Bio-Medical Materials and Engineering 24 (2014) 53–59 DOI 10.3233/BME-130783 IOS Press
53
Automatic detection of microcalcifications using mathematical morphology and a support vector machine Erhu Zhang*, Fan Wang, Yongchao Li, and Xiaonan Bai Department of Information Science, Xi’an University of Technology, Xi’an,Shaanxi, 710048, China
Abstract. In this paper, we propose a novel method for the detection of microcalcifications using mathematical morphology and a support vector machine (SVM). First, the contrast in the original mammogram was improved by gamma correction and two carefully designed structural elements were used to enhance any microcalcifications. Next, the potential regions were extracted using our proposed dual-threshold technique. Finally, a SVM classifier was used to reduce the number of false positives. The performance of the proposed method was evaluated using the MIAS database. The experimental results demonstrated the efficiency and effectiveness of our method. Keywords: feature extraction, mathematical morphology, microcalcification, support vector machine
1. Introduction Breast cancer is one of the most common malignant diseases in women and about 25% of all cancers diagnosed in women are breast cancers [1]. The early signs of breast cancer are microcalcifications and their early detection can increase the chance of survival [2]. Automatic detection remains the most challenging task in mammography[3,4,5]. This is due to the poor contrast in mammogram images and the microcalcifications are often embedded in dense tissues, which can cause false positives. In this study, we developed a new method for detecting microcalcifications using mathematical morphology and a support vector machine(SVM). The method has three stages. In the first stage, gamma correction and mathematical morphology, is applied to improve the image contrast and the microcalcifications. The second stage is coarse detection and we developed a dual-threshold method to detect potential microcalcification regions. Finally, features are extracted from each region and a SVM classifier is used to reduce false positives. The performance of our proposed method was evaluated using the MIAS database and the experimental results demonstrated the effectiveness of our approach. The main novel aspect of our approach is the comprehensive exploitation of mathematical morphology properties. Our main contributions are as follows. 1) Two structural elements were designed carefully to enhance microcalcifications: the center symmetry is used to enhance the object details near the *
E-mail: [email protected].
0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
54
E. Zhang et al. / Automatic detection of microcalcifications using mathematical morphology and SVM
center position; elements outside the center symmetry are used to improve the details of the object edge. 2) We developed a strategy to facilitate the coarse detection of microcalcifications. The suspected microcalcifications can then be extracted using the proposed dual-threshold technique. The remainder of this paper is organized as follows. Section 2 introduces the proposed approach. Our experiments are presented in Section 3, which demonstrated the effectiveness of the proposed method. Finally, our conclusions are given in Section 4. 2. Proposed method
Fine detection
Coarse detection Mammogram enhancement
Figure 1 shows a flowchart of our method, which contains three modules. 1) Mammogram enhancement: we use gamma correction and a dual-structural element based on a mathematical morphology to enhance the microcalcifications. The Top-hat transform is also used to suppress the background. 2) Coarse detection: a dual threshold technique is used to detect potential microcalcification region. 3) Fine detection: the shapes and statistical characteristics of each microcalcification identified by coarse detection are extracted and fed into the SVM to reduce the number of false positives. Read the mammogram Gamma correction
Gradient operation using dual-structural element
Top – hat transform
Coarse detection of microcalcifications using dual-threshold segmentation method Remove smaller or larger region of the segmentation results Feature extraction of suspected microcalcifications
Fine detection of microcalcifications using SVM
Fig. 1 Flowchart of the proposed method.
2.1. Gamma correction of the original mammogram Gamma correction is used to improve the lower overall contrast of the image, as follows: 1
F (x, y ) = ( I (x, y )) γ
(1)
where I ( x, y ) is the original mammogram, F ( x, y ) is the image improved by gamma correction, and γ
E. Zhang et al. / Automatic detection of microcalcifications using mathematical morphology and SVM
55
is the gamma value (3 in this study) Figure 2 shows the original mammogram and the image after improvement by gamma correction. Clearly, this method enhances the contrast of the image and the potential calcifications are identified.
Fig. 2. Effectiveness of gamma correction and dual-structural elements. (A) Original mammogram. (B) Image after gamma correction. (C) Image after using dual-structural elements.
2.2. Enhancement of microcalcifications based on dual-structural elements The key aspect of mathematical morphology is the design of structural elements. In this section, we describe the design of the two structural elements in detail. The specific processing steps are as follows.
