Int J CARS (2009) 4:27–36 DOI 10.1007/s11548-008-0267-9
ORIGINAL ARTICLE
A pilot study of architectural distortion detection in mammograms based on characteristics of line shadows Mitsutaka Nemoto · Soshi Honmura · Akinobu Shimizu · Daisuke Furukawa · Hidefumi Kobatake · Shigeru Nawano
Received: 27 December 2007 / Accepted: 14 September 2008 / Published online: 28 October 2008 © CARS 2008
Abstract Objective We present herein a novel algorithm for architectural distortion detection that utilizes the point convergence index with the likelihood of lines (e.g., spiculations) relating to architectural distortion. Materials and methods Validation was performed using 25 computed radiography (CR) mammograms, each of which has an architectural distortion with radiating spiculations. The proposed method comprises five steps. First, the lines were extracted on mammograms, such as spiculations of architectural distortion as well as lines in the mammary gland. Second, the likelihood of spiculation for each extracted line was calculated. In the third step, point convergence index weighted by this likelihood was evaluated at each pixel to enhance distortion only. Fourth, local maxima of the index were extracted as candidates for the distortion, then classified based on nine features in the last step. Results Point convergence index without the proposed likelihood generated 84.48/image false-positives (FPs) on ave-
rage. Conversely, the proposed index succeeded in decreasing this number to 12.48/image on average when sensitivity was 100%. After the classification step, number of FPs was reduced to 0.80/image with 80.0% sensitivity. Conclusion Combination of the likelihood of lines with point convergence index is effective in extracting architectural distortion with radiating spiculations.
M. Nemoto (B) Department of Radiology, The University of Tokyo Hospital, 7-3-1 Hongo Bunkyo-ku, Tokyo, Japan e-mail:
[email protected]
Breast cancer is currently the most serious cancer for women around the world and the prevalence rate has been ranked as top among all cancers of women in Japan since 1995 [1]. Screening mammography is known to be effective in detecting breast cancers at an early stage. However, some cancers might be missed by radiologists due to the heavy burden of interpreting large numbers of mammograms. To reduce the burden on radiologists and improve the objectivity of diagnosis, computer-assisted detection/diagnosis (CAD) systems have been developed [2]. Since the most frequently observed radiographic findings in breast cancers are masses and micro-calcifications, many researchers engaged in the development of CAD have focused on detecting these important signs. Architectural distortion (AD) is another important sign, representing a very subtle mammographic finding, sometimes with no visible
S. Honmura · A. Shimizu · D. Furukawa · H. Kobatake Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo, Japan e-mail:
[email protected] D. Furukawa e-mail:
[email protected] H. Kobatake e-mail:
[email protected] S. Nawano Department of Radiology, International University of Health and Welfare Mita Hospital, 1-4-3 Mita, Minato-ku, Tokyo, Japan e-mail:
[email protected]
Keywords Computer-assisted detection/diagnosis · Mammograms · Breast cancer · Architectural distortion · Point convergence index Abbreviations AD Architectural distortion CAD Computer-assisted detection/diagnosis CR Computed radiography Introduction
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masses, but showing obvious spiculations. The definition of AD in BI-RADSTM [3] is as follows: “The normal architecture of the breast is distorted with no definite mass visible. This includes spiculations radiating from a point and focal retraction or distortion at the edge of the parenchyma.” Some ADs might be missed by both radiologists [4] and CAD systems designed for the purpose of detecting masses [5]. Detection of AD would improve the prognosis of breast cancer patients, lowering mortality [6]. Development of CAD systems capable of detecting AD is thus a challenging but essential research topic in this field. Several studies have been published regarding the detection of AD with radiating spiculations. Such AD exhibits lines corresponding to spiculations from a point that might be located in the center of the cancer [3]. Zwiggelaar et al. [7] proposed a scheme for the detection of spiculated mass lesion. The abnormal pattern of linear structures and central mass are extracted individually and detection results are combined using principal component analysis (PCA)-based methods. Kegelmeyer et al. [8] used a 5-dimensional feature vector that included standard deviation of the edge orientation histogram and the output of four spatial filters to classify