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Automated Classification of Breast Parenchymal Density: Topologic Analysis of X-Ray Attenuation Patterns Depicted with Digital Mammography

Holger F. Boehm1, Tanja Schneider1, Sonja M. Buhmann-Kirchhoff1, Thomas Schlossbauer1, Dorothea Rjosk-Dendorfer2, Stefanie Britsch1 and Maximilian Reiser1

1 Department of Radiology, University of Munich, Campus Downtown, Nussbaum-Str. 20, D 80336 Munich, Germany.
2 Department of Obstetrics and Gynaecology, University of Munich, Munich, Germany.


Figure 1
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  		Fig. 1 —Schematic shows that for each object (white) pixel, number of open edges and vertices have to be counted. Open edge or vertex is one not shared by neighboring pixels. Pixel P1 has three open edges and one open vertex because two neighboring pixels share two edges of P1 and three vertices of P1.

 

Figure 2
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  		Fig. 2A —Average shape of three Minkowski functionals as function of threshold for three classes of mammograms. Dotted line indicates atrophy; dashed line, normal tissue; solid line, fibrosis. Graph shows curves for area.

 

Figure 3
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  		Fig. 2B —Average shape of three Minkowski functionals as function of threshold for three classes of mammograms. Dotted line indicates atrophy; dashed line, normal tissue; solid line, fibrosis. Graph shows curves for perimeter.

 

Figure 4
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  		Fig. 2C —Average shape of three Minkowski functionals as function of threshold for three classes of mammograms. Dotted line indicates atrophy; dashed line, normal tissue; solid line, fibrosis. Graph shows curves for Euler-Poincaré number.

 

Figure 5
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  		Fig. 3A —Results of receiver operating characteristic analysis show differentiation between tissue probes based on topologic parameter Minkowski functionals in 2D. Graph shows results for probe classified as atrophic (area under curve [AUC], 0.81).

 

Figure 6
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  		Fig. 3B —Results of receiver operating characteristic analysis show differentiation between tissue probes based on topologic parameter Minkowski functionals in 2D. Graph shows results for probe classified as normal (AUC, 0.93).

 

Figure 7
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  		Fig. 3C —Results of receiver operating characteristic analysis show differentiation between tissue probes based on topologic parameter Minkowski functionals in 2D. Graph shows results for probe classified as fibrosis (AUC, 0.68).

 

Figure 8
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  		Fig. 4A —Classes of mammographic parenchymal patterns. 61-year-old woman with atrophy, that is, fatty involution of breast tissue.

 

Figure 9
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  		Fig. 4B —Classes of mammographic parenchymal patterns. 58-year-old woman with normal parenchyma.

 

Figure 10
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  		Fig. 4C —Classes of mammographic parenchymal patterns. 67-year-old woman with fibrosis, that is, dense parenchyma.

 

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