Leila De Floriani’s research while affiliated with University of Maryland, College Park and other places

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.

Accurate and timely predictions from operational forecast systems are crucial for disaster response planning during extreme weather events. Many of these forecast systems utilize unstructured mesh representations to model seafloor topography and discretize the domain. The size of the bathymetric mesh can significantly impact the runtime performance of these systems. Mesh simplification is a technique used to reduce the number of elements composing a mesh while preserving desired characteristics, such as shape and topology. Reducing the overall size of the mesh can improve the performance of any subsequent simulations performed on the mesh. In this work, vertex removal and re-triangulation operations are used to simplify a bathymetric surface model. Differences in resulting vertical offset from the original mesh and a maximum triangle area constraint are used to identify candidate vertices for elimination. Identical tidal simulations are modelled on the original and each simplified mesh. Velocity direction, velocity magnitudes, and water levels are recorded at twelve sites in New York Harbor over time. It was demonstrated that the simplified mesh derived from using even the strictest parameters for the mesh simplification was able to reduce the overall mesh size by approximately 26.81%, which resulted in a 26.38% speed improvement percentage compared to the un-simplified mesh. Reduction of the overall mesh size was dependent on the parameters for simplification and the speed improvement percentage was relative to the number of resulting elements composing the simplified mesh.

Digital terrain models (DTMs) are pivotal in remote sensing, cartography, and landscape management, requiring accurate surface representation and topological information restoration. While topology analysis traditionally relies on smooth manifolds, the absence of an easy-to-use continuous surface model for a large terrain results in a preference for discrete meshes. Structural representation based on topology provides a succinct surface description, laying the foundation for many terrain analysis applications. However, on discrete meshes, numerical issues emerge, and complex algorithms are designed to handle them. This paper brings the context of terrain data analysis back to the continuous world and introduces ImplicitTerrain (Project homepage available at https://fengyee.github.io/implicit-terrain/), an implicit neural representation (INR) approach for modeling high-resolution terrain continuously and differentiably. Our comprehensive experiments demonstrate superior surface fitting accuracy, effective topological feature retrieval, and various topographical feature extraction that are implemented over this compact representation in parallel. To our knowledge, ImplicitTerrain pioneers a feasible continuous terrain surface modeling pipeline that provides a new research avenue for our community.

We address the problem of performing a topology-aware simplification algorithm on a compact and distributed data structure for triangle meshes, the Terrain trees. Topology-aware operators have been defined to coarsen a Triangulated Irregular Network (TIN) without affecting the topology of its underlying terrain, i.e., without modifying critical features of the terrain, such as pits, saddles, peaks, and their connectivity. However, their scalability is limited for large-scale meshes. Our proposed algorithm uses a batched processing strategy to reduce both the memory and time requirements of the simplification process and thanks to the spatial decomposition on the basis of Terrain trees, it can be easily parallelized. Also, since a Terrain tree after the simplification process becomes less compact and efficient, we propose an efficient post-processing step for updating hierarchical spatial decomposition. Our experiments on real-world TINs, derived from topographic and bathymetric LiDAR data, demonstrate the scalability and efficiency of our approach. Specifically, topology-aware simplification on Terrain trees uses 40% less memory and half the time compared to the most compact and efficient connectivity-based data structure for TINs. Furthermore, the parallel simplification algorithm on the Terrain trees exhibits a 12x speedup with an OpenMP implementation. The quality of the output mesh is not significantly affected by the distributed and parallel simplification strategy of Terrain trees, and we obtain similar quality levels compared to the global baseline method.

Cartographic sounding selection is a constraint-based bathymetric generalization process for identifying navigationally relevant soundings for nautical chart display. Electronic Navigational Charts (ENCs) are the premier maritime navigation medium and are produced according to international standards and distributed around the world. Cartographic generalization for ENCs is a major bottleneck in the chart creation and update process, where high volumes of data collected from constantly changing seafloor topographies require tedious examination. Moreover, these data are provided by multiple sources from various collection platforms at different levels of quality, further complicating the generalization process. Therefore, in this work, a comprehensive sounding selection algorithm is presented that focuses on safe navigation, leveraging both the Digital Surface Model (DSM) of multi-source bathymetry and the cartographic portrayal of the ENC. A taxonomy and hierarchy of soundings found on ENCs are defined and methods to identify these soundings are employed. Furthermore, the significant impact of depth contour generalization on sounding selection distribution is explored. Incorporating additional ENC bathymetric features (rocks, wrecks, and obstructions) affecting sounding distribution, calculating metrics from current chart products, and introducing procedures to correct cartographic constraint violations ensures a shoal-bias and mariner-readable output. This results in a selection that is near navigationally ready and complementary to the specific waterways of the area, contributing to the complete automation of the ENC creation and update process for safer maritime navigation.

Terrestrial laser scanning (TLS) is a ground-based approach to rapidly acquire 3D point clouds via Light Detection and Ranging (LiDAR) technologies. Quantifying tree-scale structure from TLS point clouds requires segmentation, yet there is a lack of automated methods available to the forest ecology community. In this work, we consider the problem of segmenting a forest TLS point cloud into individual tree point clouds. Different approaches have been investigated to identify and segment individual trees in a forest point cloud. Typically these methods require intensive parameter tuning and time-consuming user interactions, which has inhibited the application of TLS to large area research. Our goal is to define a new automated segmentation method that lifts these limitations. Our Topology-based Tree Segmentation (TTS) algorithm uses a new topological technique rooted in discrete Morse theory to segment input point clouds into single trees. TTS algorithm identifies distinctive tree structures (i.e., tree bottoms and tops) without user interactions. Tree tops and bottoms are then used to reconstruct single trees using the notion of relevant topological features. This mathematically well-established notion helps distinguish between noise and relevant tree features. To demonstrate the generality of our approach, we present an evaluation using multiple datasets, including different forest types and point densities. We also compare our TTS approach with open-source tree segmentation methods. The experiments show that we achieve a higher segmentation accuracy when performing point-by-point validation. Without expensive user interactions, TTS algorithm is promising for greater usage of TLS point clouds in the forest ecology community, such as fire risk and behavior modeling, estimating tree-level biodiversity structural traits, and above-ground biomass monitoring.