tumor is a mass of tissue which exists at the expense of healthy tissue. Malignant tumor has no distinct border. They tend to grow rapidly, increasing the pressure within the breast cells and can spread beyond the point from which they originate. Thus they grow faster than benign tumors and cause serious health problems if, left unnoticed. Benign tumors are composed of harmless cells and they have clearly defined borders. They can be completely removed and are unlikely to recur. MRI mammogram images taken after the appropriate segmentation of the tumor make classification of tumor into malignant, benign and normal a difficult task, due to complexity and variation in tumor tissue characteristics like its shape, size, grey level intensities and location. Effective segmentation techniques results in accurate classification of such cancerous masses.
Data acquisition
A database of 1,528 mammograms, originating from the mammography image analysis society (MIAS), digital database for screening mammography, University of South Florida DDSM Resource, LLNL/UCSF database (Lawrence Livermore National Laboratories (LLNL), University of California at San Francisco) and Nijmegen digital mammogram database were used for the study.
Methodology
Image preprocessing and enhancement

α = min

β1 = (α + γ)/2

β2 = (max + γ)/2

γ = max/2
Procedure:
Step 1: Fuzzification:
The following fuzzy rules are used for contrast enhancement:
Rule1:
If α ≤ u_{i} < β1 then P = 2 ((u_{i} − α)/(γ − α))^{2}
Rule2:
If β1 ≤ u_{i} < γ then P = 1 − 2 ((u_{i} − γ)/(γ − α))^{2}
Rule3:
If γ ≤ u_{i} < β2 then P = 1 − 2((u_{i} − γ)/(max − γ))^{2}
Rule4:
If β2 ≤ u_{i} < max then P = 2 ((u_{i} − γ)/(max − γ))^{2}
where u_{i} = f(x,y) is the ith pixel intensity
Step 2: Fuzzy Modification
Step 3: Defuzzification
The quality of the preprocessed image is to be checked with the following parameters like peak signal to noise ratio (PSNR), noise standard deviation (NSD), mean square error (MSE), equivalent number of looks (ENL).
Image segmentation and ROI extraction
The region of interest i.e. the tumor region is segmented using the Graph cut method. The main purpose of using this method for segmentation is that it segments the mammogram into different mammographic densities. It is useful for risk assessment and quantitative evaluation of density changes. Apart from the above advantage it produces the contour (closed region) or a convex hull which is used for analyzing the morphological and novel features of the segmented region. The above technique results in efficient formulation of attributes which helps in classification of the ROI into benign, malignant or normal. Graph cuts have been used in recent years for interactive image segmentation (Hassanien and Badr 2003). The core ideology of graph cuts is to map an image onto a network graph, and construct an energy function on the labeling, and then do energy minimization with dynamic optimization techniques. This study proposes a new segmentation method using iterated graph cuts based on multiscale smoothing. The multiscale method can segment mammographic images with a stepwise process from global to local segmentation by iterating graph cuts. The modified graph cut approach used by K. Santle Camilus (Hassanien and Badr 2003) is implemented in this project.
 1.
Form a graph
 2.
Sort the graph edges
 3.
Merging regions based on threshold
 1.
Sort the edges in ascending order of their weights such that W(e_{1}) ≤ W(e_{2}).
 2.
Pick one edge e_{i} in the sorted order from e_{i} to e_{n} where e_{i} is between two groups of pixels which determines whether to merge the two groups of pixel to form a single group or not. Each vertex is considered as a group. The two groups which satisfies the merge criteria are merged together. The different groups of pixels representing different regions or objects are obtained.
 3.Determining the merge criteria: When the pixels of a group have intensity values similar to the pixels of the other group, then intuitively the calculated IRM between these groups should be small. The expected smaller value of the IRM to merge these two regions is tested by comparing it with the dynamic threshold. Hence, the merge criterion, to merge the two regions, R _{1} and R _{2}, is defined as:$$ {\text{Merge}}\left( {{\text{R}}_{ 1} ,{\text{R}}_{ 2} } \right),\quad {\text{if IRM}}\left( {{\text{R}}_{ 1} ,{\text{R}}_{ 2} } \right) \le DT({\text{R}}1,R2) $$
Performance analysis
Performance measure of the proposed mathematical approach at each stage was estimated.
Preprocessing
Segmentation
Segmentation technique comparision
Parameters  Hassanien method  Proposed method 

Target to background contrast measure based on standard deviation  0.71  0.83 
Target to background contrast measure based on entropy  0.76  0.90 
Index of fuzziness  0.2892  0.010 
Fuzzy entropy  0.1056  −0.001 
PSNR  86.75  90.88 
Segmentation accuracy
Segmentation accuracy metrics
Specificity  95.5% 
Sensitivity  97.3% 
Positive prediction value  89% 
Accuracy  98.9% 
Area under curve  0.98 
Negative prediction value  98% 
Computational efficiency
Computational efficiency of the proposed method
Methods  References  System specification  Computational time based on implementation 

Rough set approach  Hassanien and Ali (2011)  Intel Pentium^{®} CPU B950 Processor 2 GB RAM 32bit OS Windows 7  2′19″ 
Mathematical Morphological  Bojar and Nieniewski (2008)  2′50″  
Shape and texture feature  Zakeri et al. (2012)  8′21″  
Shape, edgesharpness, and texture features  Mu et al. (2008)  0′45″  
Proposed method  Angayarkanni et al. (2002)  0′03″ 
Metrics for evaluating the segmentation technique includes
The regionbased criteria mutually compare the machine segmented regions with the correct ground truth regions.
Let A(I, J) denote the machine segmented region and B(I, J) denotes the ground truth region then the region overlap acceptance is controlled by the threshold k = 0.75 then
Edgel matching Overlay the original with segmented image and compute correspondence via mincost assignment on bipartite graph.
Conclusions
The proposed mathematical approach yields a high level of accuracy within a minimum period of time that confirms the efficiency of the algorithm. The GUI based CAD system was developed using Scilab and R2. The segmentation speed accounts to 6 ms using graph cut based Otsu’s thresholding. The main goal of classifying the tumors into benign, malignant and normal is achieved with a great accuracy compared to other techniques because of the implementation of the accurate segmentation technique employed. The proposed technique is computationally efficient as specified in the tabulation above. Further the complexity of the algorithm in asymptotic sense is equivalent to o(log n).
Declarations
Authors’ contributions
A mathematical model for effective detection and segmentation of cancerous masses has been proposed. All authors read and approved the final manuscript.
Acknowledgements
Nil.
Compliance with ethical guidelines
Competing interests The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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