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    This study unifies network localizability theory, exploring how node positions are determined by directional measurements. It offers new insights into unique node positioning in d-space, crucial for applications like structure from motion.

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    Area of Science:

    • Robotics and Computer Vision
    • Network Science
    • Computational Geometry

    Background:

    • Network localizability is key to determining node positions from inter-node measurements.
    • Existing research is fragmented across different scientific communities and formalisms.
    • Applications include global structure from motion in computer vision.

    Purpose of the Study:

    • To provide a unified theoretical framework for bearing-based network localizability.
    • To connect disparate results from various research fields.
    • To derive novel localizability results using an edge-based formulation.

    Main Methods:

    • Theoretical analysis of network localizability.
    • Formalization and integration of existing results.
    • Development of an edge-based formulation for localizability analysis.

    Main Results:

    • A coherent structure linking various localizability results.
    • New theoretical insights into unique node positioning in d-space.
    • Novel localizability findings within the edge-based framework.

    Conclusions:

    • The paper establishes a unified perspective on network localizability.
    • It enhances understanding of how directional data determines node positions.
    • New theoretical results advance the field of network localization and structure from motion.