Report
Automatic ultrasound segmentation and morphology based diagnosis of solid breast tumors
Ruey-Feng Chang
1, Wen-Jie Wu
1, Woo Kyung Moon
2, and Dar-Ren Chen
31Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan;
2Department of Diagnostic Radiology, Seoul National University Hospital, South Korea; 3Department of Surgery, Changhua Christian Hospital, Changhua, Taiwan
Key words: breast ultrasound, computer-aided diagnosis, level set, shape, support vector machine
Summary
Ultrasound (US) is a useful diagnostic tool to distinguish benign from malignant masses of the breast. It is a very convenient and safe diagnostic method. However, there is a considerable overlap benignancy and malignancy in ultrasonic images and interpretation is subjective. A high performance breast tumors computer-aided diagnosis (CAD) system can provide an accurate and reliable diagnostic second opinion for physicians to distinguish benign breast lesions from malignant ones. The potential of sonographic texture analysis to improve breast tumor clas- sifications has been demonstrated. However, the texture analysis is system-dependent. The disadvantages of these systems which use texture analysis to classify tumors are they usually perform well only in one specific ultrasound system. While Morphological based US diagnosis of breast tumor will take the advantage of nearly independent to either the setting of US system and different US machines. In this study, the tumors are segmented using the newly developed level set method at first and then six morphologic features are used to distinguish the benign and malignant cases. The support vector machine (SVM) is used to classify the tumors. There are 210 ultrasonic images of pathologically proven benign breast tumors from 120 patients and carcinomas from 90 patients in the ultrasonic image database. The database contains only one image from each patient. The ultrasonic images are captured at the largest diameter of the tumor. The images are collected consecutively from August 1, 1999 to May 31, 2000; the patients’ ages ranged from 18 to 64 years. Sonography is performed using an ATL HDI 3000 system with a L10-5 small part transducer. In the experiment, the accuracy of SVM with shape information for classifying malignancies is 90.95% (191/210), the sensitivity is 88.89% (80/90), the specificity is 92.5% (111/120), the positive predictive value is 89.89% (80/89), and the negative predictive value is 91.74% (111/121).
Introduction
Breast cancer has affected one of every eight women in United States and one of every ten women in Europe [1].
Early diagnoses of breast cancer are important. How- ever, early diagnosis requires an accurate and reliable diagnostic procedure that allows physicians to distin- guish benign breast tumors from malignant ones. Al- though there are many diagnostic modalities, biopsy is the best way to do the differential diagnosis. For the lawful and safe reasons, surgeons perform an even increasing number of breast biopsies. However, it is invasive and expensive. Biopsies are sometimes avoid- able for the reason that probability of positive findings at biopsy for cancer is low, between 10% and 31% [2–4].
Ultrasound (US) is a useful diagnostic tool to distinguish benign from malignant masses of the breast [5]. How- ever, there is a considerable overlap benignancy and malignancy in ultrasonic images and interpretation is
subjective. Stavros et al. [6] reported the frequency with which certain morphological features were associated with breast cancer. Several of malignant features referred to the margin of the mass. Descriptors of mass margins associated with a high likelihood of malignancy include:
(a) Angular margins in which obtuse or acute pointed junctions form between the mass and surrounding tissue;
(b) Speculation in which alternating hypoechoic and hyperechoic lines radiate in multiple directions from the mass into the surrounding tissue; (c) Microlobulation characterized by greater than 3 lobulations of the mass surface.
Many techniques have been explored in the segmen- tation of medical images; however, segmentation of ultrasonic images is difficult due to the existence of noise and speckle. The conventional edge-based [7] and region- based methods [8,9] cannot work well in segmenting ultrasonic images. The newly developed level set ap- proach is a kind of deformable model. This method was
begun by Osher and Sethian [10] in the Sethian’s Ph.D.
thesis. Comparing with other classical deformable model, such as snake [11], the principle of the level set approach is an active contour energy minimization that solves the computation of geodesics or minimal distance curves. It is governed by the curvature-dependent speeds of moving curves or fronts. At present, there have been many successful ultrasound segmentation researches using the level set approaches proposed [12–14].
Support vector machines (SVM) [15–17] have been recently proposed as a very effective method for pattern recognition, machine learning and data mining. It is considered a good candidate because of its high gener- alization performance. Intuitively, given a set of points which belongs to either one of two classes, a SVM can find a hyperplane leaving the largest possible fraction of points of the same class on the same side, while maxi- mizing the distance of either class from the hyperplane.
