Computers in Biology and Medicine 62 (2015) 55–64

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Automated breast-region segmentation in the axial breast MR images Jana Milenković a,b,n, Olga Chambers c, Maja Marolt Mušič d, Jurij Franc Tasič a a

Faculty for Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia Faculty of Medicine, University of Ljubljana, Vrazov trg 2, 1000 Ljubljana, Slovenia Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia d Institute of Oncology, Zaloška 2, 1000 Ljubljana, Slovenia b c

art ic l e i nf o

a b s t r a c t

Article history: Received 11 December 2014 Accepted 1 April 2015

Purpose: The purpose of this study was to develop a robust breast-region segmentation method independent from the visible contrast between the breast region and surrounding chest wall and skin. Materials and methods: A fully-automated method for segmentation of the breast region in the axial MR images is presented relying on the edge map (EM) obtained by applying a tunable Gabor filter which sets its parameters according to the local MR image characteristics to detect non-visible transitions between different tissues having a similar MRI signal intensity. The method applies the shortest-path search technique by incorporating a novel cost function using the EM information within the border-search area obtained based on the border information from the adjacent slice. It is validated on 52 MRI scans covering the full American College of Radiology Breast Imaging-Reporting and Data System (BI-RADS) breast-density range. Results: The obtained results indicate that the method is robust and applicable for the challenging cases where a part of the fibroglandular tissue is connected to the chest wall and/or skin with no visible contrast, i.e. no fat presence, between them compared to the literature methods proposed for the axial MR images. The overall agreement between automatically- and manually-obtained breast-region segmentations is 96.1% in terms of the Dice Similarity Coefficient, and for the breast-chest wall and breast-skin border delineations it is 1.9 mm and 1.2 mm, respectively, in terms of the Mean-Deviation Distance. Conclusion: The accuracy, robustness and applicability for the challenging cases of the proposed method show its potential to be incorporated into computer-aided analysis systems to support physicians in their decision making. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Breast MRI Breast-region segmentation Tunable Gabor filter Shortest-path search Cost function

1. Introduction Magnetic Resonance Imaging (MRI) is an invaluable tool in the clinical work-up of patients suspected of having breast cancer [1,2]. Moreover, the breast MRI is gaining popularity as a screening modality for patients with dense breasts or high-risk patients with BRCA 1 & 2 gene mutations (screened at a younger age when their breasts are dense) [3,4]. As the diagnostic efficiency is highly dependent on the level of experience of the radiologist [5,6], recent researches have focused on developing computer-aided analysis methods aimed at helping the radiologists in their diagnostic tasks, particularly those radiologists experienced in

n Corresponding author at: Faculty for Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia. Tel.: þ 386 1 4768 812. E-mail address: [email protected] (J. Milenković).

http://dx.doi.org/10.1016/j.compbiomed.2015.04.001 0010-4825/& 2015 Elsevier Ltd. All rights reserved.

mammography reading but less experienced in interpreting the breast MRI [7]. The automated breast-region segmentation is required for performing a fully-automated computer-aided analysis of the breast MR images overcoming drawbacks of the manual and user-assisted segmentation which are impractical for processing large amounts of the MRI data being time consuming and biased by both the intra-observer and inter-observer variability. The breast-region segmentation refers to separation of the breast as an organ from other body parts in the MR images. The importance of the automated breast-region segmentation has recently been recognized in a number of applications for the breast MRI, such as the breast-density measurement [8] and tumour detection for the subsequent tumour classification [9]. It can also facilitate the pharmacokinetic-model calibration with respect to the reference tissues for improving the diagnostic performance of the dynamic contrast-enhancement breast tumours [10] where, for the purpose of calibration, the pectoral muscle (the most anterior chest-wall

