Great strides have been made in Geographic Information Systems (GIS) research over the past half-century. However, this progress has created both opportunities and challenges. From a geographic per...

https://www.tandfonline.com/doi/pdf/10.1080/13658816.2018.1533136

Reflections and speculations on the progress in Geographic Information Systems (GIS): a geographic perspective

A virtual geographic environment (VGE) is a type of workspace for computer-aided geographic experiments (CAGEs) and geographic analyses. By supporting geo-visualization, geo-simulation, geo-collaboration, and human participation, it provides open virtual environments that correspond to the real world to assist computer-aided geographic experiments involving both the physical and human dimensions. Based on a discussion of how VGEs can contribute to CAGEs and geographic analyses, this article proposes a clear, systematic framework for VGEs. Four subenvironments are discussed according to their different functions, pertinent issues, and corresponding solutions: (1) the data environment, (2) the modeling and simulation environment, (3) the interactive environment, and (4) the collaborative environment. Furthermore, a case on the simulation of air pollution and its analysis at different geographic scales is used to demonstrate VGEs’ ability to facilitate computer-aided geographic experiments.

https://www.tandfonline.com/doi/pdf/10.1080/00045608.2012.689234

Virtual Geographic Environment – A Workspace for Computer-aided Geographic Experiments

With the increasing demand for multidimensional data processing, Geometric algebra (GA) has attracted more and more attention in the field of geographical information systems. GA unifies and generalizes real numbers and complex, quaternion, and vector algebra, and converts complicated relations and operations into intuitive algebra independent of coordinate systems. It also provides a solution for solving multidimensional information processing with a high correlation among the dimensions and avoids the loss of information. Traditional methods of computer vision and artificial intelligence (AI) provide robust results in multidimensional processing after being combined with GA and give additional feature analysis facility to remote sensing images. In this paper, we provide a detailed review of GA in different fields of AI and computer vision regarding its applications and the current developments in geospatial research. We also discuss the Clifford–Fourier transform (CFT) and quaternions (sub-algebra of GA) because of their necessity in remote sensing image processing. We focus on how GA helps AI and solves classification problems, as well as improving these methods using geometric algebra processing. Finally, we discuss the issues, challenges, and future perspectives of GA with regards to possible research directions.

/pdf/geometric-algebra-applications-in-geospatial-artificial-omm2cix1ex.pdf

Geometric Algebra Applications in Geospatial Artificial Intelligence and Remote Sensing Image Processing

Sensing multiple semantics of urban space from crowdsourcing positioning data

Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classical Fourier transform. This is applied to the so-called Clifford-Fourier transform (see [F. Brackx et al., The Clifford-Fourier transform. J. Fourier Anal. Appl. 11 (2005), 669--681]). The integral kernel of this transform is a particular solution of a system of PDEs in a Clifford algebra, but is, contrary to the classical Fourier transform, not the unique solution. Here we determine an entire class of solutions of this system of PDEs, under certain constraints. For each solution, series expressions in terms of Gegenbauer polynomials and Bessel functions are obtained. This allows to compute explicitly the eigenvalues of the associated integral transforms. In the even-dimensional case, this also yields the inverse transform for each of the solutions. Finally, several properties of the entire class of solutions are proven.

The class of Clifford-Fourier transforms

Introducing Clifford algebra as the mathematical foundation, a unified spatio-temporal data model and hierarchical spatio-temporal index are constructed by linking basic data objects, like pointclouds and Spatio-Temporal Hyper Cubes of different dimensions, within the multivector structure of Clifford algebra. The transformation from geographic space into homogeneous and conformal space means that geometric, metric and many other kinds of operators of Clifford algebra can be implemented and we then design the shortest path, high-dimensional Voronoi and unified spatial-temporal process analyses with spacetime algebra. Tests with real world data suggest these traditional GIS analysis algorithms can be extended and constructed under Clifford Algebra framework, which can accommodate multiple dimensions. The prototype software system CAUSTA (Clifford Algebra based Unified Spatial-Temporal Analysis) provides a useful tool for investigating and modeling the distribution characteristics and dynamic process of complex geographical phenomena under the unified spatio-temporal structure.

CAUSTA: Clifford Algebra-based Unified Spatio-Temporal Analysis

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CAUSTA: Clifford Algebra-based Unified Spatio-Temporal Analysis