Assessment of the invariance and discriminant power of morphological features under geometric transformations for breast tumor classification

Abstract

Background and objectives: Computer-aided diagnosis (CAD) systems are intended to assist specialists in the interpretation of images aiming to support clinical conduct. In breast tumor classification, CAD systems involve a feature extraction stage, in which morphological features are used to describe the tumor shape. Such features are expected to satisfy at least two conditions: (1) discriminant to distinguish between benign and malignant tumors, and (2) invariant to geometric transformations. Herein, 39 morphological features were evaluated in terms of invariance and discriminant power for breast tumor classification.

Methods: Morphological features were divided into region-based features, for describing the irregularity of the tumor shape, and boundary-based features, for measuring the anfractuosity of the tumor margin. Also, two datasets were considered in the experiments: 2054 breast ultrasound images and 892 mammographies. From both datasets, synthetic data augmentation was performed to obtain distinct combinations of rotation and scaling of breast tumors, from which morphological features were calculated. The linear discriminant analysis was used to classify breast tumors in benign and malignant classes. The area under the ROC curve (AUC) quantified the discriminant power of every morphological feature, whereas the relative difference (RD) between AUC values measured the invariance to geometric transformations. For indicating adequate performance, AUC and RD should tend toward unity and zero, respectively.

Results: For both datasets, the convexity was the most discriminant feature that reached AUC > 0.81 with RD<1×10^-2, while the most invariant feature was the roundness that attained RD<1×10^-3 with AUC < 0.72. Additionally, for each dataset, the most discriminant and invariant features were combined for performing tumor classification. For mammography, it was achieved accuracy (ACC) of 0.76, sensitivity (SEN) of 0.76, and specificity (SPE) of 0.84, whereas for breast ultrasound the results were ACC=0.88,SEN=0.81, and SPE=0.91.

Conclusions: In general, region-based features are more discriminant and invariant than boundary-based features. Moreover, it was observed that an invariant feature is not necessarily a discriminant feature; hence, a balance between invariance and discriminant power should be attained for breast tumor classification.

Keywords: Breast tumor; Geometric transformations; Mammography; Morphological features; Ultrasound.