Purpose
To develop a set of accurate 2D models of compressed breasts undergoing mammography or breast tomosynthesis, based on objective analysis, to accurately characterize mammograms with few linearly independent parameters, and to generate novel clinically realistic paired cranio-caudal (CC) and medio-lateral oblique (MLO) views of the breast.

Methods
We seek to improve on an existing model of compressed breasts by overcoming detector size bias, removing the nipple and non-mammary tissue, pairing the CC and MLO views from a single breast, and incorporating the pectoralis major muscle contour into the model. The outer breast shapes in 931 paired CC and MLO mammograms were automatically detected with an in-house developed segmentation algorithm. From these shapes three generic models (CC-only, MLO-only, and joint CC/MLO) with linearly independent components were constructed via principal component analysis (PCA). The ability of the models to represent mammograms not used for PCA was tested via leave-one-out cross-validation, by measuring the average distance error (ADE).

Results
The individual models based on six components were found to depict breast shapes with accuracy (mean ADE-CC = 0.81 mm, ADE-MLO = 1.64 mm, ADE-Pectoralis = 1.61 mm), outperforming the joint CC/MLO model (P ≤ 0.001). The joint model based on 12 principal components contains 99.5% of the total variance of the data, and can be used to generate new clinically realistic paired CC and MLO breast shapes. This is achieved by generating random sets of 12 principal components, following the Gaussian distributions of the histograms of each component, which were obtained from the component values determined from the images in the mammography database used.

Conclusion
Our joint CC/MLO model can successfully generate paired CC and MLO view shapes of the same simulated breast, while the individual models can be used to represent with high accuracy clinical acquired mammograms with a small set of parameters. This is the first step toward objective 3D compressed breast models, useful for dosimetry and scatter correction research, among other applications.