Measures of Contrast Enhancement 11311 Distribution Separation Measure

Using the method for labeling the Target (T) and Background (B) regions, it is possible to plot the overlap of the density functions for the gray scales comprising these two regions. In mammography, this is representative of the overlap found between a breast cancer lesion and its background border. A good enhancement technique should ideally reduce the overlap. In particular, it is anticipated that the enhancement technique should help reduce the spread of the target distribution and shift its mean gray-scale level to a higher value thus separating the two distributions and reducing their overlap. The best decision boundary for the original image between the two classes, assuming both classes have a multivariate normal distribution with equal covariances, is given using [21] as

Similarly, the best decision boundary for the original image after enhancement is given as

where lO, and ¡T are the mean and standard deviation of the gray scales comprising the background and target area, respectively, of the original image before enhancement. Similarly iB, ¡BE, lT, and ¡T correspond to the mean and standard deviation of the gray scales after the enhancement. An alternative approximation to Di and D2 can be found using the cutting score [22]. If the groups are assumed to be representative of the population, a weighted average of the group centroids will provide an optimal cutting score where Eq. (11.1) is rewritten as

and Eq. (11.2) is rewritten as

where NBO and NTO are the number of samples in the background and target prior to enhancement, and Ni and Ny the respective sample numbers after the enhancement. Again this approximation assumes that the two distributions are normal and that the group dispersion structures are known. By combining the above two equations it is possible to compute a distance measure between the decision boundaries and the means of the targets and background, before and after segmentation. This measure is termed as the distribution separation measure (DSM), and it is a measure of the quality of enhancement. It is defined as

DSM = {|(D2 - Mil + |(D2 - - {l(Di - mOI + l(Di - M?)il (11.5)

Ideally the measurement should be greater than zero; the greater the DSM value, the better the quality of enhancement. For comparing any two enhancement techniques, choose the technique that gives a higher value on the DSM measure.

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