Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file

Monte Carlo Localization in Hand-Drawn Maps

Robot localization is a one of the most important problems in robotics. Most of the existing approaches assume that the map of the environment is available beforehand and focus on accurate metrical localization. In this paper, we address the localization problem when the map of the environment is not present beforehand, and the robot relies on a hand-drawn map from a non-expert user. We addressed this problem by expressing the robot pose in the pixel coordinate and simultaneously estimate a local deformation of the hand-drawn map. Experiments show that we are able to localize the robot in the correct room with a robustness up to 80

New conserved structural fields for supercooled liquids

By considering Voronoi tessellations of the configurations of a fluid, we propose two new conserved fields, which provide structural information not fully accounted for by the usual 2-point density field fluctuations (structure factor). One of these fields is scalar and associated to the Voronoi cell volumes, whereas the other one, termed the "geometrical polarisation", is vectorial, related to the very local anisotropy of the configurations. We study the static and dynamical properties of these fields in the supercooled regime of a model glass-forming liquid. We show in particular that the geometrical polarisation is both statically correlated to the force field and contrary to it develops a plateau regime when the temperature is lowered. We attribute this behaviour to the microsopic disorder of the underlying inherent structures (IS) which dictate the dynamics on time scales larger than the true microscopic time, in the strong supercooled regime. In this respect, this work raises the issue of to what extent the inter IS dynamics, intrinsically anisotropic and collective (cf. T.B. Schr{\o}der et al. {\it J. of Chem. Phys.}, {\bf 112}, 9834 (2000)), could be related to their polarisation field.Comment: submitted to EPJE the 09/30/201

Emergence of diverse collective behaviors from local topological perception

We present a dynamical model for generic crowds in 2D in which individual agents are aware of their local environment -- i.e., neighboring agents and domain boundary features -- and may seek static target locations. Our model incorporates features common to many other "active matter" models like collision avoidance, alignment among agents, and homing toward targets. However, it is novel in key respects: the model combines topological and metrical features in a natural manner based upon the local environment of the agent's Voronoi diagram. With only two parameters, it is shown to capture a wide range of collective behaviors.Comment: 15 pages, 6 figures, Gonzalez and Tisdell contributed equall

Dynamic Detection of Topological Information from Grid-Based Generalized Voronoi Diagrams

In the context of robotics, the grid-based Generalized Voronoi Diagrams (GVDs) are widely used by mobile robots to represent their surrounding area. Current approaches for incrementally constructing GVDs mainly focus on providing metric skeletons of underlying grids, while the connectivity among GVD vertices and edges remains implicit, which makes high-level spatial reasoning tasks impractical. In this paper, we present an algorithm named Dynamic Topology Detector (DTD) for extracting a GVD with topological information from a grid map. Beyond the construction and reconstruction of a GVD on grids, DTD further extracts connectivity among the GVD edges and vertices. DTD also provides efficient repair mechanism to treat with local changes, making it work well in dynamic environments. Simulation tests in representative scenarios demonstrate that (1) compared with the static algorithms, DTD generally makes an order of magnitude improvement regarding computation times when working in dynamic environments; (2) with negligible extra computation, DTD detects topologies not computed by existing incremental algorithms. We also demonstrate the usefulness of the resulting topological information for high-level path planning tasks

Conceptual spatial representations for indoor mobile robots

We present an approach for creating conceptual representations of human-made indoor environments using mobile robots. The concepts refer to spatial and functional properties of typical indoor environments. Following findings in cognitive psychology, our model is composed of layers representing maps at different levels of abstraction. The complete system is integrated in a mobile robot endowed with laser and vision sensors for place and object recognition. The system also incorporates a linguistic framework that actively supports the map acquisition process, and which is used for situated dialogue. Finally, we discuss the capabilities of the integrated system

Autonomous Navigation and Mapping using Monocular Low-Resolution Grayscale Vision

Vision has been a powerful tool for navigation of intelligent and man-made systems ever since the cybernetics revolution in the 1970s. There have been two basic approaches to the navigation of computer controlled systems: The self-contained bottom-up development of sensorimotor abilities, namely perception and mobility, and the top-down approach, namely artificial intelligence, reasoning and knowledge based methods. The three-fold goal of autonomous exploration, mapping and localization of a mobile robot however, needs to be developed within a single framework. An algorithm is proposed to answer the challenges of autonomous corridor navigation and mapping by a mobile robot equipped with a single forward-facing camera. Using a combination of corridor ceiling lights, visual homing, and entropy, the robot is able to perform straight line navigation down the center of an unknown corridor. Turning at the end of a corridor is accomplished using Jeffrey divergence and time-to-collision, while deflection from dead ends and blank walls uses a scalar entropy measure of the entire image. When combined, these metrics allow the robot to navigate in both textured and untextured environments. The robot can autonomously explore an unknown indoor environment, recovering from difficult situations like corners, blank walls, and initial heading toward a wall. While exploring, the algorithm constructs a Voronoi-based topo-geometric map with nodes representing distinctive places like doors, water fountains, and other corridors. Because the algorithm is based entirely upon low-resolution (32 x 24) grayscale images, processing occurs at over 1000 frames per second

Semi-Global Stereo Matching with Surface Orientation Priors

Semi-Global Matching (SGM) is a widely-used efficient stereo matching technique. It works well for textured scenes, but fails on untextured slanted surfaces due to its fronto-parallel smoothness assumption. To remedy this problem, we propose a simple extension, termed SGM-P, to utilize precomputed surface orientation priors. Such priors favor different surface slants in different 2D image regions or 3D scene regions and can be derived in various ways. In this paper we evaluate plane orientation priors derived from stereo matching at a coarser resolution and show that such priors can yield significant performance gains for difficult weakly-textured scenes. We also explore surface normal priors derived from Manhattan-world assumptions, and we analyze the potential performance gains using oracle priors derived from ground-truth data. SGM-P only adds a minor computational overhead to SGM and is an attractive alternative to more complex methods employing higher-order smoothness terms.Comment: extended draft of 3DV 2017 (spotlight) pape