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muscle) can be used given its properties [11]. This would require, among others, a precise breast-chest wall border determination which is a part of the breast-region segmentation. To automatically segment the breast-region in the MR images, the segmentation algorithm needs to determine the breast-chest wall and breast-skin borders as well as the lateral-posterior breast ends. In the T1-weighted MR images – which are almost always included in the typical clinical breast MRI protocols for tumour analysis and used for the breast-density measurement – the fibroglandular tissue, skin and chest wall have a similar signal intensity. Therefore, for the challenging cases where a part of the fibroglandular tissue is connected to the chest wall and/or skin resulting in no visible contrast between them, automated breastregion segmentation is a highly demanding task. Moreover, the MRI signal intensity is usually affected by inhomogeneity, partial volume effect, aliasing, ghosting artefacts, etc., furtherly aggravating the breast-region segmentation. There have been a few methods proposed in the literature to automatically segment the breast region from the MR images. The simplest ones are based on the intensity threshold usually followed by morphological operations [12,13]. The more advanced ones, such as fuzzy C-mean (FCM) clustering [14], sign of gradients [9,15], region growing [16,17], and Markov random field [18], use various connectivity rules between pixels. These methods are highly dependent on the visible contrast between the breast region and chest wall/skin, i.e. on the presence of the fat along the breast-region border, and therefore tend to fail in the challenging cases. The performance of the model-based [19] and atlas-based [20,21] methods for the breast-region segmentation depends on the size and variety of the training database which is critical in achieving a reasonable accuracy. Moreover, the atlas-based segmentation techniques rely on an accurate intensity-based registration of the image to be segmented with the population atlas where the intensity-based registration assumes a similar greylevel distribution in the image compared to the atlas which it is impossible to account for the wide range of the clinical acquisition protocols (e.g., T1-weighted, T1-fat suppressed, T2-weighted), while it is impractical to create high-quality, expert-annotated atlases for every different acquisition protocol [19]. The absence of one or both breasts, as a result of the mastectomy surgery, might also challenge the model-based methods for the breast-region segmentation. Moreover, the previously proposed atlas-based methods have not been validated for the challenging cases while the proposed model-based method has failed in the cases when the contrast between the breast and chest wall is lower than the contrast between the chest wall and chest. The edge-based methods [17,22,23] for the breast-chest wall border determination incorporate classical edge-detectors, such as Canny and Hessian, that are highly sensitive to the noise, low contrast and weak-textural edges affecting the accuracy of the breast-region segmentation. Moreover, the edge-based methods developed for the axial MR images [17,23] rely on the presence of the fat along the anterior side of the chest wall (according to their authors) and, therefore, they are not applicable for segmentation of the challenging cases. In this paper we present a novel fully-automated method for segmenting the breast region in the axial MR images using a tunable Gabor filter which sets its parameters according to the local MR image characteristics to detect non-visible transitions between different tissues having a similar MRI signal intensity. The breastchest wall border is determined using a multi-slice approach where the border information from the adjacent slice is used to specify the border-search area in the current slice due to the high similarity in the chest-wall morphology (shape and inner structure) between two adjacent breast MRI slices. The method applies the shortest-path search technique within the border-search area by incorporating a

novel cost function using the edges obtained with a tunable Gabor filter and subsequent extension of the resulting path along the fat up to the lateral-posterior breast ends. The lateral-posterior breast ends are determined using the body-contour landmarks, while the breastskin border is determined by incorporating the edge information of the tunable Gabor filter in a slice-wise manner. Validated on 52 MRI scans covering the full range of American College of Radiology Breast Imaging-Reporting and Data System (BI-RADS) breast-density categories, our method shows to be independent from the visible contrast between the breast-region and surrounding chest wall and skin, i.e., independent from the presence of the fat along the breastregion border. Our paper is organized as follows. After presenting the aim of our research and overview of the works related to the breastregion segmentation in Section 1, Section 2 describes the clinical breast MRI scans used in our research. Section 3 provides a detailed explanation of the proposed method for the breastregion segmentation. Section 4 introduces the validation metrics used to measure the segmentation accuracy. Section 5 reports our experimental results. Section 6 discusses the main findings of our research, outlines its limitations and determines the areas of our future work. Finally, Section 7 draws conclusions of our research.

2. Materials The used database of 52 pre-contrast MRI breast scans (i.e. volumes) was obtained from the Institute of Oncology, Ljubljana, Slovenia. These were all clinical cases of different patients where the screening MRI revealed a lesion suspected of being malignant. The age of the patients included in our database ranged from 28 to 67 years with an average of 46 years. The patients were scanned in a prone position. The axial T1-weighted images were acquired using a 3D fast low-angle shot-pulse sequence (FLASH) through both breasts (TR/ TE 7.8/4.72, flip angle 251) at 1.5 T (Magnetom Avanto, Siemens, Erlangen, Germany) with a dedicated bilateral breast-surface coil in the prone position. The single-slice dimensions were 448  448, the field of view (FOV) was 340  340 mm2 and the in-plane resolution was 0.76  0.76 mm2 with the slice thickness of 1 mm. Each MRI scan counted 144 slices. The database covers the full range of the BI-RADS breastdensity categories. With a consensus of two radiologists experienced in interpreting the breast MRI, the breasts in our database were classified into four categories: I—extremely fatty, II—minimally dense, III—heterogeneously dense, and IV—extremely dense breast (I: o 25%; II: 25–50%; III: 51–75%; IV: 475%). Our database contained 14, 15, 12, 11 cases of the BI-RADS density categories I, II, III, and IV, respectively. All the scans from category IV and some scans from category III from our database contain the slices where a part of the fibroglandular tissue is connected to the chest wall and/or to the skin with no visible contrast between them, however, the scans from category IV contain a considerably larger number of these slices compared to the scans from category III. The scans from category I and II do not contain such slices. The manual segmentation of the breast region – considered as a gold standard (i.e., ground truth) – was performed by two experienced radiologists (K.H., 18 years of experience, and M.M., 15 years of experience) by using the MIPAV software version 7.0.1 [24], specifically utilizing the Draw polygon VOI tool making a sequence of the left-clicks with the mouse along the breast-chest wall and breast-skin border. MIPAV automatically connects the points along each border, thus forming two contours giving rise to a binary mask corresponding to both borders (the border binary mask). In order to accommodate the varying sizes of the breast in different slices and MRI scans, the radiologists use a varying

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number of points to obtain a relatively smooth contour along both borders. The generated border binary mask is then stored and the procedure is repeated for each slice of the MRI scan. One half of the MRI scans was randomly assigned to one and the other half to another radiologist for manual delineations that were then all reviewed by both radiologists for error checking.

