Topology Aware Neural Interpolation of Scalar Fields

TL;DR

This paper introduces a neural interpolation method for time-varying scalar fields that preserves topological features, improving the accuracy of missing data estimations in 2D and 3D datasets.

Contribution

It proposes a topology-aware neural architecture with specialized loss functions for better topological and geometrical reconstruction of scalar fields during interpolation.

Findings

Outperforms reference schemes in data fitting.

Enhances topological accuracy in interpolated scalar fields.

Efficient single-pass interpolation at query time.

Abstract

This paper presents a neural scheme for the topology-aware interpolation of time-varying scalar fields. Given a time-varying sequence of persistence diagrams, along with a sparse temporal sampling of the corresponding scalar fields, denoted as keyframes, our interpolation approach aims at "inverting" the non-keyframe diagrams to produce plausible estimations of the corresponding, missing data. For this, we rely on a neural architecture which learns the relation from a time value to the corresponding scalar field, based on the keyframe examples, and reliably extends this relation to the non-keyframe time steps. We show how augmenting this architecture with specific topological losses exploiting the input diagrams both improves the geometrical and topological reconstruction of the non-keyframe time steps. At query time, given an input time value for which an interpolation is desired, our approach instantaneously produces an output, via a single propagation of the time input through the network. Experiments interpolating 2D and 3D time-varying datasets show our approach superiority, both in terms of data and topological fitting, with regard to reference interpolation schemes. Our implementation is available at this GitHub link : https://github.com/MohamedKISSI/Topology-Aware-Neural-Interpolation-of-Scalar-Fields.git.