ª0 1 0º ª1 0 1 º « » « » 1) The dual-structural elements are B1 = 1 1 1 B2 = 0 1 0 « » « » «¬1 0 1 »¼ «¬0 1 0»¼ 2) Two gray-scale gradient operations are applied to image F ( x, y ) using B1 and B2 as follows:
G1 ( x, y ) = ( F ( x, y ) ⊕ B1 ( x, y )) − ( F ( x, y )ΘB1 ( x, y ))
(2)
G2 ( x, y ) = ( F ( x, y ) ⊕ B2 ( x, y )) − ( F ( x, y )ΘB2 ( x, y ))
(3)
where the operator “ ⊕ ” is a dilation operation and “ Θ ” is an erosion operation. 3) The final enhanced image F1 ( x, y ) is obtained using Eq. (4).
F1 ( x, y ) = F ( x, y ) + G1 ( x, y ) + G2 ( x, y )
(4)
Figure 2(C) shows the image obtained using this method, which illustrates that the microcalcifications have been enhanced. 2.3. Object detection based on the Top-hat transform The Top-hat transform is a useful method for extracting objects similar to the structural elements. Based on this property, a circular structural element can be designed that is larger than the potential microcalcification object and used to suppress the background. The specific process is as follows.
56
E. Zhang et al. / Automatic detection of microcalcifications using mathematical morphology and SVM
ª0 «0 « 1) The structural element is: B3 = «1 « «0 «¬0
0 1 1 1 0
1 1 1 1 1
0 1 1 1 0
0º 0»» 1» » 0» 0»¼
2) The background-suppressed image, F2 ( x, y ) , is obtained by applying the Top-hat transform, as follows:
F2 ( x, y ) = F ( x, y ) − ( F ( x, y ) D B3 ( x, y ))
(5)
where “ D ” denotes the morphological open operation. 2.4. Coarse detection of microcalcifications In this section, we describe the dual-threshold method that we developed to segment images F1 ( x, y ) and F2 ( x, y ) , which were described in sections 2.2 and 2.3. By taking the size of microcalcifications into consideration, we can remove false calcification regions with smaller or larger areas. Suppose Vm1 is the maximum value of image F1 ( x, y ) and Vm 2 is the maximum value of image F2 ( x, y ) , then the advisable dual-threshold for T1 and T2 is:
T1 = αVm1 ® ¯T2 = β Vm 2
(6)
where the coefficients α and β can be determined experimentally. In this study, we determined the value of α as 0.85 and β was 0.80. The microcalcification regions can be segmented using thresholds T1 and T2 as follows.
1 F1 ( x, y ) > T1 & F2 ( x, y ) > T2 F3 ( x, y ) = ® ¯0 otherwise
(7)
Given that an object has a specific size, we can use a connected component method to remove areas with less than two pixels or greater than 20 pixels from image F3 ( x, y ) . Figure 3 (A) shows the coarse detection results from Fig. 2(A). Figure 3(B) shows the results obtained by adding Fig. 3(A) and Fig. 2(A). Figure 3(C) shows the results obtained by expert marking. A comparison of Fig. 3(B) and Fig. 3(C) shows that there are many false positive regions in the coarse detection results. Thus, further feature extraction and classification are required to remove these false positive regions.
E. Zhang et al. / Automatic detection of microcalcifications using mathematical morphology and SVM
57
Fig. 3. The effects of coarse detection and fine detection on the appearance of the potential microcalcifications. (A) The results obtained by coarse detection. (B) The results obtained by coarse detection marking in the original image. (C) The results obtained by expert marking. (D) The results obtained by fine detection.
2.5. Feature extraction Many features have been proposed for the characterization of microcalcifications [6,7]. In this section, the most effective four features are selected for charactering microcalcifications. Suppose that Ω f is the set of pixels in the coarse object and N f is the number of pixels in the object region. The object is surrounded by a minimum circumscribed rectangle, which can be expanded one pixel up, down, left, or right to form the region Ωb , where Nb is the number of pixels in Ωb . Each feature is defined as follows: 1 1 2 Mean value: μ = Variance: σ 2 = F ( x, y ) ( F ( x, y ) − μ ) ¦ ¦ N f ( x , y )∈Ω f N f ( x , y )∈Ω f Degree of circularity: ρ =
P2 4π S
Contrast:
C=
μ −b μ +b
where P is the perimeter of the object and S is the area of the object, b =
1 Nb
¦
F ( x, y ) .
