Automatically extracting breast tumor boundaries in ultrasound images is a difficult task due to the speckle noise, the low image contrast, the variance in shapes, and the local changes of image intensity. In this paper, an improved edge-based active contour model in a variational level set formulation is proposed for semi-automatically capturing ultrasonic breast tumor boundaries. First, we apply the phase asymmetry approach to enhance the edges, and then we define a new edge stopping function, which can increase the robustness to the intensity inhomogeneities. To extend the capture range of the method and provide good convergence to boundary concavities, we use the phase information to obtain an improved edge map, which can be used to calculate the gradient vector flow (GVF). Combining the edge stopping term and the improved GVF in the level set framework, the proposed method can robustly cope with noise, and it can extract the low contrast and/or concave boundaries well. Experiments on breast ultrasound images show that the proposed method outperforms the state-of-art methods.
Breast cancer is one of the major causes of death among women [
Active contour models (also called snakes) have been proved to be very useful for image segmentation [
Parametric active contour models use parametric equation to explicitly represent the evolving curve. The problems of the traditional parametric active contour model are its limited capture range and its inability to handle concave boundaries. Xu and Prince [
Geometric active contour models implicitly represent evolving curve as the zero-level set of a higher dimensional function, called level set function. Commonly, this function is defined by computing the closest distances between pixels and a given closed curve in an image domain. The points that have positive distances are inside the curve, and ones that have negative distances are outside the curve [
Using an additional edge stopping function (ESF) allows the active contour to stop at the edges [
In this paper, a novel segmentation method of ultrasonic breast tumor is proposed within the level set framework. First, we present a novel ESF, which is independent of the intensity gradient of image, as most of the active contour models do, but instead is related to local phase information obtained by using the phase asymmetry approach. The use of this ESF is more robust than the traditional gradient magnitude-based ESF because local phase is theoretically invariant to intensity magnitude. Subsequently, in order to increase the capture range of the method and its ability to move into acute concave boundaries, the improved gradient vector flow (GVF) field is adopted as external force and it is added to the proposed model. The results show that the proposed method can obtain better segmentation performance in comparison with some state-of-art methods [
The rest of this paper is organized as follows. In Section
The basic idea of the level set methods is to implicitly represent a closed curve
In the level set framework, the general evolution equation of the level set function
In most of the traditional level set methods, reinitialization is used as a numerical remedy for keeping sound curve evolution and guaranteeing reliable results. The main problem with this procedure is its high computational cost. To avoid this problem, Li et al. [
Let
As can be seen, the level set function
The associated Euler-Lagrange equations, obtained by minimizing function equation (
In (
In practice, the Dirac delta function
The Dirac function with different epsilon values.
The goal of our method is to extract a breast tumor from a given US image. This method consists of three stages: ESF definition, improved GVF construction, and model generation. Figure
Block diagram of the proposed method for breast tumor segmentation.
The sine and cosine functions with specific amplitudes (energies) can represent any discrete signal. In the time domain, these functions cause a set of scaled waves, synthesizing the original signal. Morrone and Owens [
Kovesi [
The measure of phase congruency provides inaccurate localization, noise sensitivity, and high computational cost. Motivated by the properties of the phase congruency, Kovesi considered that symmetries and asymmetries cause special phase patterns in the values of the image intensity [
Extension to two-dimensional (2D) images uses the 1D analysis over several orientations and then combines the results to offer a single measure of the feature significance [
Based on the analysis mentioned above, one can see that
Comparison between gradient-based ESF and phase-based ESF of the US image. (a) Speckled homogeneous image; (b) and (c) are the gradient-based ESF and phase-based ESF of (a); (d) Speckled image with contour; (e) and (f) are the gradient-based ESF and phase-based ESF of (d).
As can be seen from Figure
Xu and Prince [
An obvious problem with this edge map is that the traditional GVF could be attracted to strong edges which are caused by noises in an inhomogeneous region with high gray values.
In order to eliminate this shortcoming, we define an edge map as
The GVF field is defined by the vector field
The force vector field
For an example of breast US image, Figures
Comparison between original GVF field (Niter = 10) and improved GVF (Niter = 10) of the breast US image. (b) and (c) are zoomed-in views of the original GVF and improved GVF in square window marked in (a). As shown by the arrows, more gradient vectors in the improved GVF field point to the true boundaries.
The major difference between the traditional GVF and the improved GVF is that the former edge map is dependent on gradient magnitude while the latter is dependent on phase congruency. The advantage of the latter over the former is that it makes use of the phase information in the cure convolution and, thus, achieves better edge detection results for objects with intensity inhomogeneities or speckle noise.