spiculated lesions. These detection techniques achieved more than 80% sensitivity, but specificity was low. Mudigonda et al. [9] studied the use of a texture flow-field to detect mass lesions, which might be effective in extracting AD, but no specific validation results for extracting AD were described in the paper. Sampat et al. [10] proposed a technique for enhancing both spiculated masses and AD, using filtering in the radon-transform domain and detecting spiculated lesions, which generated 14 false-positives (FPs) per image with a sensitivity of 80%. Ayres and Rangayyan [11] presented a method for AD detection by analyzing the oriented texture obtained from a bank of Gabor filters. A sensitivity of 88% was achieved, but with 15 FPs per image. In the latest paper [12], success was achieved in reducing FP numbers by introducing a geometrically constrained phase portrait model. Ichikawa et al. [13] developed a detection technique that determined point convergence index of line structures using mean curvature, obtaining 80% sensitivity with 0.9 FPs per image. Guo [14] and Tourassi [15] proposed fractal analysis-based methods to discriminate between normal regions of interest (ROIs) and ROIs with AD, but this required setting ROIs on mammograms in advance. Most of the promising methods that can detect AD automatically from mammograms employ a similar scheme that extracts lines and analyzes spatial distribution of these extracted lines. However, no papers have focused on the discrimination of lines before evaluating the spatial distribution pattern of lines. Generally speaking, a variety of lines are extracted by the line extraction process in a conventional AD detection scheme, such as breast ducts and vessels, in addition to spiculations. If we reduce lines other than spiculations
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before analyzing the spatial distribution of the lines, detection performance of the spiculated pattern will be improved. We present herein a new method for detecting ADs with radiating spiculations. The main idea for the method comes from the fact that the lines corresponding to spiculations of AD differ in characteristics from lines in the normal mammary gland. In the proposed method, we compute the likelihood of spiculation, showing how the line relates to spiculations in AD. A modified point-convergence index weighted by likelihood is then calculated to enhance ADs, while the conventional method evaluates convergence index without any weighting. We applied the proposed method to 25 CR mammograms, each of which included an AD with spiculations to validate performance. Materials and methods Materials The dataset for validation comprised 25 Fuji computed radiography (FCR) mammograms taken at National Cancer Center Hospital East (Chiba, Japan). Each mammogram has an AD with radiated spiculations and no definite visible mass. All cases were confirmed as malignant by biopsy and no AD due to scarring was present. Image size, pixel size and density resolution of each mammogram were 1,185 × 885 pixels, 0.2 mm/pixel and 10 bits, respectively. This study aimed to detect focal regions of AD surrounded by radiating spiculations, which were confirmed by a radiologist. An example of the regions is presented in Fig. 1. The FCR mammography system used in our experiment was equipped with advanced image processing, including gradation processing (GP) [16], multi-objective frequencyprocessing (MFP) [17], and pattern enhancement processing for mammography (PEM) [18]. GP is a process to customize image intensity and contrast in accordance with the imaging area or the purpose of diagnosis. Parameters of GP were set as follows: rotation amount (GA), 1.0; gradation type (GT), curve-R (fundamental form of the non-linear conversion curve); rotation center (GC), 1.4; gradation shift amount, 0.06. MFP is a process to enhance any structures regardless of size, offering two functions: a frequency enhancement function; and a dynamic range compression function. For MFP, parameter MRE (for frequency enhancement) was 1.5 and MDE (for dynamic range compression) was 0.2. PEM is a process to specifically enhance microcalcifications in FCR mammograms. The enhancement factor of PEM, called PRE, was set to 2.0. Methods Figure 2 illustrates the flow of the proposed CAD system. The proposed system includes five steps. First, the lines
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Fig. 1 An example of the mammogram with AD. The boundary in black shows the focal region of the AD to be detected in this study and the upper left partial image shows sketches of spiculations in AD, both of which were approved by a radiologist
Mammogram
Extraction of line structure
Calculation of likelihood of line associating with architectural distortion
