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

TL;DR

This paper introduces a topology-aware loss function for 3D reconstruction that incorporates multi-scale topological features, improving shape accuracy in neural network models like SHAPR.

Contribution

It presents a novel differentiable topological loss based on cubical complexes and optimal transport, enhancing 3D shape reconstruction from 2D images.

Findings

Topological loss improves reconstruction quality.

Method is fully differentiable and compatible with neural networks.

Topological features extract more relevant shape information.

Abstract

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