3. Method The proposed method for breast-region segmentation revolves around an edge-enhancement algorithm (see Section 3.1) originally designed for the fingerprint edge-enhancement in automatic fingerprint matching [25]. This algorithm performs a tunable Gabor filtering by setting the filter parameters according to the local MR image characteristics which is particularly suitable for detecting non-visible transitions between different tissues having a similar MRI signal intensity. 3.1. The edge-enhancement algorithm The edge-enhancement algorithm consists of three basic steps: estimation of the orientation field, estimation of the frequency field, and edge detection by using the Gabor filter. Step 1. Estimation of the orientation at each pixel provides information about the orientation of the dominant edge at a given pixel. According to this orientation, the filter in each pixel will be enhanced in the same direction toward the dominant edge in that pixel, reducing any edge different from the direction of the dominant edge (e.g. noise, weak textural edges) at the same location. The orientation field is estimated by using the gradient computation in each pixel of the image by the Gaussian operator and averaging them in the pixel neighbourhood due to the gradient sensitivity to the noise, yielding a smoother orientation field. Since the opposite gradients will cancel each other out, although they indicate the same orientation, the gradient vectors

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are squared (the angle is doubled and the length is squared) before being averaged. The orientation of the dominant edge is obtained perpendicularly to the average gradient direction (its single-angle representation). Step 2. Estimation of the frequency field provides a local estimate of the frequency content in an image which is a second prerequisite for edge detection by using the Gabor filter. The frequency (of a local texture pattern) is estimated in nonoverlapping square blocks rotated to have its dominant orientation in the vertical position. The grey-level values of the pixels located inside the block are projected along the direction orthogonal to its dominant orientation, forming a discrete signal with its frequency determining the spatial frequency of the texture pattern in the block. Step 3. The edge detection in an MR image is performed by tuning the Gabor filter in every pixel according to the pixel orientation and frequency estimation. The edge-enhancement algorithm detects the dominant edges in each pixel neighbourhood, assuring connectivity of the adjacent pixels belonging to the same orientation flow. This provides a higher connectivity of the border pixels which is the major advantage compared to the classical edge-detection methods. By applying a global threshold of zero, a binary image is obtained termed here the Edge Map (EM). An illustration of each algorithm step and the resulting EM is presented in Fig. 1(b)–(e) for the middle slice of one MRI scan (see Fig. 1(a)) from our database. Fig. 1(f) does not belong to the result of the edge-enhancement algorithm showing the original EM after subtracting the eroded EM. Its role will be explained in Section 3.2.3.3.

3.2. Breast-region segmentation work-flow The segmentation work-flow comprises three major steps: determination of the lateral-posterior breast ends (Section 3.2.1), determination of the breast-skin (Section 3.2.2) and breast-chest wall (Section 3.2.3) borders. In this paper, the term chest wall is used for all the muscles (i.e., all the soft tissues) in the transition

Fig. 1. EM computing flow: (a) the original image; (b) estimation of the orientation field; (c) estimation of the frequency field; (d) edge detection by using the Gabor filter; (e) EM obtained by applying a global threshold of zero; (f) EM after subtracting the eroded EM.

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band between the chest cavity and breast. The steps taken to segment the breast region according to the proposed method are presented on unenhanced image scans acquired before contrast administration. 3.2.1. Determination of the lateral-posterior breast ends Since there are no precisely defined anatomical landmarks indicating the position of the lateral-posterior breast ends in the bilateral breast MRI, the rectangular region of interest (ROI) is defined using the body-contour landmarks in the middle slice so that its posterior end determines the lateral-posterior breast ends and then it is perpendicularly projected to other slices superiorly and inferiorly from the middle slice. The middle slice is chosen because this slice is under the pectoralis tendon where the arms are separated from the body providing the body-contour information required for the ROI definition. ROI is defined using the three body-contour landmarks (PL, PR and PM) shown in Fig. 2. To obtain the body contour, we identified the EM edges that intersect the body fat mask which is the class containing the highest intensity values obtained after applying 3class FCM clustering. To ensure connectivity of the edges corresponding to the body contour, the identified edges were merged using morphological dilation by b, morphology filled and then morphology eroded by b, where b is a circular structuring element of type disk with a 3-pixel radius. The body contour is then obtained as a resulting binary mask outer contour. Points PL and PR represent the left and right laterally-outermost body-contour point, respectively, with a minimum and maximum x-coordinate. Point PM is the body-contour point with the minimal y-coordinate located between the local maxima corresponding to left and right breasts. ROI is limited by the anterior MRI image end, horizontal line at distance D under point PM and two vertical lines passing the intersection between the previous horizontal line and body contour (PL0 and PR0 point). Value D is determined experimentally

