On the statistical nature of mammograms

We show that digitized mammograms can be considered as evolving from a simp le process. A given image results from passing a random input field through a linear filtering operation, where the filter transfer function has a sel f-similar characteristic. By estimating the functional form of the filter a nd solving the corresponding filtering equation, the analysis shows that th e input field gray value distribution and spectral content can be approxima ted with parametric methods. The work gives a simple explanation for the va riegated image appearance and multimodal character of the gray value distri bution common to mammograms. Using the image analysis as a guide, a simulat ed mammogram is generated that has many statistical characteristics of real mammograms. Additional benefits may follow from understanding the function al form of the filter in conjunction with the input field characteristics t hat include the approximate parametric description of mammograms, showing t he distinction between homogeneously dense and nondense images, and the dev elopment of mass analysis methods. (C) 1999 American Association of Physici sts in Medicine. [S0099-2405(99)00311-9].