Calculation of point convergence index with likelihood
Extraction of candidates
Classification of candidates
Architectural distortion
Fig. 2 Flowchart of the proposed system to detect AD. The second step computes the likelihood of spiculation for AD, enabling the enhancement of AD compared to conventional methods
in mammograms are extracted, including spiculations and lines in the mammary gland, using the combination of the line convergence filter and the Laplacian filter followed by binarization of the filter output. Second, the likelihood of spiculation of AD is calculated based on 12 features, such as contrast and location of the lines. In the third step, the modified point convergence index weighted by the proposed likelihood is calculated at each pixel, to enhance the AD. In the fourth step, local maxima of the index are extracted as candidates of AD. The last step classifies candidates based on the nine features. (a) Extraction of lines This process extracts the lines corresponding to spiculation of the AD, along with lines in the mammary gland by applying
the combination of the line convergence index filter [19] and the Laplacian filter followed by binarization of the filter output. The line convergence filter can enhance lines with various contrast and width. In a three-dimensional space where the first and second axes show spatial coordinates of an image and the third axis corresponds to density of the coordinate, a typical line is described as a long, narrow and semi-cylindrical shape where the gradient vectors concentrate on the ridge of the line (Fig. 3). The line convergence index filter outputs high values along the ridge of the line by evaluating the concentration of gradient vectors. However, output for the curvilinear structure might slightly lower in cases where curvature of the line is high, as this filter assumes the shape of the line as piecewise linear. We therefore adopted a Laplacian filter to reinforce the performance of extracting the lines with high curvature. Of note is the fact that when the differential distance of the Laplacian filter is roughly equal to the width of the line, the Laplacian filter works as a matched filter to enhance the line [20]. The present study applied the Laplacian filter with several differential distances at each pixel and computed the maximum among outputs to deal with various sizes of lines. We finally combined the output of the line convergence index filter with those of the Laplacian filter by linear-coupling. In our experiments, after applying the 3 × 3 median filter to reduce noise on the mammogram, lines were enhanced using the above two filters (Fig. 4b–d). Length and width of the line convergence index filter were set as 20 and 5 pixels, respectively. Differential distance of the Laplacian filter was changed from 2 to 5 pixels to deal with the various widths of shadows. Enhanced images were binarized by discriminant analysis [21] and center lines were extracted using Hilditch’s thinning algorithm (Fig. 4e, f).
(b) Calculation of likelihood of spiculation Likelihood of spiculation is computed at each line element defined on the line obtained from the previous Step (a). First, the line is divided into a set of line elements, each of which consists of three connected pixels [22]. Mahalanobis distance
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Fig. 3 A typical line as supposed in this study. Left A model of the line. Middle Profile of the gray value. Right An illustration explaining that gradient vectors are concentrated on the ridge of the line
Fig. 4 Outputs of the line extraction process. a An example of an original mammogram. b Output of the line convergence filter. c Output of the Laplacian filter. d Line-enhanced image by linear coupling of out-
puts from the two filters. e Binarized image using discriminant analysis. f Extracted lines after applying Hilditch’s thinning algorithm
from the lines of AD and that from other lines are then computed based on the 12 features listed below at each line element. Subsequently, ratio of the distance from normal line to that from line of AD is computed and used as likelihood of spiculation. A larger likelihood means a higher possibility of spiculation. Likelihoods of lines exceeding 2.0 were considered as 2.0 to avoid excessive influence on the convergence index as evaluated in the next step from lines with extremely high likelihood. The following 12 features of each line were measured in this study. These features were selected based on the fact that spiculations of AD differ in characteristics from those of lines in normal mammary gland without distortion, due to tension by the invisible mass. Details of each calculation procedure are presented below.
