Zhaoyuan Yu

Multidimensional-unified topological relations computation: a hierarchical geometric algebra-based approach

This article presents a geometric algebra-based model for topological relation computation. This computational model is composed of three major components: the Grassmann structure preserving hierarchical multivector-tree representation (MVTree), multidimensional unified operators for intersection relation computation, and the judgement rules for assembling the intersections into topological relations. With this model, the intersection relations between the different dimensional objects (nodes at different levels) are computed using the Tree Meet operator. The meet operation between two arbitrary objects is accomplished by transforming the computation into the meet product between each pair of MVTree nodes, which produces a series of intersection relations in the form of MVTree. This intersection tree is then processed through a set of judgement rules to determine the topological relations between two objects in the hierarchy. Case studies of topological relations between two triangles in 3D space are employed to illustrate the model. The results show that with the new model, the topological relations can be computed in a simple way without referring to dimension. This dimensionless way of computing topological relations from geographic data is significant given the increased dimensionality of geographic information in the digital era.

Data environment construction for virtual geographic environment

Virtual geographic environment (VGE) aims to express the real-world naturally, and support the complex geographic analysis. The data environment, fundamental of VGE, is expected to support the data management, analysis, sharing and application requirements of the massive complex geographic spatio-temporal data. In this paper, we summarized the key problems in the construction of the data environment of VGE. The unified spatio-temporal data model and a new data structure were developed according to the geographic rules. The organization and compress storage mechanism of massive spatio-temporal data were also developed. With these foundations, case studies, which integrate the global, regional and city scale data to operate complex data modeling and analysis, are performed. The results showed that the construction of the integrated data environment of VGE can largely improve the efficiency of GIS analysis, which also provides a potential new tool to support the complex geographic analysis.

Change detection for 3D vector data: a CGA-based Delaunay–TIN intersection approach

In this paper, conformal geometric algebra (CGA) is introduced to construct a Delaunay–Triangulated Irregular Network (DTIN) intersection for change detection with 3D vector data. A multivector-based representation model is first constructed to unify the representation and organization of the multidimensional objects of DTIN. The intersection relations between DTINs are obtained using the meet operator with a sphere-tree index. The change of area/volume between objects at different times can then be extracted by topological reconstruction. This method has been tested with the Antarctica ice change simulation data. The characteristics and efficiency of our method are compared with those of the Möller method as well as those from the Guigue–Devillers method. The comparison shows that this new method produces five times less redundant segments for DTIN intersection. The computational complexity of the new method is comparable to Möller’s and that of Guigue–Devillers methods. In addition, our method can be easily implemented in a parallel computation environment as shown in our case study. The new method not only realizes the unified expression of multidimensional objects with DTIN but also achieves the unification of geometry and topology in change detection. Our method can also serve as an effective candidate method for universal vector data change detection.

A dynamic evacuation simulation framework based on geometric algebra

Abstract Integrating dynamic analysis models into geographic information system (GIS)-based evacuation simulations is important yet complex. Different models must be smoothly assembled according to the data processing flow to obtain a dynamic, data-forced evacuation simulation. However, because of the diversity of data types and dynamic data updating among different models, closely integrated evacuation simulations are complex and inefficient. In this study, geometric algebra (GA) is introduced to develop a dynamic evacuation simulation framework for a hazardous gas diffusion scheme. In the framework, geospatial data are first integrated into a unified virtual scene with different forms of multivector representation. The major simulation models of gas diffusion, risk assessment, and dynamic evacuation routing compose the major steps of the evacuation simulation. On the basis of the generalized multivector structure, dynamic exchange and updating geospatial data at different evacuation steps can be performed seamlessly with the multivector structure and GA operators. The framework is tested with a case study of a three-dimensional residential area, which shows that our framework can support the integration of dynamic evacuation processes and the model integration is direct and smooth. This framework may also provide a new solution for the integration and dynamic data updating in spatiotemporal GIS.

A Hierarchical Tensor-Based Approach to Compressing, Updating and Querying Geospatial Data

With the rapid development of data observation and model simulation in geoscience, spatial-temporal data have become increasingly multidimensional, massive and are consistently being updated. As a result, the integrated maintenance of these data is becoming a challenge. This paper presents a blocked hierarchical tensor representation within the split-and-merge paradigm for the compressed storage, continuously updating and data querying of multidimensional geospatial field data. The original multidimensional geospatial field data are split into small blocks according to their spatial-temporal references. These blocks are represented and compressed hierarchically, and then combined into a single hierarchical tree as the representation of original data. With a buffered binary tree data structure and corresponding optimized operation algorithms, the original multidimensional geospatial field data can be continuously compressed, appended, and queried. Data from the 20th Century Reanalysis Monthly Mean Composites are used to evaluate the performance of this approach. Compared to traditional methods, the new approach is shown to retain the quality of the original data with much lower storage costs and faster computational performance. The result suggests that the blocked hierarchical tensor representation provides an effective structure for integrated storage, presentation and computation of multidimensional geospatial field data.

