Diedrich Wolter

Qualitative spatial representation and reasoning in the SparQ-toolbox

A multitude of calculi for qualitative spatial reasoning (QSR) have been proposed during the last two decades. The number of practical applications that make use of QSR techniques is, however, comparatively small. One reason for this may be seen in the difficulty for people from outside the field to incorporate the required reasoning techniques into their software. Sometimes, proposed calculi are only partially specified and implementations are rarely available. With the SparQ toolbox presented in this text, we seek to improve this situation by making common calculi and standard reasoning techniques accessible in a way that allows for easy integration into applications. We hope to turn this into a community effort and encourage researchers to incorporate their calculi into SparQ. This text is intended to present SparQ to potential users and contributors and to provide an overview on its features and utilization.

Optimal partial shape similarity

Humans are able to recognize objects in the presence of significant amounts of occlusion and changes in the view angle. In human and robot vision, these conditions are normal situations and not exceptions. In digital images one more problem occurs due to unstable outcomes of the segmentation algorithms. Thus, a normal case is that a given shape is only partially visible, and the visible part is distorted. To our knowledge there does not exist a shape representation and similarity approach that could work under these conditions. However, such an approach is necessary to solve the object recognition problem. The main contribution of this paper is the definition of an optimal partial shape similarity measure that works under these conditions. In particular, the presented novel approach to shape-based object recognition works even if only a small part of a given object is visible and the visible part is significantly distorted, assuming the visible part is distinctive.

Qualitative reasoning with directional relations

Qualitative spatial reasoning (QSR) pursues a symbolic approach to reasoning about a spatial domain. Qualitative calculi are defined to capture domain properties in relation operations, granting a relation algebraic approach to reasoning. QSR has two primary goals: providing a symbolic model for human common-sense level of reasoning and providing efficient means for reasoning. In this paper, we dismantle the hope for efficient reasoning about directional information in infinite spatial domains by showing that it is inherently hard to decide consistency of a set of constraints that represents positions in the plane by specifying directions from reference objects. We assume that these reference objects are not fixed but only constrained through directional relations themselves. Known QSR reasoning methods fail to handle this information.

Qualitative Spatial Reasoning for Applications: New Challenges and the SparQ Toolbox

About two decades ago, the field of Qualitative Spatial and Temporal Reasoning (QSTR) emerged as a new area of AI research that set out to grasp human-level understanding and reasoning about spatial and temporal entities, linking formal approaches to cognitive theories. Empowering artificial agents with QSTR capabilities is claimed to facilitate manifold applications, including robot navigation, Geographic Information Systems (GIS), natural language understanding, and computer-aided design. QSTR is an active field of research that has developed many representation and reasoning approaches so far, but only comparatively few applications exist that actually build on these QSTR techniques. This chapter approaches QSTR from an application perspective. Considering the exemplary application domains of robot navigation, GIS, and computer-aided design, the authors conclude that reasoning must be interpreted in a broader sense than the often-considered constraint-based reasoning and that supporting tools must become available. The authors then discuss the newly identified reasoning tasks and how they can be supported by QSTR toolboxes to foster the dissemination of QSTR in applications. Furthermore, the authors explain how they aim to overcome the lack-of-tools dilemma through the development of the QSTR toolbox SparQ.

Shape matching for robot mapping

We present a novel geometric model for robot mapping based on shape. Shape similarity measure and matching techniques originating from computer vision are specially redesigned for matching range scans. The fundamental geometric representation is a structural one, polygonal lines are ordered according to the cyclic order of visibility. This approach is an improvement of the underlying geometric models of todays SLAM implementations, where shape matching allows us to disregard pose estimations. The object-centered approach allows for compact representations that are well-suited to bridge the gap from metric information needed in path planning to more abstract, i.e. topological or qualitative spatial knowledge desired in complex navigational tasks.

Shape Similarity and Visual Parts

Human perception of shape is based on visual parts of objects to a point that a single, significant visual part is sufficient to recognize the whole object. For example, if you see a hand in the door, you expect a human behind the door. Therefore, a cognitively motivated shape similarity measure for recognition applications should be based on visual parts. This cognitive assumption leads to two related problems of scale selection and subpart selection. To find a given query part Q as part of an object C, Q needs to have a correct size with regards to C (scale selection). Assuming that the correct size is selected, the part Q must be compared to all possible subparts of C (subpart selection). For global, contour-based similarity measures, scaling the whole contour curves of both objects to the same length usually solves the problem of scale selection. Although this is not an optimal solution, it works if the whole contour curves are ‘sufficiently’ similar. Subpart selection problem does not occur in the implementation of global similarity measures.

A qualitative approach to localization and navigation based on visibility information

In this paper we describe a model for navigation of an autonomous agent in which localization, path planning, and locomotion is performed in a qualitative manner instead of relying on exact coordinates. Our approach is grounded in a decomposition of navigable space based on a novel model of visibility and occlusion relations between extended objects for agents with very limited sensor abilities. A graph representation reflecting the adjacency between the regions of the decomposition is used as a topological map of the environment. The visibility-based representation can be constructed autonomously by the agent and navigation can be performed by simple reactive navigation behaviors. Moreover, the representation is well-qualified to be shared between multiple agents.

Algebraic Properties of Qualitative Spatio-temporal Calculi

Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of relation algebra.

Geometric robot mapping

The purpose of this paper is to present a technique to create a global map of a robots surrounding by converting the raw data acquired from a scanning sensor to a compact map composed of just a few generalized polylines (polygonal curves). To merge a new scan with a previously computed map of the surrounding we use an approach that is composed of a local geometric process of merging similar line segments (termed Discrete Segment Evolution) of map and scan with a global statistical control process. The merging process is applied to a dataset gained from a real robot to show its ability to incrementally build a map showing the environment the robot has traveled through.

Structural knowledge transfer by spatial abstraction for reinforcement learning agents

In this article we investigate the role of abstraction principles for knowledge transfer in agent control learning tasks. We analyze abstraction from a formal point of view and characterize three distinct facets: aspectualization, coarsening, and conceptual classification. The taxonomy we develop allows us to interrelate existing approaches to abstraction, leading to a code of practice for designing knowledge representations that support knowledge transfer. We detail how aspectualization can be utilized to achieve knowledge transfer in reinforcement learning. We propose the use of so-called structure space aspectualizable knowledge representations that explicate structural properties of the state space and present a posteriori structure space aspectualization (APSST) as a method to extract generally sensible behavior from a learned policy. This new policy can be used for knowledge transfer to support learning new tasks in different environments. Finally, we present a case study that demonstrates transfer of generally sensible navigation skills from simple simulation to a real-world robotic platform.