According to [15], this hyperplane, called optimal sep- arating hyperplane (OSH), can minimize the risk of misclassifying examples of the test set. In this study we evaluated a set of breast US images using SVM and shape information for classifying breast tumors. Tumors are first segmented by the level set method and then six morphologic features are used.
Materials and methods
Image data acquisition and feature extraction
The US breast image databases include only histologi- cally confirmed cases; 90 malignant tumors and 120 be- nign tumors which were recorded from August 1, 1999 to May 31, 2000. The ages of the patients were ranged from 18 to 64 years. All the digital images were obtained prior to biopsy using by an ATL HDI 3000 system with a L10-5 small part transducer which is a linear-array transducer with a frequency of 5–10 MHz and a scan width of 38 mm. All the images were supplied by one of the author (Dr. Moon). The region of interest (ROI) which contains the tumor was selected by one of the author (Dr. Chen).
Through out this study, only the ROI sub-images are used to investigate the texture characteristics of benign and malignant lesions. Note that only one lesion is extracted from a patient.
The monochrome ultrasonic images are quantized into 8 bits, i.e. 256 gray levels and the features were stored via the magneto–optical (MO) disks. Then these
images can be analyzed in a personal computer and serve as our experimental data. All solid nodules at US belong over C3 according to ACR (American College of Radiology) Breast Imaging Reporting and Data System (BI-RADS) category. We will utilize these images as our breast images database to further investigate the shape characteristics of benign and malignant tumors.
Morphologic feature extraction
Benign tumors usually have smooth shape and malig- nant tumors tend to have irregular border. According to this hypothesis, six morphologic features were extracted from each tumor to account for such sonographic features. These features are form_factor, roundness, aspect_ratio, convexity, solidity, and extent, respec- tively. Each feature is defined as follows:
1: FormFactor¼ 4p Area
Perimeter2; ð1Þ
2: Roundness¼ 4 Area
p MaxDiameter2; ð2Þ 3: AspectRatio¼MaxDiameter
MinDiameter ð3Þ
4: Convexity¼ConvexPerimeter
Perimeter ; ð4Þ
5: Solidity¼ ConvexArea Area PN
i¼1
ConvexAreai Areai=N
ð5Þ
6: Extent¼ Area
BoundingRectangle; ð6Þ where Area and Perimeter is the area and perimeter of the tumor, Max_Diameter and Min_Diameter are the maximal and minimal dimensions of a tumor at different projection angles, as shown in Figure 1, Con- vex_Perimeter and Convex_Area are the perimeter and area of the convex hull of a tumor, N is the number of tumors in database, and Bounding_Rectangle is the area of the minimal rectangle including the tumor. We show the convex hull and bounding rectangle of a tumor in Figures 2 and 3, respectively.
By the way, when we find Max_Diameter, Min_Diameter, and Bounding_Rectangle, the US ima- ges should be rotated at different angles and then the maximal and minimal features can be found. Because of
Maximal
Diameter Minimal
Diameter
(a) (b)
Figure 1. The maximal and minimal diameters of a tumor. (a) Maximal diameter (b) minimal diameter.
the symmetry property and computation reduction, we only consider the rotation angles from 0 to 180 and the interval is 10. We illustrate the rotated tumors at different angles in Figure 4.
Tumor segmentation
Due to the noise and speckles in the ultrasonic images, first, some noise filtering and edge-enhanced method are needed to reduce the noise and enhance the edge infor- mation in ultrasonic images. And then, the segmentation method will work more efficiently. In this section, the pre-processing and segmentation methods used in this paper are described.
Anisotropic diffusion filtering
There are several fundamental requirements of the noise filtering methods for medical images. First, it should not to lose the important information for object boundaries and detailed structures, second, it should efficiently
remove the noise in the homogeneous regions, and third, it should enhance morphological definition by sharp- ening discontinuities [18].
The anisotropic diffusion filter [19] can get rid of the major drawback of the conventional spatial filters and improve the image quality significantly while preserve the important boundary information. The power of the anisotropic smoothing scheme lies in its dealing with local estimates of the image structures. Smoothing is formulated as a diffusive process, suppressed or stopped at boundaries by selecting locally adaptive diffusion strengths. Hence, in this filter, the smoothing operation could be prevented from across edges, the discontinuities can be preserved, and a weak slope remains nearly un- changed if the slope falls within the monotonically increasing part of the gradient values.
