David A. Randell

Qualitative and Topological Relationships in Spatial Databases

In this paper, we present a spatial logic which can be used to reason about topological and spatial relationships among objects in spatial databases. The main advantages of such a formalism are its rigorousness, clear semantics and sound inference mechanism. We also show how the formalism can be extended to include orientation and metrical information. Comparisons with other formalisms are discussed.

Computing Transivity Tables: A Challenge For Automated Theorem Provers

Implementations of Allens interval-based temporal logic and a recently developed simulation system for reasoning about space and time, both require the use of transitivity tables. Although strategies exist to construct such tables, the proofs which underly the entries in the table are both tedious to do and in some cases difficult to secure. Often a difficult proof is only obtained via lemmas; moreover, finding models for satisfiable sets of dyadic relations in the theory introduces its own difficulties. This paper presents the problems. Any automated theorem prover which can effectively generate the entries for such transitivity tables would mark significant progress in automated theorem proving.

Exploiting lattices in a theory of space and time

Abstract We outline an axiomatic theory expressed in a first order predicate logic formalism. The theory modifies and extends Bowman Clarkes calculus of individuals. The theory is primarily concerned with a topological description of space and time. From this theory various classification hierarchies are singled out and expressed as lattice structures. The nodes of these lattices correspond to concepts expressed in the theory as monadic predicates, but also concepts expressed using higher arity predicates. We concentrate upon that part of the theory that is used to describe space. The logical structure and interrelationship of these different lattice structures are discussed. Some attention is given to how, by singling out such structures, the theory may be effectively implemented within a resolution-based automated reasoning setting.

Taxonomies of logically defined qualitative spatial relations

This paper develops a taxonomy of qualitative spatial relations for pairs of regions, which are all logically defined from two primitive (but axiomatized) notions. The first primitive is the notion of two regions being connected, which allows eight jointly exhaustive and pairwise disjoint relations to be defined. The second primitive is the convex hull of a region which allows many more relations to be defined. We also consider the development of the useful notions of composition tables for the defined relations and networks specifying continuous transitions between pairs of regions. We conclude by discussing what kind of criteria to apply when deciding how fine grained a taxonomy to create.

The application of support vector machine classification to detect cell nuclei for automated microscopy

The detection of cell nuclei for diagnostic purposes is an important aspect of many medical laboratory examinations. Precise location of cell nuclei can aid in correct diagnosis and aid in automated microscopy applications, such as cell counting and tissue architecture analysis. In this paper, we investigate the use of support vector machine classification based on Laplace edge features for this task. Compared with existing applications, we used only one type of cell nucleus images to train the classifier but this classifier can locate other two types of cell nuclei with different stains and scales successfully. The results illustrate that such a data driven approach has remarkable detection and generalization performance.

Discrete Mereotopology for Spatial Reasoning in Automated Histological Image Analysis

Discrete mereotopology (DM) is a first-order spatial logic that fuses together mereology (the theory of parthood relations) and topology to model discrete space. We show how a set of quasitopological functions defined within DM can be mapped to specific operators defined in mathematical morphology (MM) and easily implemented in scientific image processing programs. These functions provide the means to model topological properties of individual regions and spatial relations between them such as contact, overlap, and the relation of part to whole. DM not only extends the expressive power of image processing applications where mathematical morphology is used, but by functioning as a logic it also supplies the formal basis with which to prove the correctness of implemented algorithms as well as providing the computational basis to mechanically reason about segmented digital images using automated reasoning programs. In particular, we show how DM can supply a model-based and algorithmic context to the otherwise blind pixel-based image processing routines still dominating conventional imaging approaches. A number of worked examples drawn from the histological domain are given, including segmentation of cells in culture, identifying basal cell layers from stratified epithelia sections, and cell sorting in blood smears.

Automatic thresholding from the gradients of region boundaries

We present an approach for automatic threshold segmentation of greyscale images. The procedure is inspired by a reinterpretation of the strategy observed in human operators when adjusting thresholds manually and interactively by means of ‘slider’ controls. The approach translates into two methods. The first one is suitable for single or multiple global thresholds to be applied globally to images and consists of searching for a threshold value that generates a phase whose boundary coincides with the largest gradients in the original image. The second method is a variation, implemented to operate on the discrete connected components of the thresholded phase (i.e. the binary regions) independently. Consequently, this becomes an adaptive local threshold procedure, which operates relative to regions, rather than to local image subsets as is the case in most local thresholding methods previously published. Adding constraints for specifying certain classes of expected objects in the images can improve the output of the method over the traditional ‘segmenting first, then classify’ approach.

Ontological Levels in Histological Imaging

This research is supported by EPSRC through funding under grant EP/M023869/1 “Novel context-based segmentation algorithms for intelligent microscopy”.

The RaPiD Project: Knowledge-based design of dental prostheses

Abstract RaPiD is a knowledge-based assistant for designing removable partial dentures. 1t employs techniques from logic data bases, declarative graphics, and critiquing, along with expert design knowledge, to provide a CAD-style graphical interface for both instructional and professional use, the latter offering some design automation. RaPiD is being evaluated in terms of usability, clinical correctness, and pedagogical value. The potential for applying the same approach to other small to medium design activities is also being investigated.

Ordering Spatio-Temporal Sequences to Meet Transition Constraints: Complexity and Framework

Time and space are fundamental concepts of study in Artificial Intelligence and, in particular, Knowledge Representation. In this paper, we investigate the task of ordering a temporal sequence of qualitative spatial configurations to meet certain transition constraints. This ordering is constrained by the use of conceptual neighbourhood graphs defined on qualitative spatial constraint languages. In particular, we show that the problem of ordering a sequence of qualitative spatial configurations to meet such transition constraints is (mathcal{NP})-complete for the the well known languages of RCC-8, Interval Algebra, and Block Algebra. Based on this result, we also propose a framework where the temporal aspect of a sequence of qualitative spatial configurations is constrained by a Point Algebra network, and again show that the enhanced problem is in (mathcal{NP}) when considering the aforementioned languages. Our results lie within the area of Graph Traversal and allow for many practical and diverse applications, such as identifying optimal routes in mobile robot navigation, modelling changes of topology in biological processes, and computing sequences of segmentation steps used in image processing algorithms.