Fig. 2. ROI definition scheme for the lateral-posterior breast ends determination; ROI is defined in the middle slice using the body-contour landmarks and propagated inferiorly and superiorly to other slices.

as 2/3 of the shortest distance between point PM and the horizontal middle-line between PL and PR. The inhomogeneity correction method for the bias-field removing, published in our previous work [26], is applied in order to normalize the MRI signal intensity, thus allowing for a more accurate determination of the body fat mask. After defining ROI in the middle slice and projecting it to the superior and inferior slices, the breast-skin and the breast-chest wall borders are found within ROI in each slice. 3.2.2. Breast-skin border determination The breast-skin border, the border between the breast tissue and the skin, is determined by using EM. The breast-skin border is obtained as the anterior body contour between the PL0 and PR0 points (procedure for obtaining the body contour already explained in Section 3.2.1). This procedure is performed slicewise without the need of incorporating any information from the adjacent slices. 3.2.3. Breast-chest wall border determination The basic idea used to determine the breast-chest wall border relies on the border information from the adjacent slice. The reasoning comes from the fact that there is a high similarity in the chest-wall morphology between two adjacent breast MRI slices. The general work-flow for the breast-chest wall border determination is presented in Fig. 3. The border determination starts from the initial slice automatically selected among the higher superior slices (detailed description of the initial-slice selection is presented in Section 3.2.3.1). The breasts in these slices are mostly fatty structures and, even though, there might be some fibroglandular tissue, this tissue is centralized in the breast with the fatty tissue located along the breast-chest wall border which provides the initial border of a high accuracy. Thus, in the initial slice, the breast-chest wall border is determined as the posterior border of the maximumarea element of the body fat mask within ROI after performing morphological closing. This border is termed the initial border and is used to specify the border-search area in the adjacent slice, superiorly and inferiorly. The border-search area is specified to reduce the impact of irrelevant information on border determination. For this purpose, a tube is created around the initial border by using the border morphological dilation by a structuring element of type disk with a 3-pixel radius and projected perpendicularly to the adjacent slice to specify its border-search area. Then, the shortest-path search within the border-search area is performed followed by an extension of the resulting shortest path along the body-fat-mask contour up to the lateral-posterior breast ends to determine the border. The shortest-path search is performed between two automatically placed seed points, the starting and ending point (detailed description to obtain these points is presented in Section 3.2.3.2), by incorporating EM to calculate the path cost (detailed description of the shortest path search is presented in Section 3.2.3.3). The path with the minimum cost is identified as the shortest path and is used to re-determine the tube, i.e. create a new tube, for the following slice border determination. This procedure is continued until all the slices of the breast scan have been processed. 3.2.3.1. Initial-slice selection. The initial slice is selected automatically as a slice where the breast-chest wall border can be determined with a high accuracy which is of crucial importance in a multi-slice approach relying on the information from the adjacent slices. It is selected among the higher superior slices due to the mostly fatty structures of the breasts in these slices providing the breast-chest wall border with a high accuracy. The borders are first approximated in these slices using

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Fig. 3. General work-flow of the proposed multi-slice approach for the breast-chest wall border determination; the input into the work-flow is the MRI scan within ROI.

FCM clustering as the posterior border of the maximum-area element of the body fat mask within ROI after morphological closing. As the first few extremely superior slices might be highly affected by the ghosting artefacts, strong inhomogeneity and poor contrast between the breast fat and the chest wall, the obtained borders in the extremely superior slices can represent only a rough approximation highly deviating from the truth borders. It was experimentally confirmed, however, that the border approximations in the following slices begin to faithfully represent the truth border. Starting from the first slice, each slice is checked whether it meets the following two criteria: (i) the Dice similarity coefficient (see Section 4) for the area of ROI under the obtained border approximation between the current slice and its adjacent (following) slice is at least 0.98; (ii) the standard deviation of the following ten Dice similarity coefficients is not higher than 0.015. The first slice meeting both criteria is selected as the initial slice. The second criterion is taken to prevent that the slice with the rough border approximation, which meets the first criteria, becomes an initial because the border rough approximation has a tendency to experience big changes through the slices (causing a higher standard deviation). The threshold values for both criteria are obtained experimentally. For each MRI scan, the radiologist manually selected the slice from where the border approximation begins to faithfully represent the truth border. The Dice similarity coefficient for the area of ROI under the border approximation between the manually selected and the adjacent (following) slice is calculated for each MRI scan and then the minimum coefficient is taken as the threshold value for the first criterion. The standard deviation for the following ten Dice similarity coefficients is calculated for each MRI scan and then the maximum coefficient is taken as the threshold value for the second criterion.

