Average distance error calculation—the automatically generated breast edge (dark) and the PCA modeled edge (white) are shown here on the left for a CC view mammogram. The image shown on the right represents , where T b and Y b are binary images depicting the PCA modeled breast shape and the original mammogram, respectively. The area of the region in white shown in the right image is divided by the average of the length of the two edges to obtain the ADE.
Breast edges—shown here, in white, are edges generated by our automated edge detection algorithm on CC view (top) and MLO view mammograms (bottom). The extraneous tissue seen at the bottom of the CC view mammograms was excluded by our algorithm.
Modeled breast shapes using two and six principal components—shown here are breast shapes generated from six-component PCA models (dark) of the CC (top) and MLO (bottom) views overlaid on the shapes generated by two-component models (white) and their respective ADEs. In some cases, the two-component model generates adequate breast shape representations (left, top, and bottom). However, in other cases (middle and right) a model with a greater number of components is needed to recapture the intricacies of the breast shapes.
Box-Whisker plot of average distance error—PCA models with more components consistently performed better than those of the same view with fewer components, exhibiting not only lower means but also lower ADEs for the 10th, 25th, 50th/median, 75th, and 90th percentiles. Shown here are the models of the CC-view (left) and MLO-view (right) with components numbering from 2 to 6. All differences in paired ADE values of the PCA models with different number of principal components were statistically significant (p < 0.025).
PCA parameter distributions—The distributions of the first six PCA parameters (α, β, γ, δ, ɛ, ζ) of the PCA breast shape models for both the CC (left) and MLO (right) views can be fitted with Gaussian distributions. The mean and standard deviation of each fit is also shown for each parameter.
Novel breast shapes generated by the six-component PCA model—These breast shapes were generated by the selection of a set of values for the PCA data vector r m . The top CC and MLO view modeled breasts were generated using the mean values of the Gaussian fits for each principal component, so they represent an “average” breast shape. The bottom breast shapes were generated using randomly generated values from the Gaussian distributions for each principal component. Axes are in units of centimeters.
Varying PCA parameters of the six-component CC view model—shown here are CC view breast shapes generated by varying each of the six PCA parameters (α, β, γ, δ, ɛ, ζ) individually. Each parameter was set to the mean (μ) value from the fitted Gaussian distributions shown in Fig. 5 , as well as μ +/− one standard deviation (σ), and μ +/− 2σ. The arrows indicate the overall direction in which that portion of the breast shape shifts as each parameter is increased. Within each panel, the average breast (in which all the values are set to their mean) is shown in solid black. Axes are in units of centimeters.
Varying PCA parameters of the six-component MLO view model—shown here are MLO view breast shapes generated by varying each of the six PCA parameters (α, β, γ, δ, ɛ, ζ) individually. The process by which this was accomplished is the same as in Fig. 7 . The arrows indicate the overall direction in which that portion of the breast shape shifts as each parameter is increased. Within each panel, the average breast (in which all the values are set to their mean) is shown in solid black. Axes are in units of centimeters.
Relationship between α and breast size—for both the CC (top) and MLO (bottom) views, a strong relationship was found between α and the breast area (left). However, for the compressed breast thickness (right), there was no strong correlation found.
Percentage of total variance contained in the first six principal components—shown here is the variance contained within each individual component and the cumulative variance contained within each component and its predecessors.
Average distance error—the mean ADEs of the two-component PCA model breast shapes was 2.99 mm for the CC view and 4.63 mm for the MLO view, but the six-component model produced more accurate shapes on average and in the worst cases (maximum).
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