Curve Segment Neighborhood-based Vector Field Exploration

TL;DR

This paper proposes a Curve Segment Neighborhood Graph (CSNG) to capture the relationships between neighboring curve segments, and incorporates the proposed techniques into an interactive system to enable effective analysis and interpretation of complex patterns in large-scale integral curve datasets.

Abstract

Integral curves have been widely used to represent and analyze various vector fields. In this paper, we propose a Curve Segment Neighborhood Graph (CSNG) to capture the relationships between neighboring curve segments. This graph representation enables us to adapt the fast community detection algorithm, i.e., the Louvain algorithm, to identify individual graph communities from CSNG. Our results show that these communities often correspond to the features of the flow. To achieve a multi-level interactive exploration of the detected communities, we adapt a force-directed layout that allows users to refine and re-group communities based on their domain knowledge. We incorporate the proposed techniques into an interactive system to enable effective analysis and interpretation of complex patterns in large-scale integral curve datasets.

Figures (5)

• Figure 1: Illustration of our framework. 1) Load the streamline dataset. 2) Perform curve decomposition, then CSNG construction with either KNN or RBN. 3) Perform community detection on the CSNG to categorize each curve segment into community clusters. 4) Manually adjust the community results such as merging and splitting communities to fix misclassification.
• Figure 2: a) The multi-layered force-directed graph layout, generated by applying the Louvain community detection algorithm (with a resolution of 1) to the Cylinder dataset. The group of nodes enclosed by a dashed outline highlights a split operation performed on a node using the Louvain method at a finer resolution of 0.3. b) Displays the same nodes represented as segment clusters in a 3D view. c) merging a sub-group with a parent group (yellow) results in the sub-groups being part of the parent group (green). (d) merging two sub-groups from two branches results in a new parent group.
• Figure 3: Impact of different values of the resolution parameter for community detection. (a) the community detection result on the cylinder data with a resolution value of 0.05 and (b) the result with a resolution value of 0.1. A larger resolution leads to a finer result.
• Figure 4: A level-of-detail analysis of the Plume streamline data set.
• Figure 5: Detailed comparison of the best clustering results for the Plume dataset using PCA K-means and Louvain algorithms. PCA K-means parameters: dim=5, k=12; Louvain parameters: resolution=1, RBN radius=1%. 3D rendering of PCA K-means clustering result and community detection result are shown in (a) and (b), respectively. (c) and (d) are force directed graphs of (a) and (b).