用神经网络根据拓扑图生成缺失的标量场数据，兼顾几何与拓扑一致性。
Topology Aware Neural Interpolation of Scalar Fields
- 基于时间点与标量场的映射关系，学习关键帧间的拓扑感知插值。
- 引入拓扑损失函数，使非关键帧的重建在几何和拓扑上均更准确。
- 实时推理，适用于2D/3D动态标量场的高质量插值，适合可视化与科学计算。
本文提出一种用于时变标量场的拓扑感知神经插值方法。给定一系列时变的持久性图（persistence diagrams）以及稀疏采样的对应标量场（即关键帧），该方法旨在“逆向”推断非关键帧的持久性图，以生成合理的缺失数据估计。为此，我们设计了一个神经架构，通过关键帧样例学习时间值到标量场的映射关系，并可靠地将其推广至非关键帧时间步。我们证明，通过引入利用输入持久性图的特定拓扑损失，可显著提升非关键帧在几何与拓扑上的重建质量。查询时，仅需将时间输入单次前传即可即时输出结果。在2D与3D时变数据集上的实验表明，本方法在数据拟合与拓扑保真度方面均优于现有基准插值方案。代码已开源：https://github.com/MohamedKISSI/Topology-Aware-Neural-Interpolation-of-Scalar-Fields.git。
原文摘要 · Abstract (English)
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.
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