3.2.3.2. Seed-point placing. The shortest-path search is performed between two seed points. The seed-point placing at the current slice is performed in a tube perpendicularly projected from the previous slice. The seed point is found in each tube side as a point of the body fat mask contour (of the current slice) closest to the tube endpoint. If more than one seed point is found, then the point with the maximum x-coordinate for the left tube side and minimum x-coordinate for the right tube side is selected. If the distance between the selected point of

the body fat mask contour and the tube endpoint is more than the predefined distance (10 pixels equivalent to 7.6 mm), then the seed point is placed at the position of the seed point from the previous slice. An illustration of the procedure for the seed-point placing within ROI (for the slice from Fig. 1(a)) is presented in the top row of Fig. 4 where the seed points are represented with red dots and the tube is coloured yellow. 3.2.3.3. Shortest-path search. The shortest-path search between two seed points is performed by using the Dijkstra algorithm [27] where the image pixels are associated with the nodes in the graph while the connection between the two 8-adjacent image pixels is associated with the graph edges. A local cost is assigned to each graph edge to weight their probability of being included in the path. The shortestpath search problem is then the problem of finding a path with a minimum sum of costs between two seed points. To guarantee the effectiveness of the breast-chest wall border determination by using the Dijksta’s shortest-path search algorithm, an exponential cost function incorporating the EM information is introduced. It is presented in Eq. (1) where Sk ¼ Sðxk ; yk Þ is the pixel of binary mask S obtained after subtracting an eroded version of EM ðEM eroded;1 Þ from the original EM as shown in Eq. (2), where EM eroded;1 is obtained using a morphological erosion by a circular structuring element of type disk with a 1-pixel radius (3-pixel diameter).   cost ij ¼ exp 1  Si  Sj ð1Þ S ¼ EM  EM eroded;1

ð2Þ

The operation from Eq. (2) converts the thick EM edges to their one-pixel wide representation preserving the EM edge connectivity (see Fig. 1(f)). It is performed to provide that the cost function of the shortest-path search does not incorporate all pixels of the ‘thick’ EM edge (incorporation of all pixels results in a non-smooth path along the breast-chest wall border). The middle row in Fig. 4 shows binary mask S (from Fig. 1(f)) within ROI overlaid by the tube perpendicularly projected from the previous slice specifying the border-search area in the current slice. The result of the Dijksta’s shortest-path search using the proposed cost function applied in the border-search area is visualized in the bottom row in Fig. 4. The proposed cost function enforces the path to have a non-linear form, due to the

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continuous non-linear form of the breast-chest wall border, which is crucial for the image regions with no edge score.

4. Validation metrics To measure the breast-region segmentation accuracy of the proposed method, the agreement between the automatically- and manually-generated segmentation is assessed slice-wise within ROI using two validation metrics: the Dice Similarity Coefficient (DSC) [20,22,28–30] and the Mean-Deviation Distance (MDD)

[17,22]. It should be noted that the manual segmentation (described in Section 2) is performed within ROI to have the consistency in the lateral-posterior breast ends between the manual and automated segmentations. The DSC metric is calculated by using Eq. (3) characterizing an overlap rate, i.e. the area agreement, between the automatically (A)- and manually (M)-obtained breast-region areas. DSC ¼

2ðA \ MÞ  100 ð%Þ ðA þ MÞ

ð3Þ

By using the MDD metric, the automated and manual delineations of the breast–chest wall border and the breast–skin border are compared. MDD is calculated by using  Eq. (4),  where the points of manually-delineated border C kM ¼ C M xk ; yk ; k ¼ 1; …; N (points of the border binary mask described in Section 2) are paired  to the  closest points of automatically-delineated border C kA ¼ C A xk ; yk ; k ¼ 1; …; N by using the Euclidean distance; m is the MRI imaging parameter referring to the pixel size in the vertical direction (unit: mm/pixel).   PN  k k  k ¼ 1 C A  C M   μ ðunit: mmÞ MDD ¼ ð4Þ N 5. Results

Fig. 4. Shortest-path search for the middle slice ROI of one MRI scan from our database. Top row: The procedure for the seed-point placing as a point of the body fat mask contour closest to the tube endpoint. Middle row: Binary mask S overlaid by the tube perpendicularly projected from the previous slice specifying the border-search area in the current slice. Bottom row: The result of the Dijksta’s shortest-path search between two seed points using the proposed cost function performed in the border-search area. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The proposed method was implemented using MATLAB (v. R2009b; Mathworks, Natick, MA) requiring  4.1 min running on a PC desktop (Intel Core CPU 3.67 GHz, 8 GB RAM) for processing one breast MRI scan (having a resolution of 448  448  144) compared to  53 min required for the manual segmentation. This is a considerable increase in the time-efficiency requiring no user involvement. The speed of our method can be further increased by its implementation in C/C þ þ. The edge-enhancement algorithm is performed by using the Kovesi MATLAB implementation [31] with its default parameters. Fig. 5 shows the breast-region segmentation results for twelve equidistant slices of the MRI scan, which middle slice is presented in Fig. 1(a). A volumetric reconstruction of the breast-region segmentation results is generated by connecting the adjacent breast-region borders. The right top image represents the breastchest wall border surface overlaid by the middle slice while the right bottom image is the breast-skin border surface overlaid by the middle slice.

