BEHAVIOUR ANALYSIS OF MULTI-DETAILED REPRESENTATION OF SPATIAL AND CARTOGRAPHIC OBJECTS

Michael Govorov

Department of Surveying and Land Studies, The Papua New Guinea University of Technology, Private Mail Bag, Lae, Papua New Guinea

Fax: 675-4734977

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Abstract

Many controlling factors of cartographic generalization do not allow creation of a comprehensive model of this process and its further holistic automation. All previous experience of studies shows that automation of cartographic generalization process is possible only with intellectual approaches. One of such approaches is semantically enriched object-oriented analysis (OOA).

The main idea of this article is lying in the study of behavioral or dynamic features of the cartographic generalization. The very term of cartographic generalization of spatial objects presupposes that it is a process. In that respect, behavior object-oriented specification of the given process provides more advantages in understanding and formulating of model-oriented and cartographic generalization than structure static approach.

This paper presents the study of behavior modeling of a spatial and map object by using object-oriented behavior analysis approach. The behavior of objects is modeled using transition networks. There are no restrictions on the complexity of an action associated with a transition. Three levels of spatial object’s interactions are considered in such approach. One of the frame problems in behavior analysis concerned with using of description language for spatial behavior modeling is discussed.

Introduction

A model-oriented and cartographic generalization is the application of abstraction mechanism to the world's entities for the formulation of image of reality by means of distraction and addition. There are several conceptual meta-metamodels for a spatial and cartographic generalization in digital environment [Shea, 1989; Muller, 1995; etc.]. But these models are far from complete formalized description of automation generalization process. The difficulties, for the complete rigorously solution of these problems, are caused mainly by the multifactor nature of the generalization. The main controlling factors of generalization can be classified as follows [Map generalization…, 1991]:

a) Phenomenon-based factors, which are caused due to the conceptual nature of modeled entity (the essential of the analyzable phenomenon; the features of territory; the relationship among entities etc.);

b) Purpose-orientation factors (user’s needs and purpose; contents; scale; technology of the compilation map etc.);

c) Graphic media and format factors (the visualization purpose, the technology of compilation map; the kinds of cartographic object; the methods of cartographic representation; the rules of map design etc.);

d) Computational factors (the effectiveness of information system realization).

First, second and fourth factors can control the generalization of spatial object. All of these factors can affect the cartographic generalization process. Sometimes it is difficult to separate impacts of these factors on the final generalization decision. For example, it can be assumed, that the topographical features are modeled and purpose-oriented controls are eliminated due to multiple purpose of topographical spatial model (e.g. general reference mapping). But it will be still impossible to model geographical phenomenon, which is traded by holistic declarative descriptions, due to the infinite of uniqueness of the nature.

The generalization process can be applied on single feature, groups of connected in space features or whole environment, parts of a feature (e.g. feature geometry), hierarchical organization of features, topological and semantic relations among features or their parts. Map design of spatial objects also can be accompanied by cartographical generalization of geometry, semantic attributes, topology of map objects, map legend etc. Generalization factors can drive process on the different levels and for the different types of attributes of feature (geometry, topology, semantic, visualization).

There are various methods and algorithms for implementation of different generalization techniques, which are working with different formats (integration problems) and with completely different nature of objects. The nature of these algorithms is also different. Some algorithms are functional, other are discrete etc.

Such complexity of spatial and cartographic generalizations causes the lack of success in theirs holistic automation by declarative modeling methods. Richness of nature causes impossibility to algorithm geographic situation and to integrate heterogeneous declarative methods together in holistic manner.

All previous experience of cartographic generalization’s automation shows, that it is possible to model such process only using intellectual approaches. One of such approaches is the object-oriented analysis. Another one, for instance, is Multi-Agent system, which is holding considerable potential for automation cartographic generalization according to the members of AGENT programme [Project AGENT…, 2000].

Modeling levels of behavior and abstraction level for its specification

Spatial and cartographic generalizations are describing behavior of objects or their interactions on different levels of abstraction and “fighting” for the place on the map. It is known from the cartographic literature, that the factors, which are driving generalization can have impacts with different extent - some factors have local influence, some - global. As a result of this, generalization techniques can be applied to independent object (e.g. simplification, collapsing), group of objects (e.g. aggregation) or for entire class of objects in database or on the map (e.g. classification, selection for omitting). Parameters of the techniques can control the scale level of abstraction. Control conditions or for object’s transition and triggering can be also different for different analysis level (e.g. minimum object width; minimum space between objects; maximum density of object per sq. unit).

An important feature of behavior analysis methods is that they support a structure leveling of complex processes. Operation can be expressed by method at the subsequent levels. Behavior specifications can be constructed by leveling down or leveling up.

Another question: “What notation can be employed to describe behavior?” Notation language must be both precise and approachable.

