Classification of compressed breast shapes for the design of equalization filters in x-ray mammography

We are developing an external filter method for equalizing the x-ray exposure in mammography. Each filter is specially designed to match the shape of the compressed breast border and to preferentially attenuate the x-ray beam in the peripheral region of the breast. To be practical, this method should require the use of only a limited number of custom built filters. It is hypothesized that this would be possible if compressed breasts can be classified into a finite number of shapes. A study was performed to determine the number of shapes. Based on the parabolic appearance of the outer borders of compressed breasts in mammograms, the borders were fit with the polynomial equations y = ax2 + bx3 and y = ax2 + bx3 + cx4. The goodness-of-fit of these equations was compared. The a,b and a,b,c coefficients were employed in a K-Means clustering procedure to classify 470 CC-view and 484 MLO-view borders into 2-10 clusters. The mean coefficients of the borders within a given cluster defined the "filter" shape, and the individual borders were translated and rotated to best match that filter shape. The average rms differences between the individual borders and the "filter" were computed as were the standard deviations of those differences. The optimally shifted and rotated borders were refit with the above polynomial equations, and plotted for visual evaluation of clustering success. Both polynomial fits were adequate with rms errors of about 2 mm for the 2-coefficient equation, and about 1 mm for the 3-coefficient equation. Although the fits to the original borders were superior for the 3-coefficient equation, the matches to the "filter" borders determined by clustering were not significantly improved. A variety of modified clustering methods were developed and utilized, but none produced major improvements in clustering. Results indicate that 3 or 4 filter shapes may be adequate for each mammographic projection (CC- and MLO-view). To account for the wide variations in exposures observed at the peripheral regions of breasts classified to be of a particular shape, it may be necessary to employ different filters for thin, medium and thick breasts. Even with this added requirement, it should be possible to use a small number of filters as desired.