Critical Features Tracking on Triangulated Irregular Networks by a Scale-Space Method

TL;DR

A novel scale-space analysis pipeline for TINs is introduced, addressing the multiple challenges in extending grid-based scale-space methods to TINs and capable of analyzing terrains with irregular boundaries, which poses challenges for grid-based methods.

Abstract

The scale-space method is a well-established framework that constructs a hierarchical representation of an input signal and facilitates coarse-to-fine visual reasoning. Considering the terrain elevation function as the input signal, the scale-space method can identify and track significant topographic features across different scales. The number of scales a feature persists, called its life span, indicates the importance of that feature. In this way, important topographic features of a landscape can be selected, which are useful for many applications, including cartography, nautical charting, and land-use planning. The scale-space methods developed for terrain data use gridded Digital Elevation Models (DEMs) to represent the terrain. However, gridded DEMs lack the flexibility to adapt to the irregular distribution of input data and the varied topological complexity of different regions. Instead, Triangulated Irregular Networks (TINs) can be directly generated from irregularly distributed point clouds and accurately preserve important features. In this work, we introduce a novel scale-space analysis pipeline for TINs, addressing the multiple challenges in extending grid-based scale-space methods to TINs. Our pipeline can efficiently identify and track topologically important features on TINs. Moreover, it is capable of analyzing terrains with irregular boundaries, which poses challenges for grid-based methods. Comprehensive experiments show that, compared to grid-based methods, our TIN-based pipeline is more efficient, accurate, and has better resolution robustness.

Figures (17)

• Figure 1: Critical point types by vertex signature. For each neighbor vertex, $\blacktriangle$ indicates its elevation is higher than the center vertex; otherwise, $\blacktriangledown$ is drawn. Derived from edelsbrunner2001hierarchical.
• Figure 2: Preset edge connection of a gridded DEM affects critical point types. Vertices with $\blacktriangle$/$\blacktriangledown$ markers have elevations higher/lower than $v_0$. For the type of $v_0$, the left model implies Saddle, while the right model implies Minimum.
• Figure 3: A 1D illustration of maximum transition at the edge-flip event. $\blacktriangle$ denotes the maximum moving from vertex $v_m$ to $v_n$. Intermediate scale $s_{i+\delta}$ illustrates the timestamp that the edge flip happens.
• Figure 4: PFPS method result of Reichenburg suburban region. (a) is the hillshade of the Reichenburg Suburban region, and (c) is the Bird's Eye View (BEV) of the TIN generated. (b) and (d) are wireframe plots of the TIN and gridded DEM.
• Figure 5: $\alpha$-shape method (right) removes long triangles on the border from the Delaunay triangulation result (left). Green lines in the left figure highlight the boundary of the processed triangle mesh.