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1 Department of Electro-Optics, Jerusalem College of Technology, Jerusalem,
Israel.
2 Department of Radiology, Hadassah University Hospital, Jerusalem,
Israel.
3 Department of Radiology, Montefiore Medical Center, Albert Einstein College of
Medicine, Bronx, NY.
4 Staten Island University Hospital, 475 Seaview Ave., Staten Island, NY
10305.
5 Department of Electronics, Jerusalem College of Technology, Jerusalem,
Israel.
Received January 17, 2003;
accepted after revision September 4, 2003.
Address correspondence to S. S. Buchbinder.
Abstract
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MATERIALS AND METHODS. Three hundred twenty-four cases of clustered microcalcifications with biopsy-proven results were digitized at 42-µm resolution and analyzed on a computerized system. The shape factor and number of neighbors were computed for each microcalcification, and the eccentricity of the cluster was computed as well. The shape factor is related to the individual microcalcification; the average number of neighbors and the cluster eccentricity reflect the cluster geometry. Stepwise discriminant analysis was used to evaluate the contribution of the extracted features in predicting malignancy. The performance of a classifier based on the features selected by stepwise discriminant analysis was evaluated by receiver operating characteristic (ROC) analysis.
RESULTS. To obtain the best discrimination model, we used stepwise discriminant analysis to select the average number of neighbors and the shape of the individual microcalcification, but excluded cluster eccentricity. A classification scheme assigned the average number of neighbors a weighting factor, which was 1.49 times greater than that assigned to the shape factor of the individual microcalcification. A scheme based only on these two features yielded an ROC curve with an area under the curve (Az) of 0.87, indicating a positive predictive value of 61% for 98% sensitivity.
CONCLUSION. Computerized analysis permitted calculations reflecting the shape of individual microcalcification and the geometry of clusters of microcalcifications. For the computerized classification scheme studied, the cluster geometry was more effective in differentiating benign from malignant clusters than was the shape of individual microcalcification.
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The terminology used to describe clusters of microcalcifications can be ambiguous. Although it is well established that the morphologic characteristics of microcalcifications are the most important elements in the analysis of the cluster [8–10], the term "morphologic characteristics" can refer to either the distribution function (heterogeneity) of the shape and size of the individual microcalcifications in the cluster [11, 12] or the distribution (geometric arrangement) or shape of the cluster in the breast [13].
Methods to improve visualization and analysis have been sought because of the low radiographic contrast and the small size of the microcalcifications. In recent years, computerized analyses based on features such as size, shape, and distribution of the microcalcifications in the cluster have been introduced to increase the accuracy of mammographic diagnosis [11, 12, 14–18]. This study evaluated computer-extracted features to characterize clusters, which are similar to the features used intuitively by the radiologist in the conventional interpretation of mammograms. The diagnostic roles of features reflecting the shape of the cluster and the shape of the individual microcalcification were compared to assess their usefulness in a computer-aided diagnosis system.
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The best image showing the lesion was digitized, using a PowerLook III digitizer (Umax, Taipei, Taiwan) with a transparency adaptor. First the radiologist demarcated the lesion on the radiograph, and the entire radiograph was digitized at low resolution (72 dots per inch [dpi]) with 256 gray levels. This image was displayed on the computer screen to localize the region of the lesion on the computer. The area containing the cluster of microcalcifications was then delimited on the digital image using the computer mouse, and this region of interest (ROI) on the film was redigitized at high resolution, 600 dpi (42 µm pixels). All subsequent image processing and feature extraction were performed on this high-resolution digitized image. Because of variability in the radiodensity of film-screen mammograms, proprietary software has been developed to control the operation parameters of the digitizer and maximize the amount of information in the resulting digital image. By analyzing the range of optical densities in the ROI and using preliminary data characterizing the response of the digitizer to the various optical densities in the film, the software adjusted the scanning parameters of the digitizer. Thus, the brightness and contrast in the digitizing process were automatically optimized to produce a digital image with the highest information content, which was then displayed on the computer monitor for further evaluation.
