Knowledge diffusion from GIScience to other fields: the example of the usage of weighted surface networks in nanotechnology

This article demonstrates how the generalisation of topographic surfaces has been formalised by means of graph theory and how this formalised approach has been integrated into an ISO standard that is employed within nanotechnology. By applying concepts from higher-dimensional calculus and topology, it is shown that Morse functions are those mappings that are ideally suited for the formal characterisation of topographic surfaces. Based on this result, a data structure termed weighted surface network is defined that may be applied for both the characterisation and the generalisation of the topological structure of a topographic surface. Hereafter, the focus is laid on specific issues of the standard ISO 25178-2; within this standard change trees, a data structure similar to weighted surface networks, are applied to portray the topological information of topographic surfaces. Furthermore, an approach termed Wolf pruning is used to simplify the change tree, with this pruning method being equivalent to the graph-theoretic contractions by which weighted surface networks can be simplified. Finally, some practical applications of the standard ISO 25178-2 within nanotechnology are discussed.     

A Review of: “Applications of Spatial Data Structures: Computer Graphics,Image Processing,and GIS”. By H. SAMET. (Addison-Wesley Publishing Company,Inc, 1989.) [Pp. xv + 507; figures,tables, appendix,references, name and credit index,subject index.] Price US $49.95. ISBN 020150300 X (hardback).

The introduction of automated generalisation procedures in map production systems requires that generalisation systems are capable of processing large amounts of map data in acceptable time and that cartographic quality is similar to traditional map products. With respect to these requirements, we examine two complementary approaches that should improve generalisation systems currently in use by national topographic mapping agencies. Our focus is particularly on self‐evaluating systems, taking as an example those systems that build on the multi‐agent paradigm. The first approach aims to improve the cartographic quality by utilising cartographic expert knowledge relating to spatial context. More specifically, we introduce expert rules for the selection of generalisation operations based on a classification of buildings into five urban structure types, including inner city, urban, suburban, rural, and industrial and commercial areas. The second approach aims to utilise machine learning techniques to extract heuristics that allow us to reduce the search space and hence the time in which a good cartographical solution is reached. Both approaches are tested individually and in combination for the generalisation of buildings from map scale 1:5000 to the target map scale of 1:25 000. Our experiments show improvements in terms of efficiency and effectiveness. We provide evidence that both approaches complement each other and that a combination of expert and machine learnt rules give better results than the individual approaches. Both approaches are sufficiently general to be applicable to other forms of self‐evaluating, constraint‐based systems than multi‐agent systems, and to other feature classes than buildings. Problems have been identified resulting from difficulties to formalise cartographic quality by means of constraints for the control of the generalisation process.     

A modified binary space partitioning tree for geographic information systems

We present a reactive data structure, that is, a spatial data structure with detail levels. The two properties, spatial organization and detail levels, are the basis for a geographic information system (GIS) with a multi-scale database. A reactive data structure is a novel type of data structure catering to multiple detail levels with rapid responses to spatial queries. It is presented here as a modification of the binary space partitioning tree that includes the levels of detail. This tree is one of the few spatial data structures that does not organize space in a rectangular manner. A prototype system has been implemented. An important result of this implementation is that it shows that binary space partitioning trees of real maps have O(n) storage space complexity in contrast to the theoretical worst case O(n² ), with n the number of line segments in the map.     

Understanding Chorematic Diagrams: Towards a Taxonomy

Abstract

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Chorematic diagrams are prospective candidates for communicating highly generalised geographic information about a given region of interest. Chorematic diagrams were popularized in France as the graphical artefacts of a specific school of geographic thought established by Roger Brunet, with GIP-RECLUS as his institutional backing. Although many maps were created and a lively debate ensued, only few consolidated cartographic findings were generated and even less were made known to the international scientific community. This article presents a contextualizing review and proposes a cartographic taxonomy aimed at being a first step towards efforts for the automated generation of chorematic diagrams.     

Cartographically Wordy but not Necessarily Worthy

Abstract

A novel method called multidirectional visibility index (MVI) has been developed and verified. The MVI improves standard cartographic analytical shading with a number of enhancements to topographic detail and prominent structures, i.e. the portrayal of flat areas in lighter tones, the accentuation of morphologic edges, and the multiscale visualisation of morphologic terrain features. The procedure requires a digital elevation model (DEM) and involves the following steps: visibility mask computation; the respective multidirectional altering of the azimuth and elevation angle; the generation of continuous grid MVIs that indicate upper/lower views, quasi-slope, and relative relief; and an appropriate visualisation of the relevant MVI as a standalone technique or in combination with standard hill-shaded relief. The modelling parameters are robust and therefore highly adaptive to different landforms.     

