Estimation and Visualization of Isosurface Uncertainty from Linear and High-Order Interpolation Methods

TL;DR

This paper introduces a visualization tool that uses high-order interpolation methods with Marching Cubes to estimate, visualize, and analyze uncertainties and errors in isosurface extraction from complex 3D data.

Contribution

It presents a novel interactive visualization approach that highlights interpolation errors and detects features missed by linear methods in isosurface extraction.

Findings

High-order methods reveal regions of significant interpolation error.

The tool enables comparison between different interpolation methods.

Synthetic and real-world data demonstrate improved error understanding.

Abstract

Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is easy to implement, it has limitations when the underlying data is complex and high-order, which is the case for most real-world data. Linear interpolation can output vertices at the wrong location. Its inability to deal with sharp features and features smaller than grid cells can lead to an incorrect isosurface with holes and broken pieces. Despite these limitations, isosurface visualizations typically do not include insight into the spatial location and the magnitude of these errors. We utilize high-order interpolation methods with MC algorithms and interactive visualization to highlight these uncertainties. Our visualization tool helps identify the regions of high interpolation errors. It also allows users to query local areas for details and compare the differences between isosurfaces from different interpolation methods. In addition, we employ high-order methods to identify and reconstruct possible features that linear methods cannot detect. We showcase how our visualization tool helps explore and understand the extracted isosurface errors through synthetic and real-world data.