Breast cancer is the leading cause of death for women all over the world [1
]. At present, the major risk factors for breast cancer cannot be avoided and the survival is closely related to early detection [2
]. Mammography is the most common modality for detecting the early-stage breast cancer and the only modality recommended for population screening programs [3
]. Many computer-aided diagnosis (CAD) systems based on mammograms have been developed to improve the detection rate of breast cancer [4
]. Lesion segmentation is one of the most important steps in CAD systems. It can produce approximate contours of suspicious regions to provide features which enable discrimination between true lesions and regions corresponding to normal tissue. Since lesion boundaries are usually embedded and hidden in varying densities of parenchyma structures and may become obscured, irregular, and low contrast, lesion segmentation is a challenging task.
In recent years, a number of methods have been developed for lesion segmentation. Yuan et al. presented a dual-stage method for lesion segmentation in a region of interest (ROI) [7
]. Their method consisted of a radial gradient index-based segmentation method to yield an initial contour and a geometric active contour model for shape refinement. The boundaries obtained by the segmentation method were compared to hand-drawn results in terms of area overlap metric (AOM). Timp and Karssemeijer presented a robust and automated segmentation technique based on dynamic programming boundary tracing (DPBT) to segment lesions [8
]. At the heart of the dynamic programming method is the so-called local cost function, which is used to find the path that most efficiently represents the contour of lesions. Rojas Domínguez and Nandi modified the local cost function and designed two improved DPBT methods [9
]. Song et al. segmented breast lesions using plane fitting and dynamic programming (PFDP) [10
]. First, the edge candidate points were obtained using a plane fitting method. Then, dynamic programming technique was used to find the optimal contour of a lesion from the edge candidate points. All these dynamic programming-based methods were compared to radiologist’s manual segmentation using the AOM metric. Rojas Domínguez and Nandi’s method is difficult to reproduce; so we compared our proposed algorithm to Timp and Karssemeijer’s method and Song et al.’s method, using the AOM, Hausdorff distance (HD), and average minimum Euclidean distance (AMED) metrics.
The watershed transformation is a powerful tool for image segmentation based on mathematical morphology [11
]. We can consider the image as a landscape or topographic relief where the gray level of each pixel corresponds to a physical elevation. Immersing the landscape in a lake with holes pierced in local minima, catchment basins will fill up with water starting at these local minima. At points where water coming from different basins would meet, dams are built. This process ends when the water level has reached the highest peak in the landscape. As a result, the landscape is partitioned into regions or basins separated by dams, called watershed lines or simply watersheds [15
The advantages of the watershed transformation are that it is simple, intuitive, and can be parallelized. The main drawback of this method is the over-segmentation due to the presence of many local minima. To decrease the effect of severe over-segmentation, marker-controlled watershed transformations have been proposed [15
]. These are robust and flexible methods for segmenting objects with closed contours, such as breast lesions. The internal marker (a region completely inside the lesion) and external marker (a region completely free of pixels containing a lesion) are initially defined. The boundaries, even if not clearly defined, are expressed as ridges between two markers and located. Initial definition of the markers is critical in these methods. Yan and Zhao proposed a marker-controlled watershed method to segment lymphoma in sequential computerized tomography images [16
]. In their method, the external marker is obtained manually by drawing a circle enclosing the lymphoma. The internal marker is determined automatically by combining techniques including Canny edge detection, thresholding and morphological operation. Cui et al. also proposed a semi-automated method based on marker-controlled watershed transformation to segment breast lesion volumes on magnetic resonance imaging [17
]. They manually selected the ROI in a single image, followed by a Gaussian mixture model applied to a histogram of the pixels inside the ROI to distinguish the lesion class from other tissues. The internal and external markers are determined on the basis of the ROI and the intensity distribution of the lesion, and the lesion contour is delineated using a marker-controlled watershed transform. These methods can hardly be applied to mammogram CAD because of their semi-automated nature.
In this study, a robust and accurate marker-controlled watershed (MCWS) method is proposed to achieve higher segmentation performance and get more accurate lesion contours in mammograms. The focus is mainly on smoothing the gradient image and determining internal and external markers, which is crucial in the marker-controlled watershed method. To assess the performance of this method, we compared it to the DPBT and PFDP methods using the AOM, HD, and AMED metrics.