FIGURE 7 Schematic illustration of the compressed breast. Under compression the breast is considered to consist of two regions, one of approximately uniform thickness referred to as the central region, and a margin where thickness varies. In the margin, variation in transmitted X-ray fluence occurs because of changes in both breast thickness and composition.

compressed central area, it is possible to segment the dense from the nondense areas successfully as long as the dense tissue is fairly constant in thickness. Where the thickness of the stroma is reduced to wisps of density, the image signal may fall below the ¿DY setting and that tissue will be excluded from the calculation.

Similarly, near the periphery, where the thickness of the breast decreases, it is likely that, even though there may be dense tissue present, the image brightness will be lower because of increased X-ray transmission, and the region will fall below the setting of ¿DY. Near the margin of the breast, indicated by the vertical line in Fig. 7b, it is apparent that changes in brightness due to composition variations are overwhelmed by the changing brightness due to the reduction in thickness. This may be why the radiologist, who probably implicitly considers the image as representative of three-dimensional structures and compensates for the tissue roll-off, will subjectively rate the density as higher and will obtain a stronger risk prediction.

It is possible to perform a transformation on a digitized mammogram to adjust the image in the margin of the breast, accommodating for the reduction in signal associated with reduced thickness [41]. The transformed image, equalized for thickness variations, will thus more accurately represent composition variations across the breast. This might facilitate the measurement of PD and strengthen its association with risk of developing breast cancer as well as improve the performance of automated analysis algorithms.

The thickness equalization correction can be performed by identifying the margin region where the thickness is changing and then using an estimate for the thickness across the breast, derived from the image, to correct the margin for the changing thickness there. An explicit determination of thickness is not required in this technique. It is sufficient to obtain an estimate of the thickness from the change in signal in the margin of a low spatial frequency (smooth) representation of the image.

The "outer edge" of the breast (skin line) is easily identified for each row in the image by a thresholding procedure operating on each row of the image. Working from the chest-wall side of the mammogram, the algorithm identifies the point at which the signal is no longer significantly above the background. This is performed for all rows. The set of points obtained in this manner is then smoothed to provide the description of the outer edge of the breast. This outer edge is used to restrict the correction to pixels lying within the breast.

The overall thickness profile of the breast is obtained from a smoothed representation, s(x, y), of the image. Smoothing suppresses variations in signal associated with changes in composition while preserving variations due to changes in thickness. The generation of the smoothed image is illustrated schematically in Fig. 8a. This is a Fourier filtering operation in which the Fourier-transformed image is multiplied by a firstorder Butterworth lowpass filter [42] (shown in one dimension in the figure) described in the chapter entitled "Fundamental Enhancement Techniques" prior to the inverse transformation. It was found that edge artifacts were reduced if the image was mirrored before the Fourier transforms were calculated. The smoothed image corresponds to half of the transformed and filtered image.

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