Abstract We present theRegensburg Breast Shape Model(RBSM)—a 3D statistical shape model of the female breast built from 110 breast scans acquired in a standing position, and the first publicly available. Together with the model, a fully automated, pairwise surface registration pipeline used to establish dense correspondence among 3D breast scans is introduced. Our method is computationally efficient and requires only four landmarks to guide the registration process. A major challenge when modeling female breasts from surface-only 3D breast scans is the non-separability of breast and thorax. In order to weaken the strong coupling between breast and surrounding areas, we propose to minimize thevarianceoutside the breast region as much as possible. To achieve this goal, a novel concept calledbreast probability masks(BPMs) is introduced. A BPM assigns probabilities to each point of a 3D breast scan, telling howlikelyit is that a particular point belongs to the breast area. During registration, we use BPMs to align the template to the target as accurately as possibleinsidethe breast region and only roughly outside. This simple yet effective strategy significantly reduces the unwanted variance outside the breast region, leading to better statistical shape models in which breast shapes are quite well decoupled from the thorax. The RBSM is thus able to produce a variety of different breast shapes as independently as possible from the shape of the thorax. Our systematic experimental evaluation reveals a generalization ability of 0.17 mm and a specificity of 2.8 mm. To underline the expressiveness of the proposed model, we finally demonstrate in two showcase applications how the RBSM can be used for surgical outcome simulation and the prediction of a missing breast from the remaining one. Our model is available at https://www.rbsm.re-mic.de/ .

We present a novel method for guaranteeing linear momentum in learned physics simulations. Unlike existing methods, we enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional layers. We combine these strict constraints with a hierarchical network architecture, a carefully constructed resampling scheme, and a training approach for temporal coherence. In combination, the proposed method allows us to increase the physical accuracy of the learned simulator substantially. In addition, the induced physical bias leads to significantly better generalization performance and makes our method more reliable in unseen test cases. We evaluate our method on a range of different, challenging fluid scenarios. Among others, we demonstrate that our approach generalizes to new scenarios with up to one million particles. Our results show that the proposed algorithm can learn complex dynamics while outperforming existing approaches in generalization and training performance. An implementation of our approach is available at https://github.com/tum-pbs/DMCF.