Although most of the traditional level set methods require reinitialization, Li’s method [
The proposed model yields a level set evolution, called phase- and GVF-based level set evolution (PGBLSE). The PGBLSE model can be described by the following differential equations:
Now assuming that
This work was approved by Shanghai Sixth People’s Hospital in China. Our method was developed using MATLAB and evaluated using 20 US images of breast tumors. Among these images, 10 were malignant tumors and 10 were benign tumors. The patients’ ages are in the range from 18 and 75 years old. The images were collected by using three kinds of scanners with the linear transducers (7–14 MHz). The ultrasonic subimage of region of interest (ROI) was chosen by an expert radiologist. This area only was then used for image segmentation. An example of an extracted ROI subimage is illustrated in Figure
On the left is an US image captured from the sonographic scanner having a malignant tumor. On the right is the ROI subimage.
To evaluate the accuracy of the segmentation algorithms, we compared them with the gold standard, which was manually produced by an experienced radiologist. In addition to the golden standard segmentation, an error measure is required for evaluating object segmentation algorithms. Measures can be divided into region-based measures and boundary-based ones.
Region-based error measures are made by comparing the regions inside the contours. The overlapping area error [
The Dice similarity coefficient [
Boundary-based error measures evaluate segmentations based on the distance between two contours. The boundary error is defined as the average or max distance between two contours. We denote the golden standard boundary by
The average minimum Euclidean distance (AMED) [
The Hausdorff distance (HD) [
We compare our method, PGBLSE model (
The same initial contours are used in these methods. We use the following default setting of the parameters in our method:
Experiment 1 applies these three models to an US image which contains a malignant breast tumor with obvious intensity inhomogeneity and highly concave boundary as shown in Figure
Segmentation of a malignant breast tumor with intensity inhomogeneity and highly concave boundary. (a) Original image. (b) Golden standard. Segmentation results of (c) GAC [
In experiment 2, these three models are applied to an US image of the malignant tumor in Figure
Segmentation of a malignant breast tumor having intensity inhomogeneity and weak boundaries. (a) Original image. (b) Golden standard. Segmentation results of (c) GAC [
In experiment 3, Figure
Segmentation of a malignant breast tumor intensity inhomogeneity and low contrast. (a) Original image. (b) Golden standard. Segmentation results of (c) GAC [
Experiment 4 applies these three methods on an US image of a benign breast tumor, as shown in Figure
Segmentation of a benign breast tumor having low contrast and weak boundaries. (a) Original image. (b) Golden standard. Segmentation results of (c) GAC [
Experiment 5 illustrates the application of the proposed method to a relatively smooth benign breast tumor as shown in Figure
Segmentation of a benign breast tumor with low contrast and high speckle noise. (a) Original image. (b) Golden standard. Segmentation results of (c) GAC [
Clearly, the GAC and DRLSE models are sensitive to the noise which seriously affects the gradient-based stopping terms. Therefore, these two models yield many comparatively strong gradients throughout the whole image including the homogeneous regions, which distracts the evolution contours from the real boundaries. This problem can be solved by using the phase-based stopping term because this term is theoretically intensity invariant.
Experiments 1–5 illustrate the comparison results on five US images of breast tumors in comparison with the GAC model [
Bar plots of segmentation errors among the GAC, DRLSE, and PGBLSE models. (a) JS error. (b) DSC error. (c) AMES error. (d) HD error. The
Figure
Figures
Box plots of segmentation errors among the GAC, DRLSE, and PGBLSE models on 20 clinical US images of breast tumors. (a)TP, (b) FP, (c) JS, (d) DSC, (e) AMED, and (f) HD.
From Figure
As can be seen from Figure
As can be seen from Figure
Bland-Altman plots for the comparison of the tumor areas on clinical US images of breast tumors, assessed by three segmentation models and by the golden standard: (a) GAC [
The goal of this particular experiment is twofold. On the one hand, we demonstrate that tumor areas of the GAC and DRLSE models are larger than those of the proposed PGBLSE model, and, therefore, large values of TP are obtained. On the other hand, some nontumor regions are also incorrectly covered by the GAC and DRLSE models, and, therefore, large values of FP are achieved.
In our experiments, all figures (i.e., Figures
We have presented in this paper a new approach for the segmentation of the ultrasonic breast tumors. For the first time, phase asymmetry approach, which can enhance the boundaries, is used to segment the ultrasonic breast tumors. In a level set framework, we integrate the use of a novel ESF and the improved GVF, both constructed using the output of phase asymmetry. This model shows significant improvements, particularly, in robustness against the speckle noise, as well as in handling intensity inhomogeneities and capturing concave boundaries.
The performance of the proposed PGBLSE model is demonstrated on clinical US images of breast tumors. Qualitative and quantitative results show that the PGBLSE model outperforms the classical intensity-based GAC and DRLSE models. The further work will focus on developing a hybrid level set active contour model by investigating the addition of a region-based term, in order to improve the performance of the method.
This work was supported by National Basic Research Program of China, the 973 Program (Grant no. 2010CB732501).