Stick method
In order to obtain a better segmentation result in ultra- sonic images, conventional edge-detection algorithms usually use a low-pass filter to reduce the speckle noise, at the cost of blurring the edges. However, if the contrast of the edge is high, the influence of blurring can be reduced and not significantly impact the segmentation result [20]. Hence, the edge information should be en- hanced for a better segmentation result.
In this study, the anisotropic diffusion filter is used to avoid the blurry problem of conventional low-pass filter and then the stick method is applied to further reduce noise and enhance the edge information. In the ultra- sonic images, boundaries between tissue layers will ap- pear as all sorts of lines; therefore, the edge detection problem can be modeled as a line process [21]. The stick [21], as a set of short line segments of variable orienta- tion, is able to locally approximate the boundaries and to reduce speckles as well as improve the edge infor- mation in the ultrasound images.
convex hull
contour
Figure 2. The convex hull and contour of a tumor.
Bounding Rectangle
Figure 3. The bounding rectangle of a tumor.
Figure 4. The rotated tumors at different angles. (a) 0 (b) 30 (c) 60 (d) 90 (e) 120 (f) 150 (g) 180.
Automatic thresholding method
In an ultrasonic image, the region of the tumor ap- pears to be darker and the background is brighter.
After the image processed through the anisotropic diffusion filter and stick method, we use the thres- holding scheme to turn an ultrasound gray level image into a binary one to separate the tumor from its background. We adopt an automatic threshold-deter- mination method, proposed by N. Otsu [22], which can choose the threshold to minimize the intraclass variance of the black and white pixels automatically.
We also apply an additional control scheme to allow the user to change the threshold value when the user is not satisfied with the threshold value assigned by this automatic method.
Level set method
The level set method [10,23] is a numerical technique for computing and analyzing the front propagation. It
offers a highly robust and accurate method for tracking interfaces moving under complex motions. Instead of propagating the front directly, it embeds the front as the zero level set of a higher order function called the level set function. (see Appendix 1)
In the proposed method, the original ultrasonic im- age is first processed by the anisotropic diffusion filter- ing, stick method, and thresholding method. After the thresholding method, we achieve a binary image and then combine it with the original image. When com- bining, the proportion of each image is 0.5. Finally, we utilize the level set method to segment the tumor in the combined image. A segmentation result is shown in Figure 6.
Classification with support vector machine model
SVM is a very good classification tool because of its high generalization performance. It has been proved as a very effective method for many applications. The concept of SVM and the general case of nonlinear separating sur- faces were introduced in Appendix 2.
In this study, we use nonlinear SVM with Gaussian radial basis kernel as our classifier. The shape infor- mation is used as the inputs to find an OSH for distin- guishing the benign tumors from malignant ones.
Result
In our experiments, we totally use 210 pathology-proven cases (including 120 benign breast tumors and 90 malignant ones) to test the classification accuracy of the proposed method. These ultrasonic images are ran- domly divided into five groups. We first set the first group as a testing group and use the remaining four groups to train the SVM. After training, the SVM is then tested on the first group. Then we set the second group as a testing group and the remaining four groups are trained and then the SVM is tested on the second.
This process is repeated until all five groups have been set in turn as a testing group.
In this work, we first use some preprocessing and level set methods to segment the tumor of an ultrasonic image. And then we use a nonlinear SVM with Gaussian radial basis kernel as our classifier where C and c are 3 and 0.074, respectively. Six morphologic features are used as the input of the SVM to classify the experi- mental cases. In Figure 8, we compare the six morpho- logic features between benign tumors and malignant ones. These simulations are made on a single CPU Intel Pentium-VI 2 GHz personal computer with Microsoft Windows XP operating system. We list the experimental result in Table 1 and show the ROC analysis in Figure 9.
To estimate the performance of the experimental result, five objective indices are used. These indices are accuracy, sensitivity, specificity, positive predictive va- lue, and negative predictive value. In our experiment,
Figure 6. The tumor segmentation with the proposed method. (a) The original image (b) the image after the anisotropic diffusion filter (c) the image after the stick method (d) the image which combines the thresholded and original images (e) the result of level set method.
(a) (b)
(c) (d)
y
) x 0 γ(
y
(t) x γ
=C φ ) , , (xyt z=φ
y
x 0 ) (
=
= φ γt Level Set, y
) 0 , ,
( =
= xyt z φ
x
=C φ
0 )
0
( = φ=
γ Level Set,
Figure 5. Level set curve propagation. (a) and (b) show the curve c and the corresponding surface /ðx; yÞ at t ¼ 0, and (c) and (d) show the curve c and the corresponding surface /ðx; yÞ at time t.
the accuracy of SVM with shape information for clas- sifying malignancies is 90.95% (191/210), the sensitivity is 88.89% (80/90), the specificity is 92.5% (111/120), the positive predictive value is 89.89% (80/89), and the negative predictive value is 91.74% (111/121). We also list these indices in Table 2. According to the Table 2 and Figure 9, we can conclude that the classification ability for breast tumors with shape information is very well.