The behavior of the entities in spatial domains will never satisfy functional equations. Algorithmic description languages are also not available at the level of analysis. Therefore procedural behavior descriptions should be traded in favor of declarative descriptions. A precise specification should be nevertheless given to the structure of the procedural language. But one of the core problems in AI and knowledge representation is that purely declarative language has not yet solved theoretical problem.

In OO analysis, model is very often described in a combination of graphic notation, natural language and formal language.

Existing languages for modeling spatial and cartographic data and its behaviors

Digital spatial objects and its cartographic representations (designed maps) are models, which specify, construct, and store the artifacts for different spatial domains. These spatial domains can be simple or complex, and they are infinite in their uniqueness. Different kind of modeling can be used for representation of spatial and map object, with different level of abstraction and utilization of different modeling methods, techniques and functions.

It would be desirable to have one unified modeling approach, and language and specifications, which can give possibility to describe all spatial domains. Members of Open GIS Consortium (OGC) did such attempt. The purpose of the Abstract Specification of Model for Geometry and Topology, Relationships between Features etc is to create and document a conceptual model sufficient enough to allow creation of Implementation Specifications [OGC Abstract Specification…, 1999]. They are focusing on implementation of this specification for different software platform. Based on these Specifications, they recommend Geography Markup Language (now it is GML version 2.0) [Geography Markup Language…, 2001].

GML is based on XML, which uphold the principle of separating content from presentation. Last principle is incorporated in many existing GIS’s software, models of spatial objects are stored there separately form its cartographic representation. The original focus of GML was to provide means for describing and transporting data in the context of the World Wide Web. But GML can be used for modeling and storing of geographic information, including both the spatial and non-spatial properties of geographic features, for other purposes. Current version of GML follows only the geometry and simple feature models, which are described in the OGC specifications,

There are no mechanisms in GML to express behavior or to perform computations. But GML can be used in conjunction with object-oriented languages for transporting geographic behavior from one place to another [Geography Markup Language…, 2001].

Cartographical presentation of GML geometry can be done by transforming the GML into one of the graphical vector data formats such as SVG, VML or VRML [Scalable Vector Graphics…, 2000; The Virtual Reality Modeling Language, 2000;]. A companion Extensible Stylesheet Language (XSL) technology is dealing with the presentation side [XML Linking Language…, 2000]. The XSL can be used to do the querying and simple calculation, and calling out for some object-oriented language to perform necessary computation.

There are some proposals to use XSLT for real-time cartographic generalization of XML or GML-encoded spatial data on the web. Generalization can be achieved by using XSL powerful queries on a GML document and its string handling and arithmetic capabilities. The XSLT extension mechanism enables to execute more complex generalization methods by calling functions in another programming languages.

Because current version of GML supports only geometry model and only for simple feature, it is difficult to expect that cartographic generalization can be performed by GML or XML encoding in holistic way. If the relations among features are not supported, the cartographic generalization cannot be proper modeled.

Object-oriented analysis for spatial and cartographic generalization

Models of object-oriented analysis comprise object structure analysis, object behavior analysis, functional object analysis, object interaction model etc. Although object-oriented analysis is often divided into structural (static) and behavioral (dynamic) aspects, the object behavior analysis method tries to integrate these two within their process part.

By its own nature, model and cartographic generalization is a process, which is driven by behaviors of geographical features of different levels of abstraction, its geometry, relations and visual representation. Therefore, the model and cartographic generalizations should be founded on a behavioral basis. The focus of the modeling is the behavioral aspects; structural aspects are identified and described as a derivation of the behavioral aspects.

There are many OOA methods or OO models for representation of object domains [Graham, 1994]. Some of these methods are advanced in modeling of objects’ behavior and have semantically enriched approaches of object-oriented analysis. They can combine a unitary notation of OOA with knowledge-based system-style rules for describing constraints, global system controls, triggers, and quantification over relationships. They provide support for classification, composition, general associations, pre-, post-, invariance conditions, and inheritance. Some of them are also unique in supporting fuzzy classification, which is important for requirement specification in some domains such as modeling of the generalization. Model of an object can encapsulate not only attributes and methods, but also rules.

There are many of proposed structural objectschemes of features, feature geometry, and relationships between features. For instance, Feature Geometry OpenGIS Abstract Specification provides standardized conceptual schemas for the geometry and topology components. It describes corresponding stereotypes and classes, its attributes and spatial operations.

A behavior description is a notoriously more difficult problem in comparison with the structural one. The behavior of the entities in geographical domains of interest practically never satisfies differential equations. Even simple feature like a costal line is beyond the formalisms of differential equations.

Algorithmic description languages are also not available at the level of analysis. The strength of these languages lies in detailing with realization of a particular desired behavior. It needs to have only the ability to provide a precise description of a desired system's behavior. Procedural behavior descriptions should be traded in favor of declarative descriptions.

