3D Cellular Automata and Mobile Terrestrial Lidar: Simple rules for urban geography

Advances in LiDAR acquisition are providing high-resolution data of urban environments from the street perspective. In contrast to lidar acquisition from an aerial platform, mobile terrestrial lidar (MTL) captures the richness of urban space as it relates to social, economic and transportation uses and behavior at larger scales. However, with high resolution comes large data volumes and there are relatively few automated or even semi-automated methods for efficiently extracting surfaces and features into a usable and representative form. In this study, data acquired using Terrapoint’s TITAN system is resampled into a gridded three-dimensional virtual environment consisting of sampled and nonsampled space. Cellular automata are then used to build agglomerative surface structures using simple path-finding rule sets. Practically, this technique provides an abstract representation of space useful for describing and visualizing crude urban geometry at a high level of detail. Fundamentally, this work presents an interesting and novel paradigm for the exploration of sampled environments and demonstrates how simple decision rules can be used to build complex structures. Background and Relevance LiDAR datasets are generally synonymous with large data volumes and this is only exacerbated in mobile-terrestrial LiDAR given the closer proximity of sampled surfaces to the sensor(s) and the slower acquisition speed relative to aerial LiDAR systems. Such large datasets are difficult to manage since they require exhaustive spatial search to define local point sets for statistical analysis or for computational geometry or computer vision algorithms. Therefore, there is a definite need for the point cloud to be “organized” into a structure that is conducive to rapid spatial query. Ideally this organization should support a variety of subsequent tasks such as segmentation, extraction, and compression. Traditionally 3D city models are some combination of extruded 2D polygons and higher fidelity 3D geometric models reconstructed through photogrammetric methods or from surface models derived from aerial LiDAR data (Luo & Gavrilova 2006; Madhavan et al. 2006). Specific methods have been derived, for example, for reconstructing roof structure from point cloud data (Vosselman & Dijkman 2001). However, from the terrestrial point of view there has been very little focus on modeling “as-built” urban infrastructure for block scale urban settings, despite the fact that terrestrial lidar scanners are built to operate at precisely this scale. Examples of innovative work in extracting and visualizing building facades can be seen in Zhao & Shibasaki (2001) and Früh & Zakhor (2001) . This work is extended by Früh (2002) to include both aerial and groundbased techniques for a full 3D city model. These methods rely on textured polygonal meshes for visualization purposes and do not make attempts to model architectural features or smaller urban objects such as benches or light poles. Other research has used static LiDAR systems to produce “as-built” cadastral and polygonal mesh objects for industrial and small-scale architectural applications (Stemberg et al. 2004) but involve substantial 3D modeling knowledge and manual processing time to produce the finished models. There has been no research focused on creating representations and structures from ground-based LiDAR data that allow for further analysis and subsequent modeling. In other words, in most cases human processing of Lidar data produces geometric models for comparison to plans (as-built drawing) or for visualization and game uses (3D features) but not, in general, for spatial analysis and modeling. This study attempts to work in that relatively new domain – 3D spatial analysis situated in ultrahigh resolution worlds. In particular, we examine the use of cellular automata to analyze urban LiDAR data. A cellular spatial representation can be used to model the sampled urban environment (see voxels) and cellular automata (CA) techniques can be used to segment space and to build models for further analysis. CA are spatially situated, finite state, information processing software machines. That is, CA operate under locally constrained conditions and process information from their local neighborhood using state-transition functions. The central tenet behind modeling with CA is that global structure emerges from simple local interaction. CA can been used to simulate the growth of urban environments and have also been used in urban simulation using mobile CA, also known as “cellular agents” (Batty 2005; Batty et al. 2002). We propose that geometric constraints can be introduced into a cellular agent system to segment distinct surfaces from terrestrial-based lidar point clouds. Tavakoli et al. (2008) outline a similar basic framework and path-planning algorithm for cellular agents in a geometrically bounded environment. Essentially, cellular agents are constrained by the affordances provided by the environmental structure where they exist and the affordance similarity correlation between adjacent spatial regions can be used to group sampled urban structure (Gibson 1979; Raubal & Moratz 2007).