The National Archives and Public Records

Abstract

The article provides an overview of the huge cartographic holdings of The National Archives (TNA). It continues by outlining the procedures by which records are selected for permanent preservation by TNA.     

Centrality-based hierarchy for street network generalization in multi-resolution maps

This paper introduces a new hierarchy for cartographic generalisation processes, applied in street networks. The aims of implementing this hierarchy are to emphasise on significant street features, and to provide more free spaces between street features. The hierarchy is obtained from the functional classes of the features and four centrality measures in a street network, i.e. betweenness, reach, straightness and closeness extracted from a primary graph. The values of centrality measures change in every zoom level by calculating a radius parameter, which depends on the users’ field of view. The coefficients for the measures are constructed using a decision-making technique called fuzzy analytical hierarchy process (FAHP). The weights for each of the centrality measures are computed and normalised to form the proposed hierarchy. The hierarchy is applied and used later in the thinning process to omit insignificant features from the street network in medium scales.     

Spatial statistical techniques for aggregating point objects extracted from high spatial resolution remotely sensed imagery

 Using a local maximum filter, individual trees were extracted from a 1 m spatial resolution IKONOS image and represented as points. The spatial pattern of individual trees was determined to represent forest age (a surrogate for forest structure). Point attributes, based on the spatial pattern of trees, were generated via nearest neighbour statistics and used as the basis for aggregating points into forest structure units. The forest structure units allowed for the mapping of a forested area into one of three age categories: young (1–20 years), intermediate (21–120 years), and mature (>120 years). This research indicates a new approach to image processing, where objects generated from the processing of image data (rather than pixels or spectral values) are subjected to spatial statistical analysis to estimate an attribute relating an aspect of forest structure. Received: 22 April 2002 / Accepted: 23 November 2002     

Visual Abstraction and Stylisation of Maps

Abstract

We explore visual map abstraction for the generation of stylized renderings of 2D map data. We employ techniques that are centred around the concept of shape simplification and graph layout and that allow iterative abstraction of 2D maps. We use data from publicly available sources and show how we can iteratively generate aesthetic renditions of these maps. These renditions do not have the goal to allow for navigation tasks, but instead show the map data in a distorted manner. The techniques used to create these images apply simplification, abstraction/generalisation, and displacement operations to the map elements in varying orders and add stylistic shading to produce aesthetic renditions for print or electronic displays. The degree of abstraction/generalisation can be individually chosen and determines the characteristics of the distorted map: whether components retain their shape, degenerate, or are processed in a manner that the abstraction becomes the focus of the image rather than the underlying map data. The renditions can be further personalized by choosing shading and colours for this shading. Together, the presented techniques allow for playful and creative exploration of aesthetic renditions of 2D map data.     

Area aggregation in map generalisation by mixed-integer programming

Topographic databases normally contain areas of different land cover classes, commonly defining a planar partition, that is, gaps and overlaps are not allowed. When reducing the scale of such a database, some areas become too small for representation and need to be aggregated. This unintentionally but unavoidably results in changes of classes. In this article we present an optimisation method for the aggregation problem. This method aims to minimise changes of classes and to create compact shapes, subject to hard constraints ensuring aggregates of sufficient size for the target scale. To quantify class changes we apply a semantic distance measure. We give a graph theoretical problem formulation and prove that the problem is NP-hard, meaning that we cannot hope to find an efficient algorithm. Instead, we present a solution by mixed-integer programming that can be used to optimally solve small instances with existing optimisation software. In order to process large datasets, we introduce specialised heuristics that allow certain variables to be eliminated in advance and a problem instance to be decomposed into independent sub-instances. We tested our method for a dataset of the official German topographic database ATKIS with input scale 1:50,000 and output scale 1:250,000. For small instances, we compare results of this approach with optimal solutions that were obtained without heuristics. We compare results for large instances with those of an existing iterative algorithm and an alternative optimisation approach by simulated annealing. These tests allow us to conclude that, with the defined heuristics, our optimisation method yields high-quality results for large datasets in modest time.