Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices
This addresses the challenge of poor 3D shape reconstructions in computer vision when using geometric losses that ignore structural properties, though it appears incremental as it builds on an existing SOTA model.
The paper tackles the problem of reconstructing 3D images from single 2D slices in limited data regimes by proposing a novel topological loss function based on the Euler Characteristic Transform, which when incorporated into the SHAPR model improves reconstructions on Red Blood Cells and Nuclei datasets.
The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which may lead to poor reconstructions as they ignore the structural properties of the shape. To tackle this, we propose a novel topological loss function based on the Euler Characteristic Transform. This loss can be used as an inductive bias to aid the optimization of any neural network toward better reconstructions in the regime of limited data. We show the effectiveness of the proposed loss function by incorporating it into SHAPR, a state-of-the-art shape reconstruction model, and test it on two benchmark datasets, viz., Red Blood Cells and Nuclei datasets. We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.