On Embedding a Qualitative Representation in a Two-Dimensional Plane

Abstract

This paper discusses embedding in a two-dimensional plane a symbolic representation for spatial data using the simple objects, points (P), lines (L), circuits (C), and areas (A). We have proposed PLCA as a new framework for a qualitative spatial reasoning. In a PLCA expression, the entire figure is represented in a form in which all the objects are related. We investigate the conditions for two-dimensional realizability of a PLCA expression, and derive the relation that the numbers of objects in a PLCA expression should have. In this process, we use the well-known Euler's formula. We also give an algorithm for drawing the figure of the PLCA expression that satisfies this condition in a two-dimensional plane and prove its correctness. The algorithm generates a quantitative expression from qualitative expression.     

Relation algebras over containers and surfaces: An ontological study of a room space

Recent research in geographic information systems hasbeen concerned with the construction of algebras tomake inferences about spatial relations by embeddingspatial relations within a space in which decisionsabout compositions are derived geometrically. Wepursue an alternative approach by studying spatialrelations and their inferences in a concrete spatialscenario, a room space that contains such manipulableobjects as a box, a ball, a table, a sheet of paper,and a pen. We derive from the observed spatialproperties an algebra related to the fundamentalspatial concepts of containers and surfaces and showthat this container-surface algebra holds allproperties of Tarski's relation algebra, except forthe associativity. The crispness of the compositionscan be refined by considering the relative size of theobjects) and their roles (i.e., whether it isexplicitly known that the objects are containers orsurfaces).     

Selecting a reference frame

Reference frames are representations that parse space. In the case of spatial terms, reference frames mediate the mapping of linguistic expressions onto spatial configurations of objects. In the sentence ``The fly is above the cat,' ``above' is defined with respect to a reference frame that is imposed on the cat. Different types of reference frames can be used to define spatial terms, each based on a different source of information. For example, gravity, the orientation of objects in the scene or the orientation of the viewer can all be used to set the orientation of a reference frame. When these reference frames disagree (because the viewer is reclining or because the objects in the scene are overturned), there are competing definitions for the spatial term, resulting in the need for reference frame selection. The purpose of this paper is to review a line of research that examines reference frame selection in the context of spatial language. This work shows that all reference frames are initially active and assign a direction to a spatial term. Moreover, this activation is automatic, and is followed by the selection of a single reference frame, with selection accompanied by inhibition of the non-selected frames. Parallels between reference frame selection in language and in perception and attention are discussed.     

Spatial Vagueness and Second-Order

This paper presents a geometric characterization of geographic objects with vague boundaries. Since the framework is based on ordering geometry and does not rely on numerical concepts, it can be applied to qualitative spatial reasoning. The characterization describes vague regions and gradual transitions between two vague regions. This approach takes into account that the region of all points that definitely belong to an object is also vague, called higher-order vagueness. Higher-order vagueness is usually neglected by theories modeling spatial vagueness. The approach distinguishes firstand second-order vague regions and characterizes the gradual transitions of second-order vague regions. These gradual transitions allow transitions within transitions. In general, it is not possible to reduce higher-order vagueness to first-order vagueness. Using a spatial ordering structure the article shows when second-order vagueness is useful and examines the relationship between first- and second-order vagueness. An example shows how second-order vagueness can be used to represent geographic objects.     

Mereological inheritance

In recent investigations of Spatial Reasoning, SpatialKnowledge Representation, and Geographic Information Systems, asignificant effort has been spent by many scholars of the areaabout the problem of representing properties of spatial objects bymeans of logical theories.An analogous effort has been the problem of analyzingthe qualitative relations which can be established between twospace regions. These investigations have led to a generalframework of the field known by the term ``mereo-topology'.Though both the above mentioned approaches have proved to besuccessful in the investigation of formal and practically relevantaspects of spatial objects, no attempt has been carried out in the direction of integrating the approaches and looking at the relationshipbetween a general logical theory of space and mereo-topology from an analytical point of view, in particular for exploiting thecombinatorial behaviour of such an integrated model.This paper intends to fill the gap and analyze the behaviour ofspatial formulae of a logical theory of space as objects which canbe classified based on the behaviour they exhibit with respect tothe parts and supertparts of the regions where they are true. Wename these categories of behaviourinheritance modalities.     

Reasoning about Depth and Motion from an Observer's Viewpoint

ABSTRACT

The goal of this paper is to present a logic-based formalism for representing knowledge about objects in space and their movements, and show how this knowledge could be built up from the viewpoint of an observer immersed in a dynamic world. In this paper space is represented using functions that extract attributes of depth, size and distance from snapshots of the world. These attributes compose a novel spatial reasoning system named Depth Profile Calculus (DPC). Transitions between qualitative relations involving these attributes are represented by an extension of this calculus called Dynamic Depth Profile Calculus (DDPC). We argue that knowledge about objects in the world could be built up via a process of abduction on DDPC relations.     