Fig. 5. Breast-region segmentation results for twelve equidistant slices of one MRI scan from our database. Right top: Breast-chest wall border surface overlaid by the middle slice. Right bottom: Breast-skin border surface overlaid by the middle slice.

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Table 1 shows the average breast-region segmentation accuracy of the proposed method in terms of DSC for all the MRI scans from our database. It separately shows the average accuracy of the breast-skin and the breast-chest wall border in terms of MDD. The table also provides the average segmentation accuracy with respect to the BI-RADS breast-density categories according to DSC and MDD. As seen from Table 1, the maximal breast-region segmentation accuracy given in terms of DSC is achieved for category I, while the minimal breast-region segmentation accuracy is obtained for category IV, nevertheless, there is no considerable discrepancy between the breast-region segmentation results for different breast-density categories. It is observed that the highest discrepancy occurs in the extremely inferior slices and less in the extremely superior slices because of being highly affected by the acquisition artefacts. These discrepancies are higher compared to the discrepancies in slices where a part of the fibroglandular tissue is connected to the chest wall and/or skin with no visible contrast between them. These slice discrepancies occur mostly due to the low lateral fat information affecting the accuracy of the seed-point placing while the edge-map information in combination with the shortest-path search and border-search area provides a relatively high accuracy of the path along the breast-chest wall border. The obtained MDD values across the BI-RADS density categories indicate the robustness of the proposed method for the breast-skin and breast-chest wall border delineation. The minimal disagreement between the automated and manual delineations is obtained for category I, while the maximal is obtained for category IV. It is also observed that the breast-skin border delineation has a higher accuracy than the breast-chest wall border delineation for each of the four categories using the proposed method. This can be explained by the fact that there is less fibroglandular tissue connected to the skin compared to the chest wall. Fig. 6 shows the breast-region segmentation results obtained with the proposed method for one representative slice of three MRI scans for each of the four BI-RADS density categories from our database. It can be observed that our method provides connection

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of the hardly visible pixels at the breast-chest wall border as well as at the breast-skin border. The breast MRI slices in the third and fourth row – BIRADS III and IV, respectively – represent the challenging cases for the breast-region segmentation methods relying on the presence of the fat along the anterior side of the chest wall and posterior side of the breast skin.

6. Discussion In this paper we present a novel fully-automated method for the breast-region segmentation in the axial MR images. The method first determines the lateral-posterior breast ends and then the breast-chest wall and breast-skin borders where each step relies on the edge map obtained by the edge-enhancement algorithm based on a tunable Gabor filter. This filter preserves the edges in the local pixel neighbourhood having the same orientation as the orientation of the tuned filter and attenuating the edges not being parallel to that orientation (usually the weak-textural edges). As a result, it detects the dominant edges in each pixel neighbourhood providing connectivity of the adjacent pixels belonging to the same orientation flow. This is especially important in detection of hardly visible pixels at the breast-region border making the edge-enhancement algorithm useful for the breast-region segmentation particularly in challenging cases. Validation of our method performed on 52 clinical cases shows its robustness to a set of diverse cases covering the full BI-RADS density range and yields a mean DSC of 96.1% and mean MDD of 1.9 mm and 1.2 mm for the breast-chest wall and breast-skin borders, respectively. The method shows to be applicable for the challenging cases in which a part of the fibroglandular tissue is connected to the chest wall and/or skin with no visible contrast, i.e. no fat presence, between them, which is its major advantage compared to other literature methods proposed for the axial MR images. Compared to the model-based and atlas-based methods from the literature, the advantage of the proposed method is that it requires no training set for learning the anatomical or statistical knowledge which makes these methods inherently dependable

Table 1 Average segmentation accuracy for all the MRI scans from our database and the corresponding average accuracy for each of the four BI-RADS density categories in terms of the Dice similarity coefficient (DSC); the accuracy of the breast-skin and breast-chest wall border delineation is given in terms of the mean-deviation distance (MDD). Overall

DSC (%) breast region MDD (mm) breast–chest wall border MDD (mm) breast–skin border

96.1 ( 7 1.7) 1.9 ( 7 1.4) 1.2 ( 7 1.0)

BI-RADS breast density category I

II

III

IV

96.9 ( 7 1.4) 1.2 ( 7 1.1) 1.0 ( 7 0.9)

96.7 ( 71.6) 1.3 ( 71.0) 1.1 ( 70.8)

95.6 ( 7 1.9) 2.1 ( 7 1.6) 1.3 ( 7 0.9)

94.9 (7 1.8) 3.2 (7 2.0) 1.4 (7 1.1)

Fig. 6. Breast-region segmentation results obtained with the proposed method for one representative slice of three MRI scans from our database for each of the four BI-RADS density categories.

