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output to input contrast noise ratio (CNR). The study found that computed EF values correlated well with the feature detection performance of radiologists [45]. In addition, clinical use confirms that processing the blended mammogram with our local enhancement techniques introduced no significant artifacts and preserved the shapes of the known mammographic features (calcifications, dominant masses, and spicular lesions) contained in the original mathematical phantom.

Enhancement by multiscale edges provides a significant improvement in local contrast for each feature included in the blended mammograms. A quantitative measure of contrast improvement can be defined by a Contrast Improvement Index

(CII), CII = Cpr0CeSSed/ Coriginal, where CProcessed and CQriginal are the contrast values of a region of interest in the processed and original images, respectively.

In this chapter we adopt a version of the optical definition of contrast introduced by Morrow etal. [41]. The contrast C of an object was defined by C = (f — b)/( f + b), where f is the mean gray-level value of a particular object in the image called the foreground, and b is the mean gray-level value of a surrounding region called the background. This definition of contrast has the advantage of being independent of the actual range of gray levels in the image. We computed local masks to separate the foreground and background regions of each feature included in the blended mammogram.

Figure 18c shows the result after processing the blended mammogram with adaptive histogram equalization (AHE).

column

FIGURE 21 (a) Selected ROI within a mammogram, (b) ROI is processed based on tensor product: Each row is processed first, followed by the processing of each column.

Roi Enhancement

FIGURE 22 Blended mammogram: (a) Original mammogram blended with mathematical phantom, (b) ROI enhancement by adaptive gain processing of DD wavelet coefficients, (c) ROI enhancement by multiscale edges of DD interpolation.

mammographic features shown in Fig. 18. From the table we observed that the enhancement by GAIN and EDGE performed significantly better than UNS and AHE.

Figure 20 shows the improvement of local contrast accomplished by EDGE for a sample scan line profile taken from cross-sections of each feature. Note that in all cases contrast was improved while preserving the overall shape of each feature profile.

Given the large matrix size of digital mammograms, computational costs for processing can be large. However, by constructing wavelets which exist only on an interval [35,36] as shown in Fig. 21, it is possible to enhance an arbitrary region of interest (ROI) within a mammogram. Figure 22 shows the enhancement of an arbitrarily shaped ROI using adaptive gain processing of interval wavelet interpolation [36]. Figure 22 shows the enhancement of an arbitrary ROI using multiscale edges. By constraining the enhancement to only an interest region, computation is greatly reduced (Table 2). This makes possible interactive processing of suspicious areas on a softcopy display system.

8 Conclusion

In this chapter we have reviewed established connections between dyadic wavelet enhancement algorithms and traditional unsharp masking. We proved that two cases of linear enhancement were mathematically equivalent to traditional unsharp masking with Gaussian low-pass filtering. We designed a methodology for accomplishing contrast enhancement with a simple multiscale nonlinear operator that exploits the wide dynamic range available in medical images. By judicious selection of wavelet filters and enhancement func-

Figure 18d was obtained after reconstructing the blended mammogram from interval wavelet transform coefficients modified by multiscale adaptive gain processing (GAIN). Figure 18e shows the result after processing the blended mammogram with unsharp masking (UNS). Figure 18 shows the result obtained after reconstructing the blended mammo-gram from interval wavelet transform coefficients modified by multiscale edges (EDGE). Figure 19 shows enlarged areas containing each feature in the processed mammogram for each method of contrast enhancement. The images in each row of Fig. 19 were rescaled by the same linear transformation. Table 1 summarizes the comparison quantitatively by listing CII values computed for each case and feature.

Table 3 shows the CII values for the original and enhanced column

FIGURE 21 (a) Selected ROI within a mammogram, (b) ROI is processed based on tensor product: Each row is processed first, followed by the processing of each column.

FIGURE 22 Blended mammogram: (a) Original mammogram blended with mathematical phantom, (b) ROI enhancement by adaptive gain processing of DD wavelet coefficients, (c) ROI enhancement by multiscale edges of DD interpolation.

TABLE 2 Comparison of computation time" in seconds: whole mammogram vs ROI

Matrix size(number of pixels)

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