Knowledge about the global properties of a shape and its main features is very useful for the compre- hension and intelligent analysis of large data sets: the main features and their configuration are important to devise a surface understanding mechanism that discards irrelevant details without loosing the overall surface structure. As far as geospatial data are concerned, it is also important that a description captures important topographic elements, such as peaks, pits and passes, which have a relevant semantic content and, at the same time, are formally well-defined. Features in scalar fields are represented by critical points of the field [2]. Critical points and their con- figuration, indeed, and the related theory of differential topology give a suitable framework to formalize and solve several problems related to shape understanding. Computational topology techniques provide several tools and measures for surface analysis and coding [3]: Euler's equation, Morse theory, surface networks, Morse-Smale complexes, persistent diagrams and contour trees, for example, provide highly abstract shape descriptions, with several applications to the understanding, simplification and comparison of large data sets. Extended surveys on these topic can be found in [1,2]. Distinguishing the relevant features of the input is an important aspect of the methodologies used in the applications. For instance, it is possible to measure and rank the importance of topological features (encoded in the configuration of critical points) with respect to the input scalar function using the persistence approach [4], as well as to detect topological changes during time in geospatial data. In this contribution we will de- scribe the services for feature extraction and change detection implemented within the European Integrating Project IQmulus: A High-volume Fusion and Analysis Platform for Geospatial Point Clouds, Coverages and Volumetric Data Sets (http://www.iqmulus.eu/) which are based on some of the above techniques.
Analysis of Geospatial Data through Geometric-Topological Properties
S Biasotti;A Cerri;B Falcidieno;M Spagnuolo
2014
Abstract
Knowledge about the global properties of a shape and its main features is very useful for the compre- hension and intelligent analysis of large data sets: the main features and their configuration are important to devise a surface understanding mechanism that discards irrelevant details without loosing the overall surface structure. As far as geospatial data are concerned, it is also important that a description captures important topographic elements, such as peaks, pits and passes, which have a relevant semantic content and, at the same time, are formally well-defined. Features in scalar fields are represented by critical points of the field [2]. Critical points and their con- figuration, indeed, and the related theory of differential topology give a suitable framework to formalize and solve several problems related to shape understanding. Computational topology techniques provide several tools and measures for surface analysis and coding [3]: Euler's equation, Morse theory, surface networks, Morse-Smale complexes, persistent diagrams and contour trees, for example, provide highly abstract shape descriptions, with several applications to the understanding, simplification and comparison of large data sets. Extended surveys on these topic can be found in [1,2]. Distinguishing the relevant features of the input is an important aspect of the methodologies used in the applications. For instance, it is possible to measure and rank the importance of topological features (encoded in the configuration of critical points) with respect to the input scalar function using the persistence approach [4], as well as to detect topological changes during time in geospatial data. In this contribution we will de- scribe the services for feature extraction and change detection implemented within the European Integrating Project IQmulus: A High-volume Fusion and Analysis Platform for Geospatial Point Clouds, Coverages and Volumetric Data Sets (http://www.iqmulus.eu/) which are based on some of the above techniques.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
