Abstract
The spatial configuration of objects in a scene is important to many applications. In particular, 3D environments constructed from point cloud observations are often used for navigation and planning with real-time requirements. In these settings, the ability to recognize and distinguish one set of objects from another may depend largely on how they are positioned with respect to each other. In this article, we explore two different approaches for describing the relative spatial relationship between two objects represented as 3D points: the histogram of forces, and a method using bounding boxes and fuzzy numbers. We use 2D axis-aligned projections of the objects to facilitate the computation of force histograms, and compare this approach to the bounding box and fuzzy number method. Our experiments are performed on the NPM3D dataset, consisting of hand-labeled point cloud objects in an outdoor street-level environment. The results highlight the strengths and weaknesses of each approach and we discuss the most appropriate applications for both.