(b-1) Density-related features (4 features) The following 4 features were measured to differentiate spiculations from normal lines from the viewpoint of density. Mean density: Mean density along the line orthogonal to the interested line element was measured according to the following equation:
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Density =
n 1 fi n
(1)
i=1
Here, length of the line was set at 11 pixels for our study. Contrast of line: Contrast of the line was also evaluated using the following equation: Contrast =
f max − f min f min
(2)
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where f max and f min are maximum and minimum of the density along the orthogonal line, respectively. Mean curvature of gray surface of line: Mean curvature [23,24] of the gray surface of the line was calculated in the 3-dimensional space shown in Fig. 3, where the third axis corresponds to density. Density surface in the 7 × 7 local region was approximated by a quadratic surface based on the least-squares method and mean curvature at the line element was computed according to the equation below: Curvature =
(1 + f x2 ) f yy + (1 + f y2 ) f x x − 2 f x f y f x y 2(1 + f x2 + f y2 )3/2
(3)
q R1
α
R3 r
R2 P
R
ዘ R2
R3 R1
∂2
f (x,y) where f x means ∂ f ∂(x,y) x , and f x y means ∂ x∂ y of the fitted continuous surface. Outputs of two filters used in the line extraction process (2 features): The line convergence index and output of the Laplacian filter computed in the line extraction process were also adopted as features of the line element.
(b-2) Contribution rate to point convergence index The line element that belongs to the radiating spiculation is expected to make a large contribution to point convergence index at the pixel around the line element. We therefore measured contribution rate of the line element to the point convergence index, as defined by the following equation: Contribution = max {dq |cos θi |} i i ∈N E
(4)
where dq shows length of the line element, NE means the neighborhood of the line element, θi means angle between the line element and the segment from the centre of the line element to position i, at which point convergence index is > 0.7. (b-3) Geometric features (6 features) Length and width of the line (2 features): Length and width of the line to which the line element belongs were measured. Detected lines were separated into several lines at branching points and length of each line was approximated by the number of voxels in the line. Width of the line at the line element was defined as the distance from the center of the line element to the boundary of the line. Distance to the mammary gland, skin line and edge of image: We also evaluated location of the line element by computing distance to the skin line in addition to signed distance to the boundary of the mammary gland, for which the sign was positive when the line element existed within the mammary gland and negative if located outside of the mammary gland. Here, the mammary gland was extracted by the binarization of the original image where the threshold value was decided by discriminant analysis [21]. Minimum distance from the local element to the edge of the image was also calculated in this study.
Fig. 5 Illustration of mask and line element of point convergence index filter
Angle between line element and line from centre of line element to nipple: Direction of the spiculation differs from that of normal lines such as breast ducts in mammary glands that spread from the nipple. We therefore computed the angle as a feature between the line element and a line from the centre of the line element to the nipple.
(c) Calculation of point convergence index with likelihood of spiculation To enhance AD with radiating spiculations, the proposed method calculated the point convergence index C(P), which was originally proposed in [22] and was modified in this study by introducing the likelihood of spiculations relating to AD as follows: 1 C(P) = N +1
R
(dq/r · D · |cos α|) R (dq/r )
(5)
where dq, r and α mean length of line element q, distance between P and center of line element q, and angle between line element q and line segment from P to center of q, respectively (Fig. 5). D is the likelihood of spiculation calculated from the 12 features. (N + 1)−1 works as a weight about the uniformity of line distribution in the mask R, where N is the number of sub-regions Ri (i = 1, 2, 3) for which local point convergence index is < 0.75. This was introduced to evaluate uniformity of the distribution of spiculations. The final output of the filter was a maximum among convergence indices with various sizes of mask R to deal with various sizes of AD. External and internal diameters were changed from 36 to 123 pixels (7.2–24.6 mm) and 2–67 pixels (0.4–13.4 mm), respectively.