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from the intrinsic properties of the training data as already mentioned in Section 1. Validation was performed on tumouraffected clinical cases where the distracting effect of the tumour, partially grown into the pectoral muscle, on the breast-chest wall border determination is the same as the fibroglandular tissue connected to the chest wall for which our method showed to be robust (the signal intensity of the tumour is similar to that of the fibroglandular tissue and chest wall in the pre-contrast image). In similar breast-region segmentation studies, Gubern-Mérida et al. [20] reported a mean DSC value of 94% using an atlas-based method validating their approach on 27 cases acquired in the axial view. In the work by Wang et al. [17], an edge-based method was used to determine the breast-chest wall border with a mean distance error of 2.56 mm and mean overlap rate of 87% validating their method on a dataset containing 30 axial-view cases. The model-based method of Gallego-Ortiz et al. [19] obtained a mean DSC value of 88% after validating their approach on 409 sagittalview cases. Wu et al. [22] reported a mean DSC value of 95% and mean deviation distance of 2.3 mm by validating their edge-based method on 60 sagittal-view cases. The mean overlap rate of 79% was obtained in the work conducted by Giannini et al. [15], based on the sign of gradients, quantitatively validating their method on 31 axial-view cases. Only Gallego-Ortiz et al. [19] validated their approach developed for the sagittal MR images on a substantially larger number of cases compared to our study. Our values of the validation metrics are higher than the ones reported in the literature. However, it should be noted that it is not straightforward to directly compare our method performances with those reported in the literature since the segmentation results were determined on different data sets and using different manual annotations. Moreover, some literature studies are developed for the sagittal MR images, which visualize different anatomical properties compared to the axial MR images and, therefore, different assumptions may hold in the segmentation procedure. Furthermore, in the recent literature studies developed for the axial MR images, Gubern-Mérida et al. [20] and Giannini et al. [15] did not validate their methods for the challenging cases while the methods proposed by Wang et al. [17] and Lin et al. [23] rely on the presence of the fat along the anterior side of the chest wall, according to their reports. The accuracy of our multi-slice approach for the breast-chest wall border determination, relying on the information from the adjacent slices, depends on the accuracy of the initial-border determination. Although the breast-region tissue structure may vary substantially through the breast volume and among individual subjects, the breasts in the higher superior slices are always fatty structures. Therefore, we propose to use a higher superior slice to provide an accurate initial-border determination. The slice is selected automatically by using two criteria (Section 3.2.3.1). The effect of each criterion on our method performance is examined for four threshold values, while fixing the other criterion threshold at the value determined for our method. Selection of the threshold value in the first criterion above the value determined for our method, i.e. 0.98, does not change the method performance in terms of DSC. Therefore, the threshold values for the first criterion are selected in a decreasing order, more specifically 0.98, 0.97, 0.96 and 0.95, resulting in DSC equal to 96.1%, 95.2%, 91.4%, and 87.8%, respectively. Similarly, selection of the threshold value in the second criterion below the value determined for our method, i.e. 0.015, results in no method performance change, while by setting the threshold values in an increasing order to 0.015, 0.02, 0.025 and 0.03, results in DSC equal to 96.1%, 95.8%, 95.1% and 94.3%, respectively. From the above it can be concluded that decreasing the threshold value in the first criterion or increasing in the second criterion, in regard to the values determined for our method, rise the probability of an inaccurate initial-border determination

