## Thickness Correction

Figure 8b summarizes the essential information necessary for the thickness correction. As mentioned, the thickness is not explicitly determined; rather, an estimate of the thickness is used in the correction. The gray level of the signal at each point FIGURE 8 (a) A smoothed representation of the image, s(x, y), is obtained from a low-pass filtering operation. The low-pass filter (shown schematically in 1 dimension) is a first-order Butterworth filter with a cutoff frequency of 0.05 cycles/mm. (b) Overview of the thickness equalization processing technique. For each point in the margin, the smoothed image is used to determine a correction factor.

FIGURE 8 (a) A smoothed representation of the image, s(x, y), is obtained from a low-pass filtering operation. The low-pass filter (shown schematically in 1 dimension) is a first-order Butterworth filter with a cutoff frequency of 0.05 cycles/mm. (b) Overview of the thickness equalization processing technique. For each point in the margin, the smoothed image is used to determine a correction factor.

in the margin of the smoothed image provides an estimate of the signal due to thickness.

The smoothed image, s(i), is considered to reflect largely only that part of the signal due to thickness variation. An estimate of the signal resulting from thickness at a particular location in the margin, relative to that in the central region of the breast, is calculated as the ratio of the smoothed image signal at that location to the mean smoothed signal, C, in a selected area of the central region. The value of the corrected image, E(i), is obtained for each point by dividing the original digital signal, o(i), by the relative thickness estimate, s(i)/C, at that point.

The technique described has not been rigorously optimized. The selection of the lowpass filter was based on the empirical objective of having the same approximate average level in the corrected margin as in the central region of the image. The thickness equalization transformation of a typical mammo-graphic image is illustrated in Fig. 9. The unprocessed image with the outer edge and inner margin highlighted is shown at left, while the thickness-equalized image is shown at right. The profiles of digital gray levels taken from the same line of data near the middle of both the original and transformed images are shown in Fig. 10.

As expected, the effect of the transformation on the results obtained from the PD algorithm is to increase the estimate of PD in cases where there is some density in the peripheral region of the breast. This may improve the agreement with subjective assessment in some situations; however, where the actual thickness of peripheral dense tissue is very low, this correction may cause overestimation of density by giving this tissue the same weighting as that in thicker areas of the breast. FIGURE 9 Demonstration of the thickness correction algorithm. The left image shows the original digitized data, with the inner and outer edges defining the margin superimposed. The right image has been thickness corrected. Note that only pixels in the margin have been altered.

oential margin

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