Conclusion
Recent progress of computer-aided diagnosis (CADx) system demonstrated that the application of CADx system could increase the diagnostic confidence for a physician and provides one possible solution to improve the positive predictive value of breast biopsy. Although these proposed CAD system, examples from our pre- vious works [24–26], could be readily adaptable to US machine; there is no available data to be verified whe- ther a designed system was suitable to another US machine without any change or through the adjustment of the parameters by using intelligent selection algo- rithms according to the different US machines. In fact, with the rapid development of US technologies, many different ultrasonic systems are used in the current medical diagnosis. Subsequently, we successfully pro- posed adjustment schemes for different ultrasonic sys- tems were used to transform needed information for the differential diagnosis [27]. However, this method still
need collect different US machine data as well as ma- chine setting parameters in advance. It could not be readily adaptable to new US machines. The aim of this study using automatic ultrasound segmentation and morphology based method is to improve this drawback;
we believe that is valuable for future development of ultrasonic CAD system. The morphologic features de- scribe the shape and contour of the lesion and the tex- ture features characterize the image properties evolved from the intension distribution such as echogenicity and 0
0.5 1 1.5 2
form_factorroundness
aspect_ratioconvexity solidity extent
Benign Malignant
Figure 8. Comparison of six morphologic features between benign tumors and malignant ones.
Figure 7. Separating hyperplane. (The dashed lines identify the margin.)
Table 1. Classification of breast tumors by SVM with shape feature
Sonographic classification
Benigna Malignanta
Benign TN 111 FN 10
Malignant FP 9 TP 80
Total 120 90
Note: TP, True Positive; TN, True Negative; FP, False Positive; FN, False Negative
aHistological finding.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FPF
TPF
Az=0.9467
Figure 9. The ROC analysis of the proposed method.
Table 2. The objectively indices result for the proposed method
Index Performance
Accuracy 90.95%
Sensitivity 88.89%
Specificity 92.50%
PPV 89.89%
NPV 91.74%
Note:
Accuracy = (TP+TN) / (TP+TN+FP+FN) Sensitivity = TP / (TP+FN)
Specificity = TN / (TN+FP)
Positive Predictive Value = TP / (TP+FP) Negative Predictive Value = TN / (TN+FN)
echotexture. Texture features are helpful to classify benign and malignant tumors on sonography. The potential of sonographic texture analysis to improve breast tumor diagnosis has already been demonstrated [28–30]. However, the texture analysis is system-depen- dent. In other words, the disadvantages of these systems which use texture analysis to classify tumors are they usually perform well only in one specific ultrasound system. While Morphological based US diagnosis of breast tumor will take the advantage of nearly inde- pendent to either the setting of US system and different US machines. A CAD based on the shape analysis was proposed by Chen et al. [31] with good system perfor- mance. However, it relies on physicians to manually segment tumors. In this study, we further improved with an automatic tumor segmentation and shape analysis CAD system.
Appendix 1
Let c(0) be a closed initial planar curve in a Euclidean plane´2, and let c(t) be the family of curves which is generated by the movement of the initial curve c(0) in the direction of its normal vector N. Moreover, we assume that the speed of this movement is a scalar function F of the curvature K.