The digital image of the lesion included bright spots of various sizes, and each of them represented a potential microcalcification for feature extraction. For the analysis of clusters of microcalcifications, the radiologist defined the region encompassing the cluster on the digital images, and the computer-aided diagnosis device automatically indicated an initial selection of the bright spots above a preset threshold as candidates by highlighting them in red. The radiologist could then alter target selection by modifying the threshold, so that only appropriate spots that represent calcifications were included in the quantitative analysis. Any bright spots considered by the radiologist not to be microcalcifications could be manually excluded from the analysis, and others that were considered true microcalcifications could be added to the cluster manually. During the interactive stages, the new selection of targets was updated in real time on the computer screen and highlighted in red. After the radiologist was satisfied with the selection of targets, the algorithm automatically proceeded to extract features characterizing the cluster. The stepwise discriminant analysis procedure analyzed the features that best discriminated malignant and benign clusters and selected for the classification scheme features related to the shape of the individual microcalcification and to the cluster morphology.
Two quantitative features characterizing the cluster morphology were used to analyze the shape of the cluster. The average number of neighbors per calcification was calculated as a feature reflecting the geometric arrangement of the calcifications in the cluster, and the cluster eccentricity was calculated as a feature reflecting the shape (round or elongated) of the overall cluster contour.
The average number of neighbors per calcification was calculated according to the digital triangulation method of Delaunay as described by Toussaint [19]. For this purpose, adjacent pairs of microcalcifications had to be identified. The identification of such pairs was performed by defining a "zone of influence" for each microcalcification in the cluster. These zones have a polygonal shape, and they were defined for each microcalcification in the cluster by the bisectors of the lines connecting all pairs of microcalcifications, yielding a Voronoi diagram [20]. Two microcalcifications are considered adjacent if their zones of influence have a mutual edge. Therefore, some microcalcification might be nearest neighbors of several other microcalcifications that are all considered to be adjacent pairs. The lines connecting each microcalcification to its nearest neighbors generate the triangulation lines of Delaunay, which are shown in Figure 1 for one of the clusters the software analyzed. All adjacent pairs in the cluster were identified according to this method, and the number of nearest neighbors was evaluated for each microcalcification in the cluster. The number of nearest neighbors was then averaged for the entire cluster to yield the average number of neighbors for the cluster.
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The other feature that was calculated to describe the morphology of the cluster region as a whole was its eccentricity. For evaluating this feature, each microcalcification is represented by its center of gravity and the calculation of eccentricity is based on moments of inertia I xx, I yy, and I xy of these points [21]. A circular cluster is represented by an eccentricity of zero. Clusters with more elongated contour are assigned a higher value of eccentricity, up to 1.
A shape factor was calculated for each microcalcification in the cluster, on the basis of the ratio of the area of the microcalcification to its effective radius. This parameter reflects the moment of inertia of the microcalcification because the effective radius is defined as the square root of the ratio between the moment of inertia and the area. The shape factor was normalized to assign a value of 1 to a circle, and values greater than 1 indicated elongated or irregular shapes. The arithmetic mean of this factor over the whole cluster provided the feature that represented the shape of the individual microcalcifications.
We created a database of the values of the extracted features and the pathology results for all the microcalcifications analyzed. Stepwise discriminant analysis [22, 23] was used to evaluate the usefulness of the various features in creating a good discrimination model differentiating benign and malignant clusters. The sets of features in the benign and in the malignant groups of lesions were assumed to be multivariate normal with a common covariance matrix, as described in detail elsewhere [24].
A pattern recognition scheme based on the discriminant analysis method [25] was constructed to classify each lesion with a single numeric score. This score was derived from a combination of features selected by the stepwise discriminant analysis as contributing most significantly to the discrimination model. For training purposes, the values of the selected features were provided along with the pathology results for each lesion in a training data set. The classification scheme assigned each feature a weighting factor reflecting its relative power in discriminating benign and malignant clusters. The classification scheme then assigned a score to each lesion on the basis of the values of the selected features and on the weighting factor of each feature.
