Reasoning by the usage of mental images has been the subject of much debate in Cognitive Science, especially among the schools of depictive and descriptive imagistic representations. Whether or not reasoning with mental images involves a mechanism or a process different from language based reasoning is an important question. This paper proposes that any theory which aims for a cohesive whole needs to be constrained by neurophysiological data and such data can be obtained by the Clock Drawing Test. The Clock Drawing Test (CDT) is a screening tool for cognitive impairment and can be used as a tool to test resilience of certain factors of visual spatial representations. Thus, it can help to form an empirical case for which factors are prone to debility and which factors are not during the onset and progress of cognitive impairment from a mental representation point of view. This paper presents 50 CDT tests done on patients with cognitive impairment and analyses the results which support the case for a depictive rather than a descriptive theory for imagistic representations. Lastly, this paper proposes that there is some evidence for a more dynamic and distributed nature of representation in the observations which question the above dichotomy and can be partly explained by certain aspects of the connectionist school of thought.

This paper proposes a layered graph model for representing the internal structure of complex plane regions, where each node represents the closure of a connected component of the interior or exterior of a complex region. The model provides a complete representation in the sense that the (global) nine-intersections between the interiors, the boundaries, and the exteriors of two complex regions can be determined by the (local) RCC8 relations between associated simple regions. 

In this paper we show how the shape of a 2D-landmark configuration can be encoded based on qualitative 1D-ordering information and how relevant geometric shape properties of a landmark configuration (strictly based on ordering information) can be detected by a sequence of view-based snapshots. Furthermore we show how shape of landmark configurations supports view-based localization tasks specially in the face of erroneous and missing sensor information.

Representing and comparing two-dimensional shapes is an important problem. Our hypothesis about human representations is that that people utilize two representations of shape: an abstract, qualitative representation of the spatial relations between the shape’s parts, and a detailed, quantitative representation. The advantage of relational, qualitative representations is that they facilitate shape comparison: two shapes can be compared via structural alignment processes which have been used to model similarity and analogy more broadly. This comparison process plays an important role in determining when two objects share the same shape, or in identifying transformations (rotations and reflections) between two shapes. Based on our hypothesis, we have built a computational model which automatically constructs both qualitative and quantitative representations and uses them to compare two-dimensional shapes in visual scenes. We demonstrate the effectiveness of our model by summarizing a series of studies which have simulated human spatial reasoning.

We develop an algorithm for efficient range search when the notion of dissimilarity is given by a Bregman divergence. The range search task is to return all points in a potentially large database that are within some specified distance of a query. It arises in many learning algorithms such as locally-weighted regression, kernel density estimation, neighborhood graph-based algorithms, and in tasks like outlier detection and information retrieval. In metric spaces, efficient range search-like algorithms based on spatial data structures have been deployed on a variety of statistical tasks. Here we describe the first algorithm for range search for an arbitrary Bregman divergence. This broad class of dissimilarity measures includes the relative entropy, Mahalanobis distance, Itakura-Saito divergence, and a variety of matrix divergences. Metric methods cannot be directly applied since Bregman divergences do not in general satisfy the triangle inequality. We derive geometric properties of Bregman divergences that yield an efficient algorithm for range search based on a recently proposed space decomposition for Bregman divergences.

The use of context is critical for scene understanding in computer vision, where the recognition of an object is driven by both local appearance and the objects relationship to other elements of the scene (context). Most current approaches rely on modeling the relationships between object categories as a source of context. In this paper we seek to move beyond categories to provide a richer appearance-based model of context. We present an exemplar-based model of objects and their relationships, the Visual Memex, that encodes both local appearance and 2D spatial context between object instances. We evaluate our model on Torralbas proposed Context Challenge against a baseline category-based system. Our experiments suggest that moving beyond categories for context modeling appears to be quite beneficial, and may be the critical missing ingredient in scene understanding systems.

Nearly 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. This work received substantial interest amongst the qualitative spatial reasoning community. However, it turned out to be difficult to establish a sound constraint calculus based on these relations. In this paper, we present the results of a new investigation into dipole constraint calculi which uses algebraic methods to derive sound results on the composition of relations and other properties of dipole calculi. Our results are based on a condensed semantics of the dipole relations. In contrast to the points that are normally used, dipoles are extended and have an intrinsic direction. Both features are important properties of natural objects. This allows for a straightforward representation of prototypical reasoning tasks for spatial agents. As an example, we show how to generate survey knowledge from local observations in a street network. The example illustrates the fast constraint-based reasoning capabilities of the dipole calculus. We integrate our results into two reasoning tools which are publicly available.

We study an alternative to the prevailing approach to modelling qualitative spatial reasoning (QSR) problems as constraint satisfaction problems. In the standard approach, a relation between objects is a constraint whereas in the alternative approach it is a variable. The relation-variable approach greatly simplifies integration and implementation of QSR. To substantiate this point, we discuss several QSR algorithms from the literature which in the relation-variable approach reduce to the customary constraint propagation algorithm enforcing generalised arc-consistency.

The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by spaces. In this paper, we will examine two aspects that are common to both interpretations of the theme, namely nerve constructions and refinement. Representations change, data changes, spaces change. We will examine the possibility of a `differential geometry' of spatial representations of both types, and in the sequel give an algebra of differential forms that has the potential to handle the dynamical aspect of such a geometry. We will discuss briefly a conjectured class of spaces, generalising the Cantor set which would seem ideal as a test-bed for the set of tools we are developing.

We argue that transfer of spatial and conceptual knowledge between tasks and domains is an essential benchmark for multi-representational architectures aimed at human-level intelligence. The underlying hypothesis is that spatial relationships provide a natural level of abstraction, highlighting the similarities and differences between situations and domains. Therefore, not only will spatial representations improve domain reasoning and learning, they will also facilitate the transfer of knowledge across domains. The simulated environments of real-time strategy (RTS) games provide an excellent test-bed for exploring this hypothesis for two reasons: many different RTS domains have been constructed and RTS requires a wide range of reasoning tasks.