Environmental reference systems for large-scale spaces

Human navigation in well-known environments is guided by stored memory representations of spatial information. In three experiments (N = 43) we investigated the role of different spatial reference systems when accessing information about familiar objects at different locations in the city in which the participants lived. Our results indicate that two independent reference systems underly the retrieval of spatial knowledge. Environmental characteristics, e.g., the streets at an intersection, determine which headings are easier to imagine at a given location and lead to differences in accessibility of spatial information (orientation-specific behavior). In addition, access to spatial information depends on the relative direction of a location with respect to the imagined heading, such that information about locations imagined in front of oneself is easier to access than about locations towards the back. This influence of an egocentric reference system was found for environmental knowledge as well as map-based knowledge. In light of these reference system effects, position-dependent models of spatial memory for large-scale environments are discussed. To account for the simultaneous effect of an environmental and an egocentric reference system, we present a 2-level model of spatial memory access.     

The Space within Fisherman's Folly: Playing with a Puzzle in Mereotopology

Abstract

In this paper we propose a spatial ontology for reasoning about holes, rigid objects and a string, taking a classical puzzle as a motivating example. In this ontology the domain is composed of spatial regions whereby a theory about holes is defined over a mereotopological basis. Within this theory we define a data structure, named chain, that facilitates a clear and efficient representation of the puzzle states and its solution.     

Prioritized Spatial Updating in the Intrinsic Frame of Reference

In order to maintain valid situation awareness, people need to update the spatial representations of their surroundings as objects, including themselves, move. The present study investigates the properties of spatial updating in the intrinsic frame of reference, where spatial relations are represented with respect to an external object (other than the viewer self) with an intrinsic reference direction. Three experiments were conducted using a task of direction pointing. It was found that given a relatively stable intrinsic reference direction, responses to a small number of salient objects were faster than responses to non-salient objects (Experiment 1 and Experiment 3). The salience effect disappeared when the intrinsic reference direction was no longer stable (Experiment 2). Furthermore, all three experiments revealed a type of orientation dependence similar to that found in egocentric spatial updating. Our results indicate that spatial updating in the intrinsic reference system can be easy only if a fixed reference direction is maintained and the number of objects that need to be tracked is limited.     

基于背景差分的动目标检测算法研究

提出一种新的基于背景差分的动目标检测算法。综合利用序列图像的时、空域信息提取目标。用中值法建立初始背景,并采用一种自适应的背景更新策略。实验结果表明,该算法简单,鲁棒性好,能够解决全局光照缓变和突变的问题,在复杂环境中也能准确地检测出运动目标。     

On early cognitive mapping

In this paper we examine the nature of theearly cognitive map – the beginnings of acognitive map formed from one's earlyimpressions of the environment one is in. Twodistinct paradigms have emerged from ourstudies of what information is initially identified in a cognitive map. The first, which weterm a space-based approach, emphasises makingexplicit the spatial extent of the currentlocal environment. The second emphasises makingexplicit the relationships between objects inthe local environment and we call this anobject-based approach. For both paradigms weexamine the psychological literature to findsupport for the approach and the roboticists'attempts at implementing the idea. We arguethat a space-based approach is the moreappropriate way to compute an early cognitivemap. In particular, we find that Siegel andWhite's (1975) object-based hypothesis, whichstates that the developmental progression of acognitive map is from landmark to route tosurvey map, is not supported. The space-basedparadigm underpins our own work in this areaand we outline our own space-based theory forcomputing an early cognitive map.     

Three dimensional spatial memory and learning in real and virtual environments

Human orientation and spatial cognition partlydepends on our ability to remember sets ofvisual landmarks and imagine their relationshipto us from a different viewpoint. We normallymake large body rotations only about a singleaxis which is aligned with gravity. However,astronauts who try to recognize environmentsrotated in 3 dimensions report that theirterrestrial ability to imagine the relativeorientation of remembered landmarks does noteasily generalize. The ability of humansubjects to learn to mentally rotate a simplearray of six objects around them was studied in1-G laboratory experiments. Subjects weretested in a cubic chamber (n = 73) and aequivalent virtual environment (n = 24),analogous to the interior of a space stationnode module. A picture of an object waspresented at the center of each wall. Subjectshad to memorize the spatial relationships amongthe six objects and learn to predict thedirection to a specific object if their bodywere in a specified 3D orientation. Percentcorrect learning curves and response times weremeasured. Most subjects achieved high accuracyfrom a given viewpoint within 20 trials,regardless of roll orientation, and learned asecond view direction with equal or greaterease. Performance of the subject group thatused a head mounted display/head tracker wasqualitatively similar to that of the secondgroup tested in a physical node simulator. Body position with respect to gravity had asignificant but minor effect on performance ofeach group, suggesting that results may alsoapply to weightless situations. A correlationwas found between task performance measures andconventional paper-and-pencil tests of fieldindependence and 2&3 dimensional figurerotation ability.     

聚类分析在空间信息智能处理中的应用研究

空间信息服务平台由于实施标准,技术规范和类型格式等方面存在不一致和含糊不明确性,且空间信息数据量过于庞大,为有效的从中获取符合应用需求的空间信息,将聚类分析应用于空间信息的智能处理当中。首先进行空间信息数据的特征提取、扩充和合并,然后结合粗糙集模型和K原型算法进行聚类分析,最后通过选择和设计合适的评价指标对聚类结果进行评价,为空间信息数据的规范化和标准化处理提供一定的技术支持。