The idea of spatial and cartographic generalization in OO environment is based on messages, which pass to objects and asks them to process themselves according to their behaviors. But there are a lot of questions. How object behaviors allows individual objects to change shape, attributes and visual variables themselves differently according to surroundings and global environment, and under the pressure of the purpose-orientation factors?

OOA can help to model object’s dynamic and to understand process of spatial and cartographic generalization better. OOA methods mainly use augmented transition network diagrams (event schemas) to express the behavior of objects. Transition networks are quite declarative, especially when states, transition controls, and transition actions are defined in a rigorous way.

Independent spatial or cartographic objects can generalize themselves when they are receiving messages from external objects (due to external event) either internal object, or from layers or ensemble. Transition of object can be dependent on the state of the object (attributes of the object, e.g. object’s nature, measuresetc), occurred events (types of events), invoked and object operations (kind of operations) and other auxiliary control conditions (e.g. size of object). Semantically reached methods of OOA enable to include rules (control and exception handling rules, and triggers) in descriptions of objects. It can give the support for functional semantic, global control description for local objects. These objects consist of identifier, attributes, operations (methods) and also rules. For analysis stage rules can be expressed in the way of pre-, post- and invariant conditions.

The neighborhood spatial or cartographicgeneralization can be modeled by using interactions with other objects during the object’s transitions before entering destination states. Interactions can be invoked by events that in turn can be received by one or more other objects (more than one transition can lead out of a state). Decomposition constrictions can be used for generalization and structure integrity control of groups of objects. Analysis methods approach the decomposition by such mechanisms as aggregation, generalization, subsystems, ensembles or layers. Layers or ensembles are objects with their own rights (attributes, operations and rules), but they are existing at the top of a composition structure and each of their operations have to be implemented by operations of some object(s) within that structure.

The global generalization rules can be enforced by layers to their objects or sub-layers in the same way as described above. The objects may interact inside the layer between each other (e.g. neighboring buildings). A layer controls all interactions between objects and entities outside the layer (e.g. interaction between objects in building’s and street’s layers). A layer is responsible for the creation and deletion of its objects (e.g. selection and elimination of building by applying a density requirement).

Generalization may start from top-to-bottom, when external actor send a message to global layer, which can generalize its objects according to the message’s content, behavior of layer and distribution and density of objects. A layer may remove some object to satisfy global control conditions. Such events can also trigger an active generalization of objects, remaining in layers (e.g. displacement).

External actor may activate an independent feature object to generalize itself in accordance to occurred event’s type and object’s behavior (e.g. simplify itself). Following operation can evoke event, which may trigger generalization operations in the neighboring objects (e.g. simplify, displace). For instance, if conflict is occurred during the propagation of displacement events, the object can trigger an operation from neighborhood’s layer, which can, for example, delete object(s) or aggregate group of objects together. In case if triggered operations don’t evoked some “conflict” event, the final event from independent object can still trigger the layer’s operations for conflict detection of the results of independent generalization. Layer as neighborhood object can produce generalization operation in the independent object(s) or group of objects to satisfy layer’s behavior.

Figure 1. Scenarios for object-layer generalization.

Some OOA methods offer to elaborate sequence of steps for behavior modeling [Martin, et al, 1995; Rumbaugh, et al, 1991]. For example, step-by-step method of an event scheme construction of Martin is formal and permits to analysis the generalization of spatial and map objects on the different abstraction levels. For instance, layers can be modeled at top-down during the constricting an event schema and can be specialized on the step of refinements. The usage of multiple techniques is recommended to boost confidence in their results, which should be the same, or at least equivalent, whichever technique is used. Behavior object-oriented specification of the given process provides more advantages in understanding and formulating of spatial and cartographic generalization as compared with structure static approach. Behavior analysis describes structure of objects over time. A structure, defined and detailed by an OOA of process, can be more similar to the original.

One of the frame problems in behavior analysis is the description language that allows efficient representation of sequences of states or events. The behavior description is a core element of the requirements. Since the requirements language has usually free form, any appropriate formalism can be employed.

IT industry and individual methods are offering several modeling languages and notations for OO analysis. One of such languages, which became de facto official standard for describing application domains for many organizations, is the Unified Modeling Language (UML). Now it is version 1.3.

The UML is an evolution from Booch [Booch,G., 1990], OMT (Rumbaugh et al.), OOSE (Jacobson et al.), several other object-oriented methods, and many other sources [OMG Unified Modeling Language…, 2000]. The UML is easy to adopt for usage of many other methods. UML has supports for dynamic modeling (statechart diagram, activity diagram, interaction diagrams) and most of analysis methods. The UML has the extension mechanisms (stereotypes etc.). Object constrain language (OCL) of UML provides formal descriptions for expressions during modeling. There are various CASE tools that provide support for UML notation. Next chapter describes several factors, which motivate the UML usage for modeling of spatial and cartographic generalizations.