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: central ROI (Rc) : marginal ROI (Rm)
Fig. 6 Illustration of mask regions to calculate features for discrimination of the candidate
(d) Extraction of candidates
radius of the ROI was set to be equal to the radius of the outmost ring used in the candidate extraction step and features were defined not only on original images, but also on the unsharp masked mammogram so as to evaluate finer features. (e-1) Density-related features (8 features) Skewness, second-moment and energy of the density distribution of the ROI were calculated as features. 1 PR (i)·(i − µ)3 (6) skewness = 3 σ i 2nd-moment = PR (i) · i 2 (7) i
Local maxima of the point convergence index were detected as the candidates of AD by evaluating mean index (average of C(P)) in the triple ring area. If mean index of the minimum ring was higher than that in middle ring area and no local maximum was seen in the outmost ring area, the point was extracted as a candidate point. To deal with various size of ADs, we prepared two sets of radii: (i) 2, 4 and 14 pixels (1.0, 2.0 and 7.0 mm); and (ii) 4, 8 and 28 pixels (2.0, 4.0 and 14.0 mm). Candidates detected by the two kinds of triple ring were analyzed and classified into AD and normal tissues in Step (e). (e) Classification based on Mahalanobis distance ratio Some candidate points might correspond to parts of normal tissue. This step classified candidates into AD and normal tissues based on Mahalanobis distance to each class. Eight density features and location of the candidate were measured to calculate Mahalanobis distances. These features were selected experimentally by the sequential forward selection method [25] from the feature database, which included 175 features. The database included the 173 density features (gray level statistics, contrast, etc.) calculated from an original mammogram and unsharp masked mammogram, and 2 geometric features, but we have not shown the whole details of the feature database due to the limitations of space. We have only explained the features adopted to classify candidates. Details of the selected features are shown below and in Table 1. To calculate the selected features, a circular ROI was set so that the center of the circle coincided with the candidate point. The central region and marginal region (circular region–central region) were called Rc and Rm , respectively (Fig. 6). Each region was divided into 12 sectors. First, the feature measurement process estimated sectors corresponding to mammary gland or fat regions based on gray values. High-density regions were estimated to represent mammary gland and low-density regions to represent fat. Note that
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subtraction energy =
i PR1 (i)
2
−
i PR2 (i)
2
(8)
where µ, σ and PR (i) represent the average of gray level, standard deviation of gray level and relative frequency of density i in sectoral area R, respectively. Details of the sectoral area and image used for calculation are shown in Table 1. AD with radiating spiculations is caused by the invisible mass, meaning that the mass cannot be recognized clearly. However, slight differences are sometimes seen between central and marginal regions, which might form a difference in contrast between AD and normal tissue. In our study, the following four features [26] related to contrast were selected: Contrast-1 = µ R1 − µ R2
(9)
(µ R1 − µ R2 )2 Contrast-2 = σ R21 + σ R22 PR (i) − PR (i) Contrast-3 = 1 2 i
Contrast-6 =
1
(10) (11) 1
PR1 (i) 2 − PR2 (i) 2
2
(12)
i
(e-2) Distance to mammary gland (1 feature) We employed signed distance from the candidate point to the dense mammary gland, which was also measured in Step b-3, as a geometric feature for the likelihood of spiculation. Results This section shows the results of validation testing for the proposed method. The candidate extraction process was first evaluated to determine how well the proposed likelihood of spiculation works for detection of AD. Average number of FPs per image with a specific sensitivity was adopted as a criterion for validation and compared with that of the conventional method without using likelihood. Second, performance of the candidate classification process was
Int J CARS (2009) 4:27–36 Table 1 Details of features used in the classification step
*mg Mammary gland
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Feature
Image used for the measurement
Measured area
Skewness (a)
Original
RMAR−fat
Skewness (b)
Unsharp
Whole ROI
Second moment
Unsharp
RCEN−mg
Subtraction energy
Original
RCEN−mg , RCEN−fat
Contrast-1
Original
RCEN−mg , RMAR−fat
Contrast-2
Original
RCEN−mg , RMAR−mg
Contrast-3
Original
RCEN−fat , RMAR−fat
Contrast-6
Original
RCEN−mg , RMAR−mg
Distance to mg*
–
–
Fig. 7 Extracted lines with likelihood of spiculation. Lines with high likelihood are displayed in red and those with low likelihood are drawn in white
b)
c)
a)
a) high
b)
c)
low
analyzed using a free-response receiver operating characteristics (FROC) curve. In addition, Mahalanobis distance ratio in each line element to calculate likelihood of spiculation (explained in Step (b)) and another Mahalanobis distance ratio to classify the extracted AD candidates into true AD and normal tissues (in Method (e)) were estimated by the leave-one-out method to most effectively utilize samples for training and testing [27]. Performance of the candidate extraction process Figure 7 shows extracted lines colored by the likelihood of spiculation. From this figure, lines associating with AD are observed to present higher likelihood than normal lines. However, some lines with high likelihood can be confirmed as corresponding to normal lines, which might cause FPs in the next extraction step of AD.
