Mammographic mass segmentation: Embedding multiple features in vector-valued level set in ambiguous regions

Abstract

Mammographic mass segmentation plays an important role in computer-aided diagnosis systems. It is very challenging because masses are always of low contrast with ambiguous margins, connected with the normal tissues, and of various scales and complex shapes. To effectively detect true boundaries of mass regions, we propose a feature embedded vector-valued contour-based level set method with relaxed shape constraint.

In particular, we initially use the contour-based level set method to obtain the initial boundaries on the smoothed mammogram as the shape constraint. To prevent the contour leaking and meanwhile preserve the radiative characteristics of specific malignant masses, afterward, we relax the obtained shape constraint by analyzing possible valid regions around the initial boundaries. The relaxed shape constraint is then used to design a novel stopping function for subsequent vector-valued level set method. Since texture maps, gradient maps, and the original intensity map can reflect different characteristics of the mammogram, we integrate them together to obtain more accurate segmentation by incorporating the new stopping function into the newly proposed feature embedded vector-valued contour-based level set method.

The experimental results suggest that the proposed feature embedded vector-valued contour-based level set method with relaxed shape constraint can effectively find ambiguous margins of the mass regions. Comparing against existing active contours methods, the new scheme is more effective and robust in detecting complex masses.

Introduction

Breast cancer is the second most frequently diagnosed cancer in women all around the world [1]. Numerous studies have shown that early detection saves lives and increases treatment options. Currently, mammography is the most reliable and cost-effective tool for detecting the breast cancers at an early stage. Therefore, a dozen of mammographic computer-aided diagnosis (CAD) systems have been developed for assisting doctors in finding the symptoms earlier by using mammograms.

Mass, which always indicates the malignancy, is one of the major abnormities in mammograms. However, clinical studies show that only a minority of biopsied masses are malignant [2]. Patient information and characteristics of the symptoms are the most effective features to detect masses in CAD systems. Therefore, accurately segmentation is the most important step for diagnosing the malignancy of the symptoms, because it severely affects the performance of the feature analysis and the subsequent recognition. Masses are always of poor contrast, highly connect to surrounding parenchymal tissues, and possess various scales, complex shapes, and ambiguous margins. Thus, mass segmentation is a big challenge.

There are numerous studies on mass segmentation [3]. For example, pixel based methods [4], [5], [6], [39] such as region growing and its extensions; region based methods [7], [8], e.g., filter based methods; and simple edge based methods [9], [10], [11], [12], e.g., the gradient filters, are employed widely in the early stage for mass segmentation. These methods usually integrate pixel information and other characteristics to obtain better segmentation results. Though these types of methods are easily to implement, it is still difficult to acquire satisfied segmentation results for masses of ambiguous boundaries. This is because simple features cannot handle the complex density distributions and topologies of the masses. To find more accurate boundaries of masses, the active contour method, which is flexible and effective on capturing complex topologies, is introduced to the CAD systems [13], [14], [15], [16], [17], [18], [19]. Sahiner et al. [13] incorporated the curvature, homogeneity, and the smoothed image gradient magnitude to the active contour method; Xiao et al. [14] employed the geometric active contour model with the fusion of color and intensity priors to segment masses; Ball and Bruce [17] presented an adaptive level set segmentation method, which segments the suspicious masses in the polar domain and adaptively adjusts the border threshold to find the boundaries; and Yuan et al. [19] proposed a dual-stage segmentation method for lesion segmentation. The method detects the initial contour by using the radial gradient index method and then uses the level set method to refine the initial segmentation result based on a dynamic stopping criterion. Although these algorithms improve the performance of mass segmentation, they are still not ready for practical utilization.

In particular, general segmentation algorithms find boundaries mainly dependent on the gradient information within regions. It may not work well on mammograms, because masses are always of ambiguous margins. Though the Chan–Vese model considers the density distributions of the foreground and background, it cannot handle the case conveniently. This is because the normal regions around the masses always present so similar characteristics with masses. Thus, if we can properly combine the contour- and region-based methods, more accurate margins of masses can be captured.

In addition, original mammograms are the only material employed by the general segmentation methods. Existing methods only use the density information of the mass regions, but ignore other high-level features embedded in mammograms. It is well known that mass regions and normal ones have different textures and gradient variational features. To effectively detect masses boundaries, it is necessary to integrate texture maps, gradient maps and intensity maps.

Finally, contour leaking is a serious problem in mass segmentation, because some mass margins are ambiguous. For automatically preventing the evolving curve leaking from the true boundaries, we propose an adaptive shape constraint method [20]. This constraint strictly restrains the evolving curve within the shape constraint, and thus tend to lose some radiative characteristics or its growing tendency of masses, especially for malignant cases. Furthermore, the inside regions of masses always possess complex density distributions, which induce the evolving curve shrinking to the highlight core regions. Therefore, a flexible constraint should be considered for preventing the evolving curve shrinking and preserving the radiative characteristics of the malignant masses.

To capture more accurate mass boundaries, we propose a feature embedded vector-valued contour-based level set method with relaxed shape constraint. The new method firstly detects the initial shape constraint by employing contour-based level set method. Then, a new relaxed shape constraint is designed by analyzing the stopping function of the shape constraint, and a new stopping function is developed subsequently. Finally, to use more types of characteristics of the mammogram, we collect the texture and gradient variational features for subsequent vector-valued level set method. The experimental results on different mammograms demonstrate that the proposed method can effectively detect boundaries of masses with complex shapes. The proposed method has the following properties:

• The contour of the initial focal region is combined with the original shape constraint to form the new annular constraint region. It effectively avoids the evolving curve shrinking into the initial contour and prevents the contour leaking. In addition, the relaxed constraint considers the surrounding region of the original shape constraint, which can effectively preserve the radiative characteristics of malignant masses and capture more accurate boundaries.

• The extension to the vector-valued level set method induces the evolving curve by combining multiple features (the texture maps, the gradient maps, and the intensity map) of mammograms. It can effectively handle the instance that masses have ambiguous margins or partially connected with the parenchymal tissues, because it considers different channels, each of which represents a specific characteristic of the mammograms.

• The stopping function, inherited from the contour-based level set, is incorporated with the region distribution information to determine the segmentation results. By considering both the gradient information and the distribution of feature values, the embedded model can induce the evolving curve to the real boundaries of masses.

The rest of this paper is organized as follows. Section 2 briefly reviews the contour- and region-based level set methods. In Section 3, the proposed feature embedded vector-valued contour-based level set scheme is detailed; and the experimental results are presented in Section 4; finally, Section 5 concludes the whole paper.