( x , y )∈Ωb
2.6. Real microcalcification detection based on a SVM The identification of microcalcifications is actually a binary classification problem. Thus, we used a SVM for the fine detection of microcalcifications. The training sample set is {( xi , yi ) i = 1, 2," , n} , where x i∈ R d are the feature vectors and yi ∈ {+1, − 1} are the sample categories, so the classification function is:
§ n · f ( x) = sgn ¨ ¦αi yi K ( xi , x) + b ¸ © i =1 ¹
(8)
where K (
53
Automatic detection of microcalcifications using mathematical morphology and a support vector machine Erhu Zhang*, Fan Wang, Yongchao Li, and Xiaonan Bai Department of Information Science, Xi’an University of Technology, Xi’an,Shaanxi, 710048, China
Abstract. In this paper, we propose a novel method for the detection of microcalcifications using mathematical morphology and a support vector machine (SVM). First, the contrast in the original mammogram was improved by gamma correction and two carefully designed structural elements were used to enhance any microcalcifications. Next, the potential regions were extracted using our proposed dual-threshold technique. Finally, a SVM classifier was used to reduce the number of false positives. The performance of the proposed method was evaluated using the MIAS database. The experimental results demonstrated the efficiency and effectiveness of our method. Keywords: feature extraction, mathematical morphology, microcalcification, support vector machine
1. Introduction Breast cancer is one of the most common malignant diseases in women and about 25% of all cancers diagnosed in women are breast cancers [1]. The early signs of breast cancer are microcalcifications and their early detection can increase the chance of survival [2]. Automatic detection remains the most challenging task in mammography[3,4,5]. This is due to the poor contrast in mammogram images and the microcalcifications are often embedded in dense tissues, which can cause false positives. In this study, we developed a new method for detecting microcalcifications using mathematical morphology and a support vector machine(SVM). The method has three stages. In the first stage, gamma correction and mathematical morphology, is applied to improve the image contrast and the microcalcifications. The second stage is coarse detection and we developed a dual-threshold method to detect potential microcalcification regions. Finally, features are extracted from each region and a SVM classifier is used to reduce false positives. The performance of our proposed method was evaluated using the MIAS database and the experimental results demonstrated the effectiveness of our approach. The main novel aspect of our approach is the comprehensive exploitation of mathematical morphology properties. Our main contributions are as follows. 1) Two structural elements were designed carefully to enhance microcalcifications: the center symmetry is used to enhance the object details near the *
E-mail: [email protected].
0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
54
E. Zhang et al. / Automatic detection of microcalcifications using mathematical morphology and SVM
center position; elements outside the center symmetry are used to improve the details of the object edge. 2) We developed a strategy to facilitate the coarse detection of microcalcifications. The suspected microcalcifications can then be extracted using the proposed dual-threshold technique. The remainder of this paper is organized as follows. Section 2 introduces the proposed approach. Our experiments are presented in Section 3, which demonstrated the effectiveness of the proposed method. Finally, our conclusions are given in Section 4. 2. Proposed method
Fine detection
Coarse detection Mammogram enhancement
Figure 1 shows a flowchart of our method, which contains three modules. 1) Mammogram enhancement: we use gamma correction and a dual-structural element based on a mathematical morphology to enhance the microcalcifications. The Top-hat transform is also used to suppress the background. 2) Coarse detection: a dual threshold technique is used to detect potential microcalcification region. 3) Fine detection: the shapes and statistical characteristics of each microcalcification identified by coarse detection are extracted and fed into the SVM to reduce the number of false positives. Read the mammogram Gamma correction
Gradient operation using dual-structural element
Top – hat transform
Coarse detection of microcalcifications using dual-threshold segmentation method Remove smaller or larger region of the segmentation results Feature extraction of suspected microcalcifications
Fine detection of microcalcifications using SVM
Fig. 1 Flowchart of the proposed method.
2.1. Gamma correction of the original mammogram Gamma correction is used to improve the lower overall contrast of the image, as follows: 1
F (x, y ) = ( I (x, y )) γ
(1)
where I ( x, y ) is the original mammogram, F ( x, y ) is the image improved by gamma correction, and γ
E. Zhang et al. / Automatic detection of microcalcifications using mathematical morphology and SVM
55
is the gamma value (3 in this study) Figure 2 shows the original mammogram and the image after improvement by gamma correction. Clearly, this method enhances the contrast of the image and the potential calcifications are identified.
Fig. 2. Effectiveness of gamma correction and dual-structural elements. (A) Original mammogram. (B) Image after gamma correction. (C) Image after using dual-structural elements.
2.2. Enhancement of microcalcifications based on dual-structural elements The key aspect of mathematical morphology is the design of structural elements. In this section, we describe the design of the two structural elements in detail. The specific processing steps are as follows.
