Multi-field Visualization: Trait design and trait-induced merge trees

2025-01-08

IEEE Transactions on Visualization and Computer Graphics

AI Summary

To address the challenges of complex trait design and difficult feature selection in multi-field data visualization—particularly for Feature-Level Sets (FLS)—this paper proposes a Cartesian decomposition-based trait modeling framework coupled with a Trait-Induced Merge Tree (TIMT). TIMT generalizes classical merge trees to multivariate and tensor fields, enabling automated trait recommendation, hierarchical trait organization, and persistence-driven feature queries. Integrated with dictionary-learning–based point-trait recommendation and a multi-scale topological feature query algorithm, the framework achieves efficient and interpretable trait representation. Evaluated across five cross-domain case studies, the method significantly improves the intuitiveness of trait design, computational efficiency, and the relevance and interpretability of feature rendering. This work establishes a novel paradigm for topology-aware visualization of multi-field data.

Technology Category

• Data Mining & Knowledge Management: Data Visualization & Summarization
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Feature Construction/Reformulation

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Web data visualization

Abstract

Feature level sets (FLS) have shown significant potential in the analysis of multi-field data by using traits defined in attribute space to specify features in the domain. In this work, we address key challenges in the practical use of FLS: trait design and feature selection for rendering. To simplify trait design, we propose a Cartesian decomposition of traits into simpler components, making the process more intuitive and computationally efficient. Additionally, we utilize dictionary learning results to automatically suggest point traits. To enhance feature selection, we introduce trait-induced merge trees (TIMTs), a generalization of merge trees for feature level sets, aimed at topologically analyzing tensor fields or general multi-variate data. The leaves in the TIMT represent areas in the input data that are closest to the defined trait, thereby most closely resembling the defined feature. This merge tree provides a hierarchy of features, enabling the querying of the most relevant and persistent features. Our method includes various query techniques for the tree, allowing the highlighting of different aspects. We demonstrate the cross-application capabilities of this approach through five case studies from different domains.

Problem

• Feature Hierarchical Sets
• Feature Selection
• Multifield Data Analysis

Innovation

• Feature Induced Merge Trees
• Cartesian decomposition
• multidimensional data analysis