Polylidar - Polygons From Triangular Meshes

Abstract

This letter presents Polylidar, an efficient algorithm to extract non-convex polygons from 2D point sets, including interior holes. Plane segmented point clouds can be input into Polylidar to extract their polygonal counterpart, thereby reducing map size and improving visualization. The algorithm begins by triangulating the point set and filtering triangles by user configurable parameters such as triangle edge length. Next, connected triangles are extracted into triangular mesh regions representing the shape of the point set. Finally each region is converted to a polygon through a novel boundary following method which accounts for holes. Real-world and synthetic benchmarks are presented to comparatively evaluate Polylidar speed and accuracy. Results show comparable accuracy and more than four times speedup compared to other concave polygon extraction methods. Index Terms-Aerial systems: perception and autonomy, reactive and sensor-based planning, computational geometry. I. INTRODUCTION V IDEO and LiDAR data are widely used in robotics to provide rich information about the environment. LiDAR and RGBD cameras generate point clouds for localization and mapping [1], 3D modelling [2], and scene classification for autonomous navigation [3]. Flat surfaces such as walls and floors are key environmental elements to identify; they are often extracted using planar segmentation techniques [4]-[6]. However points clouds are dense incurring a high computational cost when used directly. A common simplifying approach transforms point clouds into lower dimensional representations such as lines and planes [7]. Furthermore, polygonal representations of planes reduces map size and may accelerate matching for localization [8]. Convex polygon representations of planar segments were proposed by [7]. Convex polygons are simple and efficient to generate but ignore boundary concavities and overestimate area of the enclosed point set. Non-convex polygon representations may be generated using techniques such as boundary following outlined in [8] or α-shapes as proposed in [9]. However few methods also capture the interior holes within non-convex polygons. Safe robot navigation demands accurate capture of non-convex polygons with interior holes in real-time, requiring both speed and robustness.

Polylidar3D-Fast Polygon Extraction from 3D Data

“…Holz et al [12] proposes this technique and the use of α-shapes to extract such polygons [13]. We developed a faster open source polygon extraction algorithm, Polylidar, which extracts non-convex polygons with holes from 2D point sets [14]. The point set is converted to a 2D mesh through Delaunay triangulation, and triangles are subsequently filtered by edge length creating the "shape" of the point set.…”

“…These tasks are executed in parallel by a threadpool and can themselves spawn additional dynamic tasks [51]. Each independent task performs a serial region growing procedure that is similar to our previous work on 2D meshes [14] and was inspired by [10]. Algorithm 5 outlines this procedure for a single group g. The routine begins by creating empty sets to store planar triangular segments and their corresponding polygonal representations, denoted T g and P L g .…”

“…Figure 6 shows examples of non-manifold meshes where condition (1) is violated. Polylidar3D handles violations of (1) using methods from our previous work [ 14 ]. The missing triangles (shown as white) are explicitly captured as holes inside a polygon for Figure 6 a–c, while the mesh is split into two polygons for ( Figure 6 d).…”

“…These tasks are executed in parallel by a threadpool and can themselves spawn additional dynamic tasks [ 51 ]. Each independent task performs a serial region growing procedure that is similar to our previous work on 2D meshes [ 14 ] and was inspired by [ 10 ]. Algorithm 5 outlines this procedure for a single group g .…”

“…It makes use of CPU multi-threading and GPU acceleration when available. Polylidar3D is a substantial extension to Polylidar, the authors' 2D algorithm that transforms 2D point sets into polygons [14]. Our previous Polylidar algorithm only operated on 2D point sets and offered no parallelism.…”