The main idea in the level set approach is to represent the front c(t) as the level set [23] of a function /. In other words, given a moving closed hypersurface c(t), that is, c(t¼ 0): [0,¥) fi ´N, we wish to produce a formulation for the motion of the hypersurface propagating along its normal direction with speed F. Hence, the idea of the level set methodology is to embed this propagating interface as the zero level set of a higher dimension function /. The function / is defined as follows. Let /(x,t¼ 0) for x is a point in ´N, be defined by
/ðx; t ¼ 0Þ ¼ d; ð7Þ
where d is the distance from x to c(t¼ 0), and the sign is chosen if the point x is outside (plus) or inside (minus) the initial hypersurface c(t¼ 0). Thus, we have an initial function /(x,t ¼ 0): ´Nfi´ with the property that
cðt ¼ 0Þ ¼ ðxj/ðx; t ¼ 0Þ ¼ 0Þ: ð8Þ
The goal is to produce an equation for the evolving function /(x,t), which contains the embedded motion of c(t) as the level set [23]. To do so, let x(t) be the path of a point on the propagating front. That is x(t¼ 0) is a point on the initial front c(t ¼ 0), and xtÆn¼ F(x(t)) with the vector xtnormal to the front at x(t). Since the evolving function / is always zero on the propagating hypersurface, we must have
/ðxðtÞ; tÞ ¼ 0: ð9Þ
By the chain rule,
/tþ r/ðxðtÞ; tÞ x0ðtÞ ¼ 0: ð10Þ Since F supplies the speed in the outward normal direction, then x¢(t) Æ n ¼ F where n ¼ //|/| and we have the evolution equation for /, namely
/tþ F jr/j ¼ 0; ð11Þ
with a given value of /(x,t¼ 0). This is the level set equation introduced by Osher and Sethian [10].
To help illustrate these ideas, Figure 5 shows the outward propa- gation of an initial curve and the accompany motion of the level set function /. Suppose the initial front c at t¼ 0 is a circle in the
xy-plane, as shown in Figure 5(a). Thus, the circle is the level set [23] of an initial surface z¼ /(x,y,t ¼ 0) in ´3, as shown in Figure 5(b). We can then match the moving curves c(t) in such a way that the level set [23] always yields the moving front, as shown in Figures 5(c) and (d).
Appendix 2
If there is a training example set S;fðxi; yiÞ1iNg, where xi2 Rnand yi2 f1; 1g is a class label. The goal of SVM is to define a hyperplane which divides S such that all the points with the same label are on the same side of the hyperplane while maximizing the distance between the two classes and the hyperplane, as shown in Figure 7. This means to find a pair (w, b) such that
yiðw xiþ bÞ > 1; i¼ 1; . . . ; N ð12Þ where w˛Rnand b˛ R.
According to Equation (12), we can know the minimal distance between the closest point and the hyperplane is 1=kwk. Besides, the OSH is a hyperplane which the distance to the closest point is maximal.
Hence, in order to find the OSH, we must minimizekwk2under con- straint Equation (12).
If we denote with a¼ ða1;a2; . . . ;aNÞ the N nonnegative Lagrange multipliers associated with constraint Equation (12), the problem of finding OSH is Equivalent to the maximization of the function
WðaÞ ¼XN
i¼1
ai1 2
XN
i;j¼1
aiajyiyjxi xj; ð13Þ
where ai 0 and under constraintPN
i¼1
yiai¼ 0:
Once the vector a¼ ða1; a2; . . . ; aNÞ solution of Equation (13) has been found, the OSHðw; bÞ has the following expansion:
w¼XN
i¼1
aiyixi; ð14Þ
while b can be determined from a and from the Ku¨hn–Tucker conditions [32]
aiðyiðw xiþ bÞ 1Þ ¼ 0; i¼ 1; 2; . . . ; N : ð15Þ By the way, the corresponding training examplesðxi; yiÞ with non- zero coefficients ai are called support vectors. At last, the decision function of classifying a new data point x can be written as:
fðxÞ ¼ sgnðXN
i¼1
aiyixi x þ bÞ: ð16Þ
The training example set that we want to classify is usually linearly nonseparable. To achieve better generalization performance, the input data can first be mapped into a high-dimensional feature space. Then the OSH is constructed in the feature space.
If UðxÞ denotes a mapping function that maps x into a high- dimensional feature space, Equation (13) is then rewritten as follows:
WðaÞ ¼XN
i¼1
ai1 2
XN
i¼1
aiajyiyjUðxiÞAUðxjÞ: ð17Þ
Now, let Kðxi; xjÞ ¼ UðxiÞ UðxjÞ we can rewrite Equation (17) as
WðaÞ ¼XN
i¼1
ai1 2
XN
i;j¼1
aiajyiyjKðxi; xjÞ; ð18Þ
where K is called a kernel function and must satisfy Mercer’s theorem [15]. Finally, the decision function becomes
fðxÞ ¼ sgnðXN
i¼1
aiyiKðxi; xÞ þ bÞ: ð19Þ
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Address for offprints and correspondence:Dar-Ren Chen, Department of Surgery, Changhua Christian Hospital, 135 Nanhsiao Street, Changhua, Taiwan; Tel.: (886)-4-7238595; Fax: (886)-4-7228289;
E-mail:dlchen88@ms13.hinet.net
