A Unified Methodology for the Generalisation of the Geometry of Features
| Autor: | Joanna Bac-Bronowicz, Tadeusz Chrobak, Stanisław Lewiński, Dorota Dejniak, Artur Krawczyk, Anna Barańska |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Source data
Similarity (geometry) cauchy convergence test 010504 meteorology & atmospheric sciences Scale (ratio) Computer science Geography Planning and Development 0211 other engineering and technologies lcsh:G1-922 Geometry 02 engineering and technology 01 natural sciences Earth and Planetary Sciences (miscellaneous) MRDB Computers in Earth Sciences Spatial analysis generalisation standard 021101 geological & geomatics engineering 0105 earth and related environmental sciences digital generalisation minimum dimensions of salishchev Feature data metric space contraction triangles lipschitz continuity condition polyline (segmented line) of binary tree structure GIS Metric space Feature (computer vision) Feature geometry contractive self-mapping lcsh:Geography (General) banach theorem |
| Zdroj: | ISPRS International Journal of Geo-Information Volume 10 Issue 3 ISPRS International Journal of Geo-Information, Vol 10, Iss 107, p 107 (2021) |
| ISSN: | 2220-9964 |
| DOI: | 10.3390/ijgi10030107 |
| Popis: | The development of generalisation (simplification) methods for the geometry of features in digital cartography in most cases involves the improvement of existing algorithms without their validation with respect to the similarity of feature geometry before and after the process. It also consists of the assessment of results from the algorithms, i.e., characteristics that are indispensable for automatic generalisation. The preparation of a fully automatic generalisation for spatial data requires certain standards, as well as unique and verifiable algorithms for particular groups of features. This enables cartographers to draw features from these databases to be used directly on the maps. As a result, collected data and their generalised unique counterparts at various scales should constitute standardised sets, as well as their updating procedures. This paper proposes a solution which consists in contractive self-mapping (contractor for scale s = 1) that fulfils the assumptions of the Banach fixed-point theorem. The method of generalisation of feature geometry that uses the contractive self-mapping approach is well justified due to the fact that a single update of source data can be applied to all scales simultaneously. Feature data at every scale s < 1 are generalised through contractive mapping, which leads to a unique solution. Further generalisation of the feature is carried out on larger scale spatial data (not necessarily source data), which reduces the time and cost of the new elaboration. The main part of this article is the theoretical presentation of objectifying the complex process of the generalisation of the geometry of a feature. The use of the inherent characteristics of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions, Salishchev measures, and Banach theorems ensure the uniqueness of the generalisation process. Their application to generalisation makes this process objective, as it ensures that there is a single solution for portraying the generalised features at each scale. The present study is dedicated to researchers concerned with the theory of cartography. |
| Databáze: | OpenAIRE |
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