Figures 8 and 9 show the point convergence index of Fig. 7 by conventional and proposed algorithms, respectively. Figure 8 contains many areas with high index that exist not only around AD but also in normal tissue, while the modified point convergence index outputs high values around AD as shown in Fig. 9. The proposed index weighted by likelihood of spiculation clearly contributes substantially to the detection of AD and the reduction of FPs. The experimental results of using 25 mammograms showed that 84.48 FPs were extracted from an image on average by the conventional method, compared to only 12.48 FPs per image using the proposed algorithm. Performance of the classification process Figure 10 shows FROC curve of the classification step. Error rate was evaluated by the leave-one (candidate)-out
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Fig. 8 Point convergence index of Fig. 7 as processed by the conventional algorithm. Areas with high index are widely distributed everywhere in the breast, causing numerous FPs
b)
c)
a)
a) high
c)
b)
low
Fig. 9 Modified point convergence index of Fig. 7 using the proposed algorithm. Areas with high index are concentrated around the AD. Black dots show candidates for AD
b)
c)
a)
a) high
b)
c)
low
method. A number of FPs of 0.8 was obtained with 80% sensitivity, comparable or even better than previous studies described in the “Introduction”.
Discussion The main contributions of this study are the proposal of likelihood of spiculation for AD and modified point convergence
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index to detect AD by taking into account likelihood. The modified index greatly contributed to reducing FPs, as shown in the previous section (from 84.48 to 12.48), with a significant difference ( p < 0.01) between number of FPs by conventional algorithm and by the proposed algorithm, as confirmed by both t-test and Wilcoxon signed-rank test. Figures 11 and 12 show examples of the resultant images of the classification step when sensitivity was fixed at 0.8. Figure 11 shows successful detection of AD but with one FP.
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1.0 0.9 0.8
Sensitivity
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
2.0
4.0
6.0
8.0
10.0
12.0
Number of FPs per image Fig. 10 FROC curve of the classification step
Figure 12 presents a case of misclassification with a falsenegative AD and two FPs due to occlusion of lines by dense mammary gland tissue. The fact that the most of the features used for classification are density-related should be kept in mind. Occlusion of the AD by dense mammary gland tissue makes the classification problem very difficult. FROC analysis of the experiment indicated that the proposed system achieved 0.910 of Az, higher than the
classification results using a single feature. Average and maximum Az values in the case of using a single feature are 0.637 and 0.743, significantly lower than that of the proposed method ( p < 0.01 tested by [28,29]). The achieved performance using the proposed method (sensitivity, 80.0%; FPs per image, 0.80) seems comparable or even better than the results of previous reports. However, fair comparison requires application of the methods under comparison to the same database, which remains as future work. The mammogram database used in this experiment included only AD cases, with no normal cases. This might have caused a difference in the frequency of FPs when applied to normal cases. We thus plan to apply the proposed system to a large database including normal mammograms in order to validate the performance of the system. In addition, the error estimated using the leave-one out method is likely to include some degree of bias, particularly in the case of small sample sizes [30]. Increasing the number of samples thus represents important future work. Differentiation between ADs due to scarring and ADs resulting from cancer is another interesting area that will be addressed in the future. To increase classification accuracy, we plan to adopt novel features other than density-related features, along with powerful classifiers such as classifier ensemble [31] and cascade scheme [32], as possible methods of boosting performance.
Fig. 11 Successful detection of AD. The proposed method detected the AD denoted in the red circle, with one FP marked in the green circle located very close to the AD
Fig. 12 Failure cases with two FPs and a false-negative AD. Failure was attributed to the upper right region of the AD being occluded by dense mammary gland tissue
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36 Acknowledgments This study was supported in part by a Grant-inAid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, and a Grant-in-Aid for Cancer Research from the Ministry of Health, Labour, and Welfare, Japan.
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