ª0 1 0º ª1 0 1 º « » « » 1) The dual-structural elements are B1 = 1 1 1 B2 = 0 1 0 « » « » «¬1 0 1 »¼ «¬0 1 0»¼ 2) Two gray-scale gradient operations are applied to image F ( x, y ) using B1 and B2 as follows:
G1 ( x, y ) = ( F ( x, y ) ⊕ B1 ( x, y )) − ( F ( x, y )ΘB1 ( x, y ))
(2)
G2 ( x, y ) = ( F ( x, y ) ⊕ B2 ( x, y )) − ( F ( x, y )ΘB2 ( x, y ))
(3)
where the operator “ ⊕ ” is a dilation operation and “ Θ ” is an erosion operation. 3) The final enhanced image F1 ( x, y ) is obtained using Eq. (4).
F1 ( x, y ) = F ( x, y ) + G1 ( x, y ) + G2 ( x, y )
(4)
Figure 2(C) shows the image obtained using this method, which illustrates that the microcalcifications have been enhanced. 2.3. Object detection based on the Top-hat transform The Top-hat transform is a useful method for extracting objects similar to the structural elements. Based on this property, a circular structural element can be designed that is larger than the potential microcalcification object and used to suppress the background. The specific process is as follows.
56
E. Zhang et al. / Automatic detection of microcalcifications using mathematical morphology and SVM
ª0 «0 « 1) The structural element is: B3 = «1 « «0 «¬0
0 1 1 1 0
1 1 1 1 1
0 1 1 1 0
0º 0»» 1» » 0» 0»¼
2) The background-suppressed image, F2 ( x, y ) , is obtained by applying the Top-hat transform, as follows:
F2 ( x, y ) = F ( x, y ) − ( F ( x, y ) D B3 ( x, y ))
(5)
where “ D ” denotes the morphological open operation. 2.4. Coarse detection of microcalcifications In this section, we describe the dual-threshold method that we developed to segment images F1 ( x, y ) and F2 ( x, y ) , which were described in sections 2.2 and 2.3. By taking the size of microcalcifications into consideration, we can remove false calcification regions with smaller or larger areas. Suppose Vm1 is the maximum value of image F1 ( x, y ) and Vm 2 is the maximum value of image F2 ( x, y ) , then the advisable dual-threshold for T1 and T2 is:
T1 = αVm1 ® ¯T2 = β Vm 2
(6)
where the coefficients α and β can be determined experimentally. In this study, we determined the value of α as 0.85 and β was 0.80. The microcalcification regions can be segmented using thresholds T1 and T2 as follows.
1 F1 ( x, y ) > T1 & F2 ( x, y ) > T2 F3 ( x, y ) = ® ¯0 otherwise
(7)
Given that an object has a specific size, we can use a connected component method to remove areas with less than two pixels or greater than 20 pixels from image F3 ( x, y ) . Figure 3 (A) shows the coarse detection results from Fig. 2(A). Figure 3(B) shows the results obtained by adding Fig. 3(A) and Fig. 2(A). Figure 3(C) shows the results obtained by expert marking. A comparison of Fig. 3(B) and Fig. 3(C) shows that there are many false positive regions in the coarse detection results. Thus, further feature extraction and classification are required to remove these false positive regions.
E. Zhang et al. / Automatic detection of microcalcifications using mathematical morphology and SVM
57
Fig. 3. The effects of coarse detection and fine detection on the appearance of the potential microcalcifications. (A) The results obtained by coarse detection. (B) The results obtained by coarse detection marking in the original image. (C) The results obtained by expert marking. (D) The results obtained by fine detection.
2.5. Feature extraction Many features have been proposed for the characterization of microcalcifications [6,7]. In this section, the most effective four features are selected for charactering microcalcifications. Suppose that Ω f is the set of pixels in the coarse object and N f is the number of pixels in the object region. The object is surrounded by a minimum circumscribed rectangle, which can be expanded one pixel up, down, left, or right to form the region Ωb , where Nb is the number of pixels in Ωb . Each feature is defined as follows: 1 1 2 Mean value: μ = Variance: σ 2 = F ( x, y ) ( F ( x, y ) − μ ) ¦ ¦ N f ( x , y )∈Ω f N f ( x , y )∈Ω f Degree of circularity: ρ =
P2 4π S
Contrast:
C=
μ −b μ +b
where P is the perimeter of the object and S is the area of the object, b =
1 Nb
¦
F ( x, y ) .
( x , y )∈Ωb
2.6. Real microcalcification detection based on a SVM The identification of microcalcifications is actually a binary classification problem. Thus, we used a SVM for the fine detection of microcalcifications. The training sample set is {( xi , yi ) i = 1, 2," , n} , where x i∈ R d are the feature vectors and yi ∈ {+1, − 1} are the sample categories, so the classification function is:
§ n · f ( x) = sgn ¨ ¦αi yi K ( xi , x) + b ¸ © i =1 ¹
(8)
where K (
