aiqbench analysis
This research introduces a method to track topological features directly within continuous implicit models like INRs and MFAs, bypassing the need for discrete grid resampling. By leveraging model derivatives, the framework eliminates discretization artifacts such as aliasing while maintaining smooth, coherent trajectories of critical points. This advancement enables more faithful feature-driven visualization workflows for scientific data analysis without resolution constraints.
Direct Topology Tracking in Continuous Implicit Models
arXiv:2609.12157v1 Announce Type: cross 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.
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.
Computational Geometry (cs.CG); Machine Learning (cs.LG)
arXiv:2609.12157 [cs.CG]
(or arXiv:2609.12157v1 [cs.CG] for this version)
https://doi.org/10.48550/arXiv.2609.12157 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 249 words
