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 e xposure 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 practica l, this method should require the use of only a limited number of cust om built filters. It is hypothesized that this would be possible if co mpressed breasts can be classified into a finite number of shapes. A s tudy was performed to determine the number of shapes. Based on the par abolic appearances of the outer borders of compressed breasts in mammo grams, the borders were fit with the polynomial equations y = ax(2) bx(3) and y = ax(2) + bx(3) + cx(4). The goodness-of-fit of these equa tions 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 withi n a given cluster defined the ''filter'' shape, and the individual bor ders were translated and rotated to best match that filter shape. The average rms differences between the individual borders and the ''filte r'' 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-coefficie nt equation. Although the fits to the original borders were superior f or the 3-coefficient equation, the matches to the ''filter'' borders d etermined by clustering were not significantly improved. A variety of modified clustering methods were developed and utilized, but none prod uced major improvements in clustering. Results indicate that 3 or 4 fi lter shapes may be adequate for each mammographic projection (CC and M LO-view). To account for the wide variations in exposures observed at the peripheral regions of breasts classified to be of a particular sha pe, it may be necessary to employ different filters for thin, medium a nd thick breasts. Even with this added requirement, it should be possi ble to use a small number of filters as desired. (C) 1998 American Ass ociation of Physicists in Medicine. [S0094-2405(98)00106-0].