Direct Topology Tracking in Continuous Implicit Models

2026-09-10

AI Summary

本文提出一种直接在连续隐式模型中跟踪拓扑特征的方法，通过查询模型及其导数来追踪临界点的演变，避免了离散化带来的伪影。

Abstract

We present a framework for tracking topological features directly within continuous implicit models. Such models, including implicit neural representations (INRs) and multivariate functional approximations (MFAs), are increasingly adopted to represent scientific data without the resolution constraints of discrete grids. They offer compact, smooth, and differentiable representations of complex fields, enabling new opportunities for high-performance data storage, reconstruction, and analysis. Given a continuous implicit model, our method tracks the evolution of critical points by querying the model and its derivatives, thereby eliminating the need to resample onto a grid. This approach enables faithful feature tracking while avoiding discretization-induced artifacts such as aliasing. We demonstrate the generality of our framework across a range of implicit representations, including analytic functions, MFAs, and INRs, and show that it produces smooth, coherent critical point trajectories. By enabling feature tracking directly on continuous representations, our method supports a new class of feature-driven visualization workflows centered on implicit models.

Problem

• continuous implicit models
• topological features
• critical points
• discretization artifacts

Innovation

• continuous implicit models
• topology tracking
• implicit neural representations (INRs)
• multivariate functional approximations (MFAs)
• critical points