Level Set Restricted Voronoi Tessellation for Large scale Spatial Statistical Analysis

TL;DR

This paper presents a novel level set-based Voronoi tessellation method for large-scale spatial statistical analysis, enabling efficient, hierarchical, and interactive exploration of complex volumetric data.

Contribution

It introduces a new spatial statistical decomposition technique combining level sets and a modified Voronoi tessellation, optimized for parallel processing and out-of-core analysis.

Findings

Supports multi-level hierarchical data organization.

Enables efficient parallel processing of large datasets.

Facilitates interactive visualization of complex spatial features.

Abstract

Spatial statistical analysis of multivariate volumetric data can be challenging due to scale, complexity, and occlusion. Advances in topological segmentation, feature extraction, and statistical summarization have helped overcome the challenges. This work introduces a new spatial statistical decomposition method based on level sets, connected components, and a novel variation of the restricted centroidal Voronoi tessellation that is better suited for spatial statistical decomposition and parallel efficiency. The resulting data structures organize features into a coherent nested hierarchy to support flexible and efficient out-of-core region-of-interest extraction. Next, we provide an efficient parallel implementation. Finally, an interactive visualization system based on this approach is designed and then applied to turbulent combustion data. The combined approach enables an interactive spatial statistical analysis workflow for large-scale data with a top-down approach through multiple-levels-of-detail that links phase space statistics with spatial features.