Tracking shape changes directly in smooth continuous models
Direct Topology Tracking in Continuous Implicit Models
Computational GeometryMachine Learning
Summary
Tracking how shapes and features change over time is often done by looking at discrete grids of points, which can cause errors. The authors developed a way to follow important points in shapes represented by smooth, continuous models without converting them back to grids. This makes the tracking process more accurate and smoother because it uses the math of the models directly. Their method works with various types of continuous mathematical models used to represent complex data.
What this means in practice
- •For scientific visualization teams: Create smoother visualizations of evolving scientific data features directly from continuous models without grid artifacts.
- •For medical imaging engineers: Track critical anatomical features in models built from imaging data without losing continuity or detail from grid resampling.
Authors
Guanqun Ma, David Lenz, Kaiyuan Tang, Hanqi Guo, Chaoli Wang, Tom Peterka, Bei Wang
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.