发表机构
University of Utah; Argonne National Laboratory; University of Notre Dame; The Ohio State University（犹他大学; 阿贡国家实验室; 圣母大学; 俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种在连续隐式模型中直接跟踪拓扑特征的方法，通过查询模型及其导数跟踪临界点，避免网格重采样和离散化伪影，适用于解析函数、MFAs和INRs，支持特征驱动可视化。
AI 中文摘要
我们提出了一种直接在连续隐式模型中跟踪拓扑特征的框架。此类模型，包括隐式神经表示（INRs）和多变量函数逼近（MFAs），正越来越多地被用于表示科学数据，而无需离散网格的分辨率限制。它们提供了复杂场的紧凑、平滑且可微的表示，为高性能数据存储、重建和分析带来了新的机遇。给定一个连续隐式模型，我们的方法通过查询模型及其导数来跟踪临界点的演化，从而无需在网格上重新采样。这种方法能够实现忠实的特征跟踪，同时避免由离散化引起的伪影，如混叠。我们展示了我们的框架在一系列隐式表示（包括解析函数、MFAs和INRs）上的通用性，并表明它能够产生平滑、连贯的临界点轨迹。通过直接在连续表示上进行特征跟踪，我们的方法支持以隐式模型为中心的新一类特征驱动可视化工作流。
英文摘要
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.
