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.

In this study, we propose a method for learning interactions among different types of objects to devise new plans using these objects. Learning is accomplished by observing a given sequence of events with their timestamps and using spatial information on the initial state of the objects in the environment. We assume that no intermediate state information is available about the states of objects. We have used the Incredible Machine game as a suitable domain for analyzing and learning object interactions. When a knowledge base about relations among objects is provided, interactions to devise new plans are learned to a desired extent. Moreover, using spatial information of objects or temporal information of events makes it feasible to learn the conditional effects of objects on each other. Our analyses show that, integrating spatial and temporal data in a spatio-temporal learning approach gives closer results to that of the knowledge-based approach by providing applicable event models for planning. This is promising because gathering spatio-temporal information does not require great amount of knowledge.

We present a study of how humans represent space when solving Tower Defense puzzles, a complex spatial reasoning task requiring the subject to protect locations by arranging a set of defense towers at strategic positions. We have discovered that the representation humans use is significantly more complex than what is needed to describe the spatial situation. Strategy and spatial representations are tightly intertwined with spatial representations forgoing objective, atomically-defined spatial features for context-sensitive, goal-oriented spatial affordances. Spatial relationships exist not only between objects but between an object’s properties, second-order properties, joint spatial properties and temporal properties.

In order to collaborate with people in the real world, cognitive systems must be able to represent and reason about spatial regions in human environments. Consider the command "go to the front of the classroom". The spatial region mentioned (the front of the classroom) is not perceivable using geometry alone. Instead it is defined by its functional use, implied by nearby objects and their configuration. In this paper, we define such areas as context-dependent spatial regions and present a cognitive system able to learn them by combining qualitative spatial representations, semantic labels, and analogy. The system is capable of generating a collection of qualitative spatial representations describing the configuration of the entities it perceives in the world. It can then be taught context-dependent spatial regions using anchor pointsdefined on these representations. From this we then demonstrate how an existing computational model of analogy can be used to detect context-dependent spatial regions in previously unseen rooms. To evaluate this process we compare detected regions to annotations made on maps of real rooms by human volunteers.

We consider the problem of learning object arrangements in a 3D scene. The key idea here is to learn how objects relate to human poses based on their affordances, ease of use and reachability. In contrast to modeling object-object relationships, modeling human-object relationships scales linearly in the number of objects. We design appropriate density functions based on 3D spatial features to capture this. We learn the distribution of human poses in a scene using a variant of the Dirichlet process mixture model that allows sharing of the density function parameters across the same object types. Then we can reason about arrangements of the objects in the room based on these meaningful human poses. In our extensive experiments on 20 different rooms with a total of 47 objects, our algorithm predicted correct placements with an average error of 1.6 meters from ground truth. In arranging five real scenes, it received a score of 4.3/5 compared to 3.7 for the best baseline method.

In this paper, we investigate the application of data mining to existing techniques for quality control/anomaly detection on weather sensor observations. Specifically we adapt the popular Barnes Spatial interpolation method to use time-series distance rather than spatial distance to develop an online algorithm that uses readings from similar stations based on current and historical observations for interpolation and we demonstrate that this new algorithm exhibits less model error than the Barnes Spatial interpolation-based method. We focus on interpolation, which is a basis for this popular quality control method and other related methods, and examine a dataset of over 233 million temperature observations from California and surrounding areas. Our approach shows improved performance as indicated by mean squared error reduced by approximately one half for predicted values versus reported values.

We introduce a challenging real-world planning problem where actions must be taken at each location in a spatial area at each point in time. We use forestry planning as the motivating application. In Large Scale Spatial-Temporal (LSST) planning problems, the state and action spaces are defined as the cross-products of many local state and action spaces spread over a large spatial area such as a city or forest. These problems possess state uncertainty, have complex utility functions involving spatial constraints and we generally must rely on simulations rather than an explicit transition model. We define LSST problems as reinforcement learning problems and present a solution using policy gradients. We compare two different policy formulations: an explicit policy that identifies each location in space and the action to take there; and an abstract policy that defines the proportion of actions to take across all locations in space. We show that the abstract policy is more robust and achieves higher rewards with far fewer parameters than the elementary policy. This abstract policy is also a better fit to the properties that practitioners in LSST problem domains require for such methods to be widely useful.