Local curvature analysis for classifying breast tumors: Preliminary analysis in dedicated breast CT

Abstract

Purpose: The purpose of this study is to measure the effectiveness of local curvature measures as novel image features for classifying breast tumors.

Methods: A total of 119 breast lesions from 104 noncontrast dedicated breast computed tomography images of women were used in this study. Volumetric segmentation was done using a seed-based segmentation algorithm and then a triangulated surface was extracted from the resulting segmentation. Total, mean, and Gaussian curvatures were then computed. Normalized curvatures were used as classification features. In addition, traditional image features were also extracted and a forward feature selection scheme was used to select the optimal feature set. Logistic regression was used as a classifier and leave-one-out cross-validation was utilized to evaluate the classification performances of the features. The area under the receiver operating characteristic curve (AUC, area under curve) was used as a figure of merit.

Results: Among curvature measures, the normalized total curvature (CT) showed the best classification performance (AUC of 0.74), while the others showed no classification power individually. Five traditional image features (two shape, two margin, and one texture descriptors) were selected via the feature selection scheme and its resulting classifier achieved an AUC of 0.83. Among those five features, the radial gradient index (RGI), which is a margin descriptor, showed the best classification performance (AUC of 0.73). A classifier combining RGI and CT yielded an AUC of 0.81, which showed similar performance (i.e., no statistically significant difference) to the classifier with the above five traditional image features. Additional comparisons in AUC values between classifiers using different combinations of traditional image features and CT were conducted. The results showed that CT was able to replace the other four image features for the classification task.

Conclusions: The normalized curvature measure contains useful information in classifying breast tumors. Using this, one can reduce the number of features in a classifier, which may result in more robust classifiers for different datasets.

FIG. 1.

This figure shows the DICE coefficient of one example segmentation result. The final DICE coefficient was computed by averaging DICE coefficients of each cross-sectional view. Any segmentation with a DICE value of less than 0.7 was removed from the study.

FIG. 2.

(A) The volumetric segmentation obtained using the semiautomated segmentation algorithm. (B) and (C) display the smoothed version of the segmentation results and its triangulated surface representation [lines in (C) represent edges of triangulated surface], respectively. The smoothing operation retains the overall shape and detail of the breast lesion, while removing noise.

FIG. 3.

An illustration of how the normal curvature at a vertex is related to the size of a circle fitted to the cross-sectional contour at the same vertex. The magnitude of the normal curvature has an inverse relationship with the radius of the circle.

FIG. 4.

The first and second columns show the relationship of the average and standard deviation of each curvature measure with the lesion size. The last column shows the relationship between the normalized versions of the curvature measures and lesion size. Pearson’s correlation analysis was conducted on (1) all lesions, (2) benign lesions only, and (3) malignant lesions only. The normalization process successfully reduced each measure’s dependency on lesion size, especially for total curvature. To visualize the dependency between lesion size and each curvature measure, third order polynomial fits for benign lesions (solid line) and for malignant lesions (dashed line) are added on each plot. Fitted lines for normalized measures also show reduced dependency on lesion size compared to measures without normalization. Note that one benign lesion shows higher magnitude in normalized curvature values than the others. The correlation analysis after removing such lesion was similar to that of the original set; the correlation coefficient values for the normalized total, Gaussian, and mean curvature were 0.03 (p-value = 0.76), −0.44 (p-value < 0.0001), and 0.49 (p-value < 0.0001), respectively.

FIG. 5.

Illustrations of how the total, mean, and Gaussian curvature values vary on the lesion surface for malignant and benign lesions. Malignant lesions tended to show more variations in curvature values than benign lesions.

FIG. 6.

This box plot displays how the averaged normalized total, mean, and Gaussian curvature values differ for the set of malignant and benign lesions.