Volume Preserving

Volume-preserving methods aim to maintain the size or volume of objects during transformations, a crucial aspect in various fields like medical image registration and dynamical systems modeling. Current research focuses on developing neural network architectures, such as volume-preserving networks (VPNets) and those incorporating symplectic preservation properties, alongside variational models with relaxed Jacobian determinant constraints to achieve this preservation while maintaining accuracy. These advancements are significant for improving the reliability of medical image analysis, particularly in tumor volume assessment, and for accurately learning and simulating physical systems where volume conservation is a fundamental principle.