Mammographic image analysis is typically performed using standard, general-purpose algorithms. We note the dangers of this approach and show that an alternative physics-model-based approach can be developed to calibrate the mammographic imaging process. This enables us to obtain, at each pixel, a quantitative measure of the breast tissue. The measure we use is h(int) and this represents the thickness of 'interesting' (non-fat) tissue between the pixel and the X-ray source. The thicknesses over the image constitute what we term the h(int) representation, and it can most usefully be regarded as a surface that conveys information about the anatomy of the breast. The representation allows image enhancement through removing the effects of degrading factors, and also effective image normalization since all changes in the image due to variations in the imaging conditions have been removed. Furthermore, the h(int) representation gives us a basis upon which to build object models and to reason about breast anatomy. We use this ability to choose features that are robust to breast compression and variations in breast composition. In this paper we describe the h(int) representation, show how it can be computed, and then illustrate how it can be applied to a variety of mammographic image processing tasks. The breast thickness turns out to be a key parameter in the computation of h(int), but it is not normally recorded. We show how the breast thickness can be estimated from an image, and examine the sensitivity of h(int) to this estimate. We then show how we can simulate any projective X-ray examination and can simulate the appearance of anatomical structures within the breast. We follow this with a comparison between the h(int) representation and conventional representations with respect to invariance to imaging conditions and the surrounding tissue. Initial results indicate that image analysis is far more robust when specific consideration is taken of the imaging process and the h(int) representation is used.