Originating from Allen's Interval Algebra, composition-based reasoning has been widely acknowledged as the most popular reasoning technique in qualitative spatial and temporal reasoning. Given a qualitative calculus (i.e. a relation model), the first thing we should do is to establish its composition table (CT). In the past three decades, such work is usually done manually. This is undesirable and error-prone, given that the calculus may contain tens or hundreds of basic relations. Computing the correct CT has been identified by Tony Cohn as a challenge for computer scientists in 1995. This paper addresses this problem and introduces a semi-automatic method to compute the CT by randomly generating triples of elements. For several important qualitative calculi, our method can establish the correct CT in a reasonable short time. This is illustrated by applications to the Interval Algebra, the Region Connection Calculus RCC-8, the INDU calculus, and the Oriented Point Relation Algebras. Our method can also be used to generate CTs for customised qualitative calculi defined on restricted domains.

While computers assist humans with tasks such as navigation that involve spatial aspects, agents that can interact in a meaningful way in this context are still in their infancy. One core issue is the mismatch in the representation of spatial information a computer-based system is likely to use, and the one a human is likely to use. Computers are better suited for quantitative schemes such as maps or diagrams that rely on measurable distances between entities. Humans frequently use higher-level, domain-specific conceptual representations such as buildings, rooms, or streets for orientation purposes. Combined with the person-centric world view that we often assume when we refer to spatial information, it is challenging for agents to convert statements using spatial references into assertions that match their own internal representation. In this paper, we discuss an approach that uses natural language processing and information extraction tool kits to identify entities and statements about their spatial relations. These extractions are then processed by a spatial reasoner to convert them from the human conceptual space into the quantitative space used by the computer-based agent.

Commonsense is a challenge not only for representation and reasoning but also for large scale knowledge engineering required to capture the breadth of our "everyday" world. One approach to knowledge engineering is to "outsource" the effort to the public through games that generate structured commonsense knowledge from user play. To date, such games have focused on symbolic and textual knowledge. However, an effective commonsense reasoning system will require spatial and physical reasoning capabilities. In this paper, I propose a tool for gathering commonsense information from ordinary people. It is a user-friendly 3D sculpting tool for modeling and annotating models of physical objects and spaces.

We present an ontology consisting of a theory of spatial dimension and a theory of dimension-independent mereological and topological relations in space. Though both are fairly weak axiomatizations, their interplay suffices to define various mereotopological relations and to make any necessary dimension constraints explicit. We show that models of the INCH Calculus and the Region-Connection Calculus (RCC) can be obtained from extensions of the proposed ontology.

GENE_ARCH is a Generative Design System that combines Pareto Genetic Algorithms with an advanced energy simulation engine. This work explores its integration with a Shape Grammar, acting as GENE_ARCH’s shape generation module. The islamic patio house typology is readdressed in a contemporary context, by improving its energy-efficiency, and rethinking its role in the genesis of high-density urban areas, while respecting its specific spatial organization and cultural grounding. Field work was carried out in Marrakesh, surveying a number of patio houses, becoming the Corpus of Design, from where a shape grammar was generated. The computational implementation of the patio house grammar was done within GENE_ARCH. The resulting program was able to generate new, alternative patio houses designs that were more energy efficient, while respecting the traditional rules captured from the analysis of existing houses. After the computational system was fully implemented, it was possible to realise a large number of experiments. The first experiments kept more restrained rules, thus generating new designs that closer resembled the existing ones. The progressive relaxation of rules and constraints allowed for a larger number of variations to emerge. Analysis of energy results provide insight into the main patterns resulting from the GA search processes.

There has been a recent push in extraction of 3D spatial layout of scenes. However, none of these approaches model the 3D interaction between objects and the spatial layout. In this paper, we argue for a parametric representation of objects in 3D, which allows us to incorporate volumetric constraints of the physical world. We show that augmenting current structured prediction techniques with volumetric reasoning significantly improves the performance of the state-of-the-art.

In this paper we introduce a method for extending binary qualitative direction calculi with adjustable granularity like OPRAm or the star calculus with a granular distance concept. This method is similar to the concept of extending points with an internal reference direction to get oriented points which are the basic entities in the OPRAm calculus. Even if the spatial objects are from a geometrical point of view infinitesimal small points locally available reference measures are attached. In the case of OPRAm, a reference direction is attached. The same principle works also with local reference distances which are called elevations. The principle of attaching references features to a point is called hidden feature attachment.

An important issue in Qualitative Spatial Reasoning is the representation of relative direction. In this paper we present simple geometric rules that enable reasoning about relative direction between oriented points. This framework, the Oriented Point Algebra OPRA_m, has a scalable granularity m. We develop a simple algorithm for computing the OPRA_m composition tables and prove its correctness. Using a composition table, algebraic closure for a set of OPRA statements is sufficient to solve spatial navigation tasks. And it turns out that scalable granularity is useful in these navigation tasks.

Autonomous agents in real-time strategy (RTS) games lack an integrated framework for reasoning about choke points and regions of open space in their environment. This paper presents an algorithm which partitions the environment into a set of polygonal regions and computes optimal choke points between adjacent regions. This representation can be used as a component for AI agents to reason about terrain, plan multiple routes of attack, and make other tactical decisions. The algorithm is tested on a set of popular maps commonly used in international Starcraft competitions and evaluated against answers made by human participants. The algorithm identified 97% of the choke points that the participants found and also identified a number of bottlenecks that human participants did not recognize as choke points.

A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a stratified space, giving a stratification for each radius level. We then use methods derived from kernel and cokernel persistent homology to cluster the data points into different strata, and we prove a result which guarantees the correctness of our clustering, given certain topological conditions; some geometric intuition for these topological conditions is also provided. Our correctness result is then given a probabilistic flavor: we give bounds on the minimum number of sample points required to infer, with probability, which points belong to the same strata. Finally, we give an explicit algorithm for the clustering, prove its correctness, and apply it to some simulated data.