Structuring Line Ensembles with Path-Integrated Fidelity and Structural Inconsistency Fields

2026-07-27

AI Summary

This work addresses the inherent tension between trajectory continuity and visual scalability in large-scale line set visualization: trajectory-based rendering suffers from occlusion, while density-field representations improve visibility at the cost of structural consistency. To resolve this, the authors propose a structural inconsistency field that quantifies, via path integration, the alignment of each trajectory with its local tensor field and projects this measure into image space to explicitly delineate regions of coherence and conflict within dense line ensembles. The method incorporates a dynamic leave-one-out correction to eliminate self-bias and leverages a fixed grid with prefix sums for efficient updates. Experiments demonstrate that the approach interactively reveals hidden structural semantics atop density views, with validation across synthetic datasets, scalability benchmarks, and real-world case studies.

Abstract

When visualizing large-scale line ensembles, trajectory continuity and visual scalability are inherently antagonistic. Trajectory-centric renderings preserve path information but rapidly degenerate into clutter as line density increases and mutual occlusion dominates. In contrast, field-based density representations enhance visibility while sacrificing structural coherence: density reflects accumulation rather than agreement, such that scalar aggregation alone cannot discriminate between consistent and conflicting configurations. Rather than replacing density-based views, we complement them with a path-integrated trajectory-fidelity measure that quantifies the agreement of each trajectory with a surrounding tensor field. By projecting this passage-centered structural support back into image space, we obtain what we call a Structural Inconsistency Field, which localizes regions where dense patterns correspond to coherent structure versus disagreement, outliers, or connectivity-induced ambiguity. Dynamic leave-one-out correction reduces self-bias in the path integral. Efficient fixed-grid updates combined with prefix-sum evaluation enable interactive analysis and iterative extraction of coherent structures. Synthetic benchmarks, scalability analyses, and real-world case studies demonstrate that, when paired with conventional density views, the proposed method disambiguates dense line patterns by exposing spatially localized coherence and structural breakdown that remain concealed in density-only representations.

Problem

• line ensembles
• trajectory continuity
• density representation
• structural coherence
• visual scalability

Innovation

• Structural Inconsistency Field
• Path-Integrated Fidelity
• Line Ensembles
• Tensor Field Consistency
• Interactive Visualization