Knowledge of the compressed breast shape can be valuable information to improve tomosynthesis reconstructions. The goal of this work was to use a convolutional neural network to refine the shape as estimated from tomosynthesis projection data. Training data was created by generating random three-dimensional breast shapes and simulating the limited angle projections. A rough approximation of the breast shape was made by segmenting and then back-projecting the projection data. Following this, a 3-layer u-net was trained on 900 pairs of simulated breast shapes and the corresponding shape estimates. The resulting network was applied to 100 test cases, where it significantly reduced the average distance between the surfaces of the true and estimated breast shapes from 2.3 mm to 0.5 mm (p < 0.001). If these results can be confirmed using patient data, it is likely that advanced image processing techniques that rely on precise knowledge of the compressed breast shape will become feasible since our work now provides a method to obtain such an accurate estimate of the breast shape without the need for any additional imaging hardware.