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.

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.

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.

Spatiotemporal reasoning is a fundamental contributor to effective problem solving. In an effort to design better problem-solving agents, we examined and evaluated the strategies that humans use to solve Tower Defense puzzles, a complex and popular class of real-time strategy games. A consistent and unexpected finding was that humans frequently treated time and space as equivalent. Players stated temporal goals but solved spatial problems. An analysis of human data and computer simulations showed that re-representing temporal problems as spatial problems was beneficial, but treating the two separately can lead to higher scores. The work presented here holds several possibilities for level designers and others who design and analyze maps and spatial arrangements for domains requiring strategic reasoning.

Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Topology, one of the most important subjects in mathematics, provides mathematical tools and interesting topics in studying information systems and rough sets. In this paper, we present the topological characterizations to three types of covering approximation operators. First, we study the properties of topology induced by the sixth type of covering lower approximation operator. Second, some topological characterizations to the covering lower approximation operator to be an interior operator are established. We find that the topologies induced by this operator and by the sixth type of covering lower approximation operator are the same. Third, we study the conditions which make the first type of covering upper approximation operator be a closure operator, and find that the topology induced by the operator is the same as the topology induced by the fifth type of covering upper approximation operator. Forth, the conditions of the second type of covering upper approximation operator to be a closure operator and the properties of topology induced by it are established. Finally, these three topologies space are compared. In a word, topology provides a useful method to study the covering-based rough sets.

RGB-D cameras, which give an RGB image to- gether with depths, are becoming increasingly popular for robotic perception. In this paper, we address the task of detecting commonly found objects in the 3D point cloud of indoor scenes obtained from such cameras. Our method uses a graphical model that captures various features and contextual relations, including the local visual appearance and shape cues, object co-occurence relationships and geometric relationships. With a large number of object classes and relations, the model's parsimony becomes important and we address that by using multiple types of edge potentials. We train the model using a maximum-margin learning approach. In our experiments over a total of 52 3D scenes of homes and offices (composed from about 550 views), we get a performance of 84.06% and 73.38% in labeling office and home scenes respectively for 17 object classes each. We also present a method for a robot to search for an object using the learned model and the contextual information available from the current labelings of the scene. We applied this algorithm successfully on a mobile robot for the task of finding 12 object classes in 10 different offices and achieved a precision of 97.56% with 78.43% recall.

Qualitative representations are suitable for sketch understanding systems because they highlight important relationships while leaving out details that are not essential for conceptual understanding. These representations can be used to perform spatial analogies between sketches, which determine qualitative similarities and differences. However, there are cases where including quantitative information is necessary for accurately representing a sketch. We describe a method for using quantitative information to constrain qualitative spatial analogies. The utility of this method is demonstrated in the context of a sketch-based educational software system. Importantly, using quantitative information to improve analogical matches is not domain-specific. It can be used in any situation where qualitative and quantitative spatial information must be combined to accurately interpret a sketch. This approach has the potential to improve sketch understanding in educational software applications for highly spatial domains.