Integration of geometric and topological uncertainties for geospatial Data Fusion and Mining

Spatial distribution of the dynamic network is a complex and dynamic mixture of its topology and geometry. Historically the separation of topology and geometry in mathematics was motivated by the need to separate the invariant part of the spatial distribution (topology) from a less invariant part (geometry). The geometric characteristics such as orientation, shape, and proximity are not invariant. This separation between geometry and topology was done under the assumption that the topological structure is certain and does not change over time. New challenges to deal with dynamic and uncertain topological structure require reexamination of this fundamental assumption. Data Fusion and Mining (DFM) are critical for current and future geospatial data analysis. Both technologies heavily depend on topological and geometrical representation and the selection of similarity measures. Capturing and representing uncertainty of orientation, shape, proximity, connectivity, and similarity are of the highest interest in DMF. Challenges include representation of the topological structure of the spatial objects when noise, obstacles, temporary loss of communication and other factors make them uncertain. The change of the network structure over time is another challenge. This work proposes a methodology for capturing, representing, and recording the uncertain and dynamic topology and geometry for spatial data fusion and mining. The capability of the methodology is demonstrated on the mathematical models and vector-to-vector and raster-to-vector conflation/registration problems.