Geographic scenario: a possible foundation for further development of virtual geographic environments

ABSTRACT It has been two decades since virtual geographic environments (VGEs) were initially proposed. While relevant theories and technologies are evolving, data organization models have always been the foundation of VGE development, and they require further exploration. Based on the comprehensive consideration of the characteristics of VGEs, geographic scene is proposed to organize geographic information and data. We empirically find that geographic scene provides a suitable organization schema to support geo-visualization, geo-simulation, and geo-collaboration. To systematically investigate the concept and method of geographic scene, Geographic Scenario is proposed as the theory on developing geographic scene, and corresponding key issues of the Geographic Scenario are illustrated in this article. Prospects of the proposed method are discussed with the hope of informing future studies of VGEs.

Spatio-Temporal Constrained Human Trajectory Generation from the PIR Motion Detector Sensor Network Data: A Geometric Algebra Approach

Passive infrared (PIR) motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA)-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks.

Exploratory Method for Spatio-Temporal Feature Extraction and Clustering: An Integrated Multi-Scale Framework

This paper presents an integrated framework for exploratory multi-scale spatio-temporal feature extraction and clustering of spatio-temporal data. The framework combines the multi-scale spatio-temporal decomposition, feature identification, feature enhancing and clustering in a unified process. The original data are firstly reorganized as multi-signal time series, and then decomposed by the multi-signal wavelet. Exploratory data analysis methods, such as histograms, are used for feature identification and enhancing. The spatio-temporal evolution process of the multi-scale features can then be tracked by the feature clusters based on the data adaptive Fuzzy C-Means Cluster. The approach was tested with the global 0.25° satellite altimeter data over a period of 21 years from 1993 to 2013. The tracking of the multi-scale spatio-temporal evolution characteristics of the 1997–98 strong El Nino were used as validation. The results show that our method can clearly reveal and track the spatio-temporal distribution and evolution of complex geographical phenomena. Our approach is efficient for global scale data analysis, and can be used to explore the multi-scale pattern of spatio-temporal processes.

Pattern forced geophysical vector field segmentation based on Clifford FFT

Vector field segmentation is gaining increasing importance in geophysics research. Existing vector field segmentation methods usually can only handle the statistical characteristics of the original data. It is hard to integrate the patterns forced by certain geophysical phenomena. In this paper, a template matching method is firstly constructed on the foundation of the Clifford Fourier Transformation (CFT). The geometric meanings of both inner and outer components can provide more attractive information about the similarities between original vector field and template data. A composed similarity field is constructed based on the coefficients fields. After that, a modified spatial consistency preserving K-Means cluster algorithm is proposed. This algorithm is applied to the similarity fields to extract the template forced spatial distribution pattern. The complete algorithm for the overall processing is given and the experiments of ENSO forced global ocean surface wind segmentation are configured to test our method. The results suggest that the pattern forced segmentation can extract more latent information that cannot be directly measured from the original data. And the spatial distribution of ENSO influence on the surface wind field is clearly given in the segmentation result. All the above suggest that the method we proposed provides powerful and new thoughts and tools for geophysical vector field data analysis.

Template-based GIS computation: a geometric algebra approach

ABSTRACT The tight coupling between geospatial data and spatial analysis results in high costs in terms of efficiency when developing algorithms to accommodate different types of data, even when the analysis tasks are the same. Universal GIS (Geographic information system) algorithms, as alternatives to tightly coupled approaches, can reduce development costs. However, a unified representation of spatial data is necessary to support the development of universal GIS algorithms. To this end, this research proposes and implements a template-based approach using geometric algebra to create a unified representation of multidimensional data. The template is composed of parameters and operators for GIS representation and computation. The template approach can support general GIS analyses with parameter unfolding and operator integration methods. A case study of intersection analysis shows that developing programming scripts based on computation templates is much simpler than traditional methods. The results suggest that the template-based method is more efficient than traditional methods and more convenient for high-dimensional applications.