A Practical Solver for Scalar Data Topological Simplification

TL;DR

This paper introduces a practical, accelerated method for topological simplification of scalar data that preserves important features and improves visualization, applicable to complex 3D datasets and filament structure extraction.

Contribution

It extends existing persistence optimization frameworks to handle a broader class of topological features, including saddle pairs, with tailored accelerations for practical use.

Findings

Significant speedups over existing frameworks.

Effective preservation of signal features during simplification.

Improved visualization and analysis of complex scalar data.

Abstract

This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of "signal" persistence pairs to maintain, our approach produces an output field g that is close to f and which optimizes (i) the cancellation of "non-signal" pairs, while (ii) preserving the "signal" pairs. In contrast to pre-existing simplification algorithms, our approach is not restricted to persistence pairs involving extrema and can thus address a larger class of topological features, in particular saddle pairs in three-dimensional scalar data. Our approach leverages recent generic persistence optimization frameworks and extends them with tailored accelerations specific to the problem of topological simplification. Extensive experiments report substantial accelerations over these frameworks, thereby making topological simplification optimization practical for real-life datasets. Our approach enables a direct visualization and analysis of the topologically simplified data, e.g., via isosurfaces of simplified topology (fewer components and handles). We apply our approach to the extraction of prominent filament structures in three-dimensional data. Specifically, we show that our pre-simplification of the data leads to practical improvements over standard topological techniques for removing filament loops. We also show how our approach can be used to repair genus defects in surface processing. Finally, we provide a C++ implementation for reproducibility purposes.