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    Solving geoinformatics parametric polynomial systems using the improved Dixon resultant

    272114.pdf (569.7Kb)
    Access Status
    Open access
    Authors
    Lewis, R.
    Paláncz, B.
    Awange, Joseph
    Date
    2018
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Lewis, R. and Paláncz, B. and Awange, J. 2018. Solving geoinformatics parametric polynomial systems using the improved Dixon resultant. Earth Science Informatics. 12 (2): pp. 229-239.
    Source Title
    Earth Science Informatics
    DOI
    10.1007/s12145-018-0366-2
    ISSN
    1865-0473
    School
    School of Earth and Planetary Sciences (EPS)
    Remarks

    The final publication is available at Springer via http://dx.doi.org/10.1007/s12145-018-0366-2

    URI
    http://hdl.handle.net/20.500.11937/70927
    Collection
    • Curtin Research Publications
    Abstract

    Improvements in computational and observational technologies in geoinformatics, e.g., the use of laser scanners that produce huge point cloud data sets, or the proliferation of global navigation satellite systems (GNSS) and unmanned aircraft vehicles (UAVs), have brought with them the challenges of handling and processing this “big data”. These call for improvement or development of better processing algorithms. One way to do that is integration of symbolically presolved sub-algorithms to speed up computations. Using examples of interest from real geoinformatic problems, we will discuss the Dixon-EDF resultant as an improved resultant method for the symbolic solution of parametric polynomial systems. We will briefly describe the method itself, then discuss geoinformatics problems arising in minimum distance mapping (MDM), parameter transformations, and pose estimation essential for resection. Dixon-EDF is then compared to older notions of “Dixon resultant”, and to several respected implementations of Gröbner bases algorithms on several systems. The improved algorithm, Dixon-EDF, is found to be greatly superior, usually by orders of magnitude, in both CPU usage and RAM usage. It can solve geoinformatics problems on which the other methods fail, making symbolic solution of parametric systems feasible for many problems.

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