Stepwise discriminant analysis was applied to select the variables that produced the best discrimination between benign and malignant clusters. The decision to enter each variable into or remove it from the model was performed according to criteria that assured the inclusion only of variables that contributed to the discriminatory power of the model. The average number of neighbors and the shape of individual microcalcification were the only two variables that were selected by stepwise discriminant analysis for inclusion in the model. Both variables were selected with the same level of significance (p < 0.0001).
The two variables selected to be incorporated into the discrimination model were used to construct a classification scheme based on the linear discriminant analysis method. When all 324 cases evaluated were included in the training procedure of the classification scheme, the average number of neighbors in the cluster was assigned a weighting factor of 1.114, which was 1.49 times greater than that assigned to the individual shape factor of the microcalcifications (0.748). The performance of the classifier was tested using the jackknife method [26]. The jackknife, or "leave-one-out" technique, consists of several rounds, the number of which equals the number of cases being analyzed. In each round, the features extracted by the computer-aided diagnosis system and the diagnostic truth standard are provided for all cases except one, and the scheme characterizes the remaining case by a single numeric classifier on the basis of the extracted features alone. The resulting values of the weighting factors in each round of training varied slightly because the database differed by one case in each round. The weighting factors obtained in each round of training were nearly identical to the values previously mentioned, and therefore the overall result could be approximated by those values.
The performance of the pattern recognition algorithm was first evaluated by a receiver operating characteristic (ROC) analysis [27]. The ROC analysis is not based on one cut point value of the classifier but allows the cut point value to be changed over a range in a set of repeated experiments. The resulting pairs of sensitivity and specificity for each cut point are examined and plotted as a set of points connected by a curve. The area under this curve (Az) reflects the performance of the method used to classify the lesions. A specific cut point value had to be defined to discriminate benign from malignant lesions with a reasonable sensitivity to calculate the specificity, positive predictive value, and accuracy of the classification scheme. The significance of the difference between the areas under the ROC curves was tested as described by Hanley and McNeil [28, 29].
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The mean average number of neighbors per microcalcification was 3.82 in benign clusters and 4.75 in malignant clusters. The mean value of this variable in malignant clusters was 24.4% higher than that in benign clusters, but the SEM (coefficient of variance) in each group was only approximately 1.6%. Analysis of the histogram of this variable in benign and malignant clusters showed that an average number of neighbors greater than 4.43 was associated with malignancies 78% of the time, and 79% of the benign cases fell below this value.
The mean value of the individual microcalcification shape in malignant clusters was higher by 28% than that in benign clusters, but the SEM in each group was only approximately 1.8%. A histogram of the individual microcalcification shape showed that this variable had a discriminative power somewhat lower than that of the average number of neighbors. An average individual shape factor greater than 1.44 was associated with malignancies 80% of the time, and 81% of the benign cases fell below this value.
For cluster eccentricity, the mean value in the malignant group was higher by 15.6% than that in the benign group, and the SEM in each group was of the same order of magnitude—approximately 5.72%. A histogram of cluster eccentricity showed low discriminative power, which is consistent with the fact that the cumulative distribution functions in the two groups were not significantly different.
The performance of the classification scheme using only the average number of neighbors in the cluster and the individual shape factor of the microcalcifications was assessed by an ROC curve, which yielded an Az value of 0.87 (Fig. 2). Table 3 depicts the performance of this classification scheme for a cut point value of the score corresponding to 98% sensitivity. For this cut point value, a comparison of classification scheme results and the pathology outcomes yielded a specificity value of 38%, a positive predictive value of 61%, and an accuracy value of 68%.
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The average number of neighbors in the cluster was assigned the greatest weighting factor by the discriminant analysis method, and, as shown in Figure 3, its distribution function showed significant discriminatory power. Therefore, we decided to explore the possibility of using an alternative scheme based on the average number of neighbors alone. When this feature was the only variable used to classify the lesion, the resulting ROC curve, as displayed in Figure 4, showed a significantly [28, 29] lower Az value of 0.84 (p < 0.002). Thus, the classification scheme based on both variables performed significantly better than that based on the average number of neighbors alone.
