Feature extraction from a signature based on the turning angle function for the classification of breast tumors

Abstract

Malignant breast tumors and benign masses appear in mammograms with different shape characteristics: the former usually have rough, spiculated, or microlobulated contours, whereas the latter commonly have smooth, round, oval, or macrolobulated contours. Features that characterize shape roughness and complexity can assist in distinguishing between malignant tumors and benign masses. Signatures of contours may be used to analyze their shapes. We propose to use a signature based on the turning angle function of contours of breast masses to derive features that capture the characteristics of shape roughness as described above. We propose methods to derive an index of the presence of convex regions (XR ( TA )), an index of the presence of concave regions (VR ( TA )), an index of convexity (CX ( TA )), and two measures of fractal dimension (FD ( TA ) and FDd ( TA )) from the turning angle function. The methods were tested with a set of 111 contours of 65 benign masses and 46 malignant tumors with different parameters. The best classification accuracies in discriminating between benign masses and malignant tumors, obtained for XR ( TA ), VR ( TA ), CX ( TA ), FD ( TA ), and FDd ( TA ) in terms of the area under the receiver operating characteristics curve, were 0.92, 0.92, 0.93, 0.93, and, 0.92, respectively.

Fig 1

a A manually drawn contour of a benign mass with a relatively smooth and convex contour with 916 points (pixels) and resolution of 50 μm per pixel. b Turning angle function of the contour with T_C(S_l) = 0° and T_C(S₉₁₆) = 360°.

Fig 2

a A manually drawn contour of a malignant tumor with a spiculated contour including concave and convex segments with 2,478 points (pixels) and resolution of 50 μm per pixel. b Turning angle function of the contour with T_C(S_l) = 315° and T_C(S₂₄₇₈) = 675°.

Fig 3

A manually drawn contour of a malignant tumor: a Adjacent segments within the dashed ellipse possess high internal angles and are small (caused by hand tremor or other limitations). Some adjacent segments within the solid ellipse present relevant internal angles. b The respective artifacts of the highlighted regions on the contour represented in the turning angle function. The region inside the dashed ellipse is represented in the turning angle function as the region between the dashed lines with a sequence of small segments with different directions. The region inside the solid ellipse is represented in the turning angle function as a sequence of segments of different sizes with large changes in direction.

Fig 4

a Filtered version of the contour in Figure 3a with reduction of artifacts. b Filtered version of the turning angle function in Figure 3b with S_min = 10 pixels and θ_max = 170°.

Fig. 5

a Filtered version of the contour in Figure 1a with reduction of artifacts. b Filtered version of the turning angle function in Figure 1b with S_min = 10 pixels and θ_max = 170°.

Fig 6

a Filtered version of the contour in Figure 2a with reduction of artifacts. b Filtered version of the turning angle function in Figure 2b with S_min = 10 pixels and θ_max = 170°.

Fig 7

Signatures based on the turning angle function with S_min = 10 pixels and θ_max = 170° of: a The benign mass with a nearly convex contour shown in Figure 1; b The malignant tumor with a spiculated contour shown in Figure 2. See also Figures 5 and 6.

Fig 8

a A manually drawn contour of a circumscribed benign mass. FD_TA = 0.0, FD_TA = 0.0, VR_TA = 0.0, XR_TA = 1.0, and CX_TA = 1.0. b The signature based on the turning angle function with S_min = 10 pixels and θ_max = 170°.

Fig 9

a A manually drawn contour of a macrolobulated malignant tumor. FD_TA = 0.14, FDd_TA = 0.11, VR_TA = 0.45, XR_TA = 0.98, and CX_TA = 0.76. b The signature based on the turning angle function with S_min = 10 pixels and θ_max = 170°.

Fig 10

a A manually drawn contour of a microlobulated malignant tumor. FD_TA = 0.32, FDd_TA = 0.30, VR_TA = 0.24, XR_TA = 0.78, and CX_TA = 0.77. b The signature based on the turning angle function with S_min = 10 pixels and θ_max = 170°.

Fig 11

a A manually drawn contour of a spiculated malignant tumor. FD_TA = 0.61, FDd_TA = 0.57, VR_TA = 0.42, XR_TA = 0.64, and CX_TA = 0.61. b The signature based on the turning angle function with S_min = 10 pixels and θ_max = 170°.