Entities in two-dimensional space are often approximated using rectangles that are parallel to the two axes that define the space, so-called minimum-bounding rectangles (MBRs). MBRs are popular in Computer Vision and other areas as they are easy to obtain and easy to represent. In the area of Qualitative Spatial Reasoning, many different spatial representations are based on MBRs. Surprisingly, there has been no such representation proposed for general rectangles, i.e., rectangles that can have any angle, nor for general solid rectangles (GSRs) that cannot penetrate each other. GSRs are often used in computer graphics and computer games, such as Angry Birds, where they form the building blocks of more complicated structures. In order to represent and reason about these structures, we need a spatial representation that allows us to use GSRs as the basic spatial entities. In this paper we develop and analyze a qualitative spatial representation for GSRs. We apply our representation and the corresponding reasoning methods to solve a very interesting practical problem: Assuming we want to detect GSRs in computer games, but computer vision can only detect MBRs. How can we infer the GSRs from the given MBRs? We evaluate our solution and test its usefulness in a real gaming scenario.

This paper presents a novel method for qualitative mapping of large scale spaces. The proposed framework makes use of a graphical representation of the world in order to build a map consisting of qualitative constraints on the geometric relationships between landmark triplets. A novel measurement method based on camera imagery is presented which extends previous work from the field of Qualitative Spatial Reasoning. Measurements are fused into the map using a deterministic approach based on iterative graph updates and permutation operators. Experimental results are presented for a robot traversing a Mars-like environment while building a relational map.

With more people accessing Online Social Networks (OSN) using their mobile devices, location-based features have become an important part of the social networking. In this paper, we present the first measurement study of a new category of location-based online social networking services, a location-based social discovery (LBSD) network, that enables users to discover and communicate with nearby people. Unlike popular check-in-based social networks, LBSD allows users to publicly reveal their locations without being associ- ated to a specific “venue” and their usage is not influenced by the incentive mechanisms of the underlying virtual community. By analyzing over 8 million user profiles and around 150 million location updates collected from a popular new LBSD network, we first present the characteristics of spatial- temporal usage patterns of the observed users, showing that 40% of updates are from the user’s primary location and 80% are from their top 10 locations. We identify events that trigger bursts of growth in subscriber numbers, showing the importance of social media marketing. Finally, we investigate how usage patterns may be utilized to re-identify individuals with e.g. different identifiers or from datasets belonging to different online services. We evaluate re-identification by usage, spatial and spatial-temporal patterns and using a number of metrics and show that the best results can be achieved using location data, with a high accuracy: our experiments demonstrate that we can re-identify up-to 85% of users with a precision of 77% using monitored spatial data. Overall, we find that although users exhibit strong periodic behavior in their usage pattern and movements, the success rate of re-identification is highly dependent on the level of activeness and the lifetime of the users in the network.

Nearly all spatial reasoning problems involve uncertainty of one sort or another. Uncertainty arises due to the inaccuracies of sensors used in measuring distances and angles. We refer to this as directional uncertainty. Uncertainty also arises in combining spatial information when one location is mistakenly identified with another. We refer to this as recognition uncertainty. Most problems in constructing spatial representations (maps) for the purpose of navigation involve both directional and recognition uncertainty. In this paper, we show that a particular class of spatial reasoning problems involving the construction of representations of large-scale space can be solved efficiently even in the presence of directional and recognition uncertainty. We pay particular attention to the problems that arise due to recognition uncertainty.

Objects in the world usually appear in context, participating in spatial relationships and interactions that are predictable and expected. Knowledge of these contexts can be used in the task of using a mobile camera to search for a specified object in a room. We call this the object search task. This paper is concerned with representing this knowledge in a manner facilitating its application to object search while at the same time lending itself to autonomous learning by a robot. The ability for the robot to learn such knowledge without supervision is crucial due to the vast number of possible relationships that can exist for any given set of objects. Moreover, since a robot will not have an infinite amount of time to learn, it must be able to determine an order in which to look for possible relationships so as to maximize the rate at which new knowledge is gained. In effect, there must be a "focus of interest" operator that allows the robot to choose which examples are likely to convey the most new information and should be examined first. This paper demonstrates how a representation based on statistical confidence intervals allows the construction of a system that achieves the above goals. An algorithm, based on the Highest Impact First heuristic, is presented as a means for providing a "focus of interest" with which to control the learning process, and examples are given.

In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field model that maintains probabilistic estimates of the occupancy state of each cell in a spatial lattice. Bayesian estimation mechanisms employing stochastic sensor models allow incremental updating of the Occupancy Grid using multi-view, multi-sensor data, composition of multiple maps, decision-making, and incorporation of robot and sensor position uncertainty. We present the underlying stochastic formulation of the Occupancy Grid framework, and discuss its application to a variety of robotic tusks. These include range-based mapping, multi-sensor integration, path-planning and obstacle avoidance, handling of robot position uncertainty, incorporation of pre-compiled maps, recovery of geometric representations, and other related problems. The experimental results show that the Occupancy Grid approach generates dense world models, is robust under sensor uncertainty and errors, and allows explicit handling of uncertainty. It supports the development of robust and agile sensor interpretation methods, incremental discovery procedures, and composition of information from multiple sources. Furthermore, the results illustrate that robotic tasks can be addressed through operations performed di- rectly on the Occupancy Grid, and that these operations have strong parallels to operations performed in the image processing domain.

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map contains the estimates of relationships among objects in the map, and their uncertainties, given all the available information. The procedures provide a general solution to the problem of estimating uncertain relative spatial relationships. The estimates are probabilistic in nature, an advance over the previous, very conservative, worst-case approaches to the problem. Finally, the procedures are developed in the context of state-estimation and filtering theory, which provides a solid basis for numerous extensions.

This article deals with plausible reasoning from incomplete knowledge about large-scale spatial properties. The availableinformation, consisting of a set of pointwise observations,is extrapolated to neighbour points. We make use of belief functions to represent the influence of the knowledge at a given point to another point; the quantitative strength of this influence decreases when the distance between both points increases. These influences arethen aggregated using a variant of Dempster's rule of combination which takes into account the relative dependence between observations.

We present a novel method for learning densities with bounded support which enables us to incorporate `hard' topological constraints. In particular, we show how emerging techniques from computational algebraic topology and the notion of Persistent Homology can be combined with kernel based methods from Machine Learning for the purpose of density estimation. The proposed formalism facilitates learning of models with bounded support in a principled way, and -- by incorporating Persistent Homology techniques in our approach -- we are able to encode algebraic-topological constraints which are not addressed in current state-of the art probabilistic models. We study the behaviour of our method on two synthetic examples for various sample sizes and exemplify the benefits of the proposed approach on a real-world data-set by learning a motion model for a racecar. We show how to learn a model which respects the underlying topological structure of the racetrack, constraining the trajectories of the car.

We present an approach for enabling in-home service robots to follow natural language commands from non-expert users, with a particular focus on spatial language understanding. Specifically, we propose an extension to the semantic field model of spatial prepositions that enables the representation of dynamic spatial relations involving paths. The relevance of the proposed methodology to interactive robot learning is discussed, and the paper concludes with a description of how we plan to integrate and evaluate our proposed model with end-users.