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The shape of individual microcalcifications and the average number of neighbors per microcalcification in the cluster were selected by stepwise discriminant analysis as features to use for the construction of a discrimination scheme. Radiologic–histologic correlations have shown [31] that casting or rodlike calcifications in the duct are characteristic of malignancy, and rounded punctate calcifications are typically benign, commonly found in sclerosing adenosis or fibrocystic mastopathy. The higher values obtained in this study for the individual microcalcification shape factor in malignant clusters reflect the fact that malignant microcalcifications are typically more elongated, and benign microcalcifications are usually more rounded.
Although the shape of microcalcifications is considered important in assessing the likelihood of malignancy [3, 4, 7, 16], the discriminant analysis method assigned this feature a weighting factor that was lower than that assigned to the average number of neighbors. This result may be attributed to the occasional presence of rounded calcifications in malignant clusters, which, according to Homer and Safaii [6], may be caused by retrograde spread of cancer to the lobule. The selection of number of neighbors as the most crucial feature apparently reflects the overriding importance of cluster geometry in evaluating microcalcifications. The number of neighbors per calcification in a cluster quantitatively reflects the intuitive impression regarding the tightness of the cluster in the conventional mammographic interpretation. This characteristic is inherent in the definition of a cluster; therefore, a quantitative feature that describes this trait would be expected to be heavily weighted in a computerized scheme for the evaluation of the likelihood of malignancy. Figure 5A, 5B depicts a cluster in which both the shape of the individual microcalcifications and the cluster geometry indicate malignancy; a typical benign cluster is shown in Figure 6A, 6B. Figure 7A, 7B depicts a cluster in which the geometry indicates malignancy, but the average shape does not, being more rounded than is typical for malignant clusters.
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The cluster contour was represented in this study by the eccentricity. This feature was not selected by stepwise discriminant analysis for the classification scheme, in keeping with the result obtained by Veldkamp et al. [12]. Eccentricity received a low weighting factor when 16 features of clusters of microcalcifications were compared. Another study [32] used circularity as one of eight features in an artificial neural network, but its weighting was not reported. An earlier study [33] reports that it is commonly accepted that benign clusters tend to be more round, whereas malignant clusters tend to be more irregular. Computerized analysis of the data in the latter study indicated a general trend confirming this notion, but considerable overlap was found in the distribution of benign and malignant cases, especially for smaller clusters. We obtained similar results; the eccentricity was slightly higher in malignant clusters, but the difference was not significant. In a recent study [34], a 3D stereoscopic analysis of clusters of microcalcifications was explored using digital images, and this technique helped the reviewer to see the geometric distribution of the cluster. It is possible that a computerized volumetric analysis of the cluster contour may be a significant feature for classifying clusters in the future.
When classifying a cluster of microcalcifications by a single score based on features characterizing the cluster, a cut point value for the score has to be selected to discriminate benign from malignant clusters. Mammography is primarily used as a screening test, so high sensitivity is required to ensure that few true-positive cases are missed, although a certain number of false-positive cases are acceptable. The cut point value for the classifier should be selected to yield high sensitivity even at the expense of obtaining lower specificity. Therefore, we chose a cut point corresponding to 98% sensitivity to evaluate the performance of our classifier. Of course, a higher sensitivity value can be selected if more features than the two we used are extracted by the computer-aided diagnosis system.
Although the appearance of fine calcifications seen in some malignant lesions and some benign lesions may overlap [31, 35], we found that for 98% sensitivity, biopsy could have been theoretically avoided in 64 cases just by computerized analysis of the number of neighbors per microcalcification in the cluster and the shape of the individual microcalcification.
Our results indicate that the average number of neighbors has a higher impact than the shape of individual microcalcifications on the ability to differentiate benign from malignant clusters. The average number of neighbors should, therefore, be a heavily weighted parameter in a classification scheme used to distinguish benign from malignant microcalcifications, with fewer neighbors being associated with benign lesions. Assessing the average number of neighbors per microcalcification by conventional means is not intuitive and cannot be practically performed without computerized analysis. However, this feature reflecting the geometry of clusters of microcalcifications showed a significant role in predicting malignancy and seems to be ideally suited to computerized analysis.
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