caused by the acquisition artefacts resulting in decrease of the method performance. The threshold values for both criteria determined for our method are not surprising because the border approximation in the slices following the first few superior slices (strongly affected by the acquisition artefacts) faithfully represent the truth border having a very high similarity of the border approximation between two adjacent slices meaning a small standard deviation of the successive slices (the slice thickness of the breast MRI is in order of only 1–3 mm [32], while our data is acquired with 1 mm). Unlike in the case with the initial slice, the breast-chest wall border determination in other slices refers to the shortest path search along the border with the proposed exponential cost function incorporating the EM information to calculate the path cost. Since the breast-chest wall border is continuous non-linear border, the path should be enforced to have a non-linear form which is crucial for the image regions with no edge score. The proposed exponential cost function achieves this and is found to give a robust result in determining the path along the breast-chest wall border. To decrease the impact of the edges not belonging to the breast-chest wall border on the shortest-path search, we specified the border-search area using the border information from the adjacent (previous) slice. The border-search area proposed in our paper provides a more accurate border determination compared to the border-search area proposed in [23] since the latter may not include the whole breast-chest wall border. It is because this border-search area is defined as a fixed-wide area above the approximated thoracic anterior border and, therefore, its shape depends on the chest shape resulting in the possibility of not including the whole breast-chest wall border, since this border has often a larger shape variability compared to the chest as is the case with the example in the third row and the column in Fig. 6. The breast-skin border is obtained by a slice-wise approach simply because the EM edges belonging to the breast-skin border are easy to identify and separate from the background EM edges allowing an accurate border determination by using only morphological operations. From the other side, the breast-chest wall border is obtained by a multi-slice approach because the EM edges belonging to the breast-chest wall border are difficult to identify and separate imposing the use of a tube (border information from the previous slice) to specify the border-search area. A direct application of the morphological operations on the EM edges in a tube does not provide the breast-chest wall border with a satisfied accuracy because of the impact of the irrelevant EM edges connected to the border EM edges, while the shortest-path search overcomes this limitation. The automatic determination of the lateral-posterior breast ends proposed in [14] uses a V-shape cut obtained with the innerbody anatomical landmarks, i.e., thoracic spine and lateral margin of the bilateral pectoralis muscles. However, this determination is challenging due to a high reduction in the signal intensity in the chest and possible lateral connection of the fibroglandular tissue to the pectoral muscle. The most recent approach in literature [23] proposes automated obtaining of the V-shape cut from [14] with a chest-region template. Nevertheless, this approach causes exclusion of the fibroglandular tissue parts in 9/52 cases from our database, these being mostly the challenging cases. Since determination of the lateral-posterior breast ends is more a problem of consistency rather than accuracy [14], we propose an approach where the position of the breast ends is determined experimentally as 2/3 of the shortest distance between the minimum point within the concavity between the breasts and horizontal middleline between the left and right laterally-outermost body point. This approach is based only on the body-contour landmarks which are easy to determine automatically. During experiment we also

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tried different proportions, such as 1/3 and 1/2, however, they showed to be suboptimal as they excluded the part of the fibroglandular tissue in 6/52 and 4/52 cases, respectively. The proportion 2/3 was determined to be the optimal choice including the whole fibroglandular tissue for all the patients from our database that was confirmed by both radiologists. Despite offering a valuable potential for the breast-region segmentation, there are some limitations in our study. First, the MRI scans used in our research were acquired following the same MRI-acquisition protocol, i.e., having the same acquisition parameters, e.g., TR, TE, flip angle, field of view, in-plane resolution and slice thickness, and were acquired with the same imaging scanner and, thus, using the same coil and magnetic-field strength. In future, we plan to demonstrate the feasibility of our segmentation method being used with data which broadens the range of the MRacquisition parameters. Nevertheless, our method already showed to be robust on a large range of contrast and is therefore expected to be able to cope with a large range of the parameters affecting the contrast in MRI. Second, our method was developed to be used specifically on the T1-weighted non-fat-suppressed MR images. It is not directly applicable to some other image types such as the T1-weightedand T2-weighted-fat-suppressed MR images because it also relies on FCM clustering through the body fat mask that cannot be obtained in these images because their fat tissue appears much darker than in the non-fat-suppressed MR images. Although our method cannot be directly generalized to some other types of the MR images, the result of our method is promising for the future research in searching the ways enabling generalisation of our approach to be used in other MR image types. Third, all the MRI scans were acquired in the axial view. The application of our method for the sagittal MR images is possible, however, this would require some adjustments that would mostly involve a procedure for obtaining the starting and ending seed point for the shortest-path search which would lie on the anterior and posterior MR image ends for each slice of the breast volume. Moreover, for the sagittal MR images, the ROI definition and the breast-chest wall border extension are not required.

7. Conclusion In this paper we present a fully-automated method for the breastregion segmentation in the axial MR images. The main advantage of our method compared to other methods proposed in the literature for the axial MR images is in its applicability for the challenging cases where a part of the fibroglandular tissue is connected to the chest wall and/or skin with no visible contrast, i.e. no fat presence, between them. The important advantage is also in not requiring any training set for learning the anatomical or statistical knowledge which makes the segmentation inherently dependable on the intrinsic properties of the training data. The method is validated on a representative database covering the full range of the BI-RADS breast-density categories indicating that the method allows for an accurate and robust segmentation. It can be concluded that the proposed method shows a potential to be incorporated into the computer-aided analysis system for the breast MRI to support physicians in their decision making.

Conflict of interest statements None declared.

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Acknowledgement The authors are grateful to Dr. Bram Platel from Department of Radiology at the Radboud University Nijmegen Medical Centre, M.Sc. Kristijana Hertl MD and radiographer Gasper Podobnik from the Radiology department at the Institute of Oncology, Ljubljana, Slovenia, for their generous assistance in realization of this paper and for valuable discussions. The project was supported by the Slovenian Research Agency under the PR-03116-1 grant.

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Automated breast-region segmentation in the axial breast MR images.

The purpose of this study was to develop a robust breast-region segmentation method independent from the visible contrast between the breast region an...
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