Capturing Shape Information with Multi-scale Topological Loss Terms for 3D Reconstruction

Reconstructing 3D objects from 2D images is both challenging for our brains and machine learning algorithms. To support this spatial reasoning task, contextual information about the overall shape of an object critical. However, such not captured by established loss terms (e.g. Dice loss). We propose to complement geometrical including multi-scale topological features, as connected components, cycles, voids, in reconstruction loss. Our method uses cubical complexes calculate features volume data employs optimal transport distance guide process. This topology-aware fully differentiable, computationally efficient, can be added any neural network. demonstrate utility incorporating it into SHAPR, a model predicting cell individual cells based on microscopy images. Using hybrid that leverages single assess their shape, we find substantially improves quality reconstructions, thus highlighting its ability extract more relevant image datasets.