Finding Space-Time Boundaries with Deformable Hypersurfaces

Dynamic 3D imaging is increasingly used to study evolving objects. We address the problem of detecting and tracking simple objects that merge or split in time. Common solutions involve detecting topological changes. Instead, we solve the problem in 4D by exploiting the observation that if objects only merge or only split, they appear as a single component in 4D. This allows us to initiate a topologically simple 3D hypersurface and deform it to fit the surface of all objects at all times. This gives an extremely compact representation of the objects’ evolution. We test our method on artificial 4D images and compare it to other segmentation methods. We also apply our method to a 4D X-ray data set to quantify evolving topology. Our method performs comparably to existing methods with better resource use and improved robustness.