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Computing the Inner Distances of Volumetric Models for Articulated Shape Description with a Visibility Graph.

Yu-Shen Liu, K Ramani, Min Liu

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    |June 15, 2011
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    A novel algorithm computes inner distances for 3D shapes using volumetric models and visibility graphs. This method accurately captures shape deformation, especially for articulated structures, without surface reconstruction.

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    Area of Science:

    • Computer Vision
    • Geometric Modeling
    • Computational Geometry

    Background:

    • Inner distance computation is crucial for understanding 3D shape structure.
    • Existing methods often struggle with articulated shapes or require surface reconstruction.
    • Accurate shape representation is vital for various applications, including robotics and medical imaging.

    Purpose of the Study:

    • To introduce a new visibility graph-based algorithm for computing inner distances in 3D volumetric models.
    • To develop a robust and efficient visibility checking method for volumetric data.
    • To provide a more accurate shape description, particularly for complex and articulated objects.

    Main Methods:

    • A visibility graph approach is employed to determine shortest paths within the 3D shape.
    • A novel clustering-based visibility checking algorithm operates directly on volumetric data.
    • Octree acceleration is utilized for efficient visibility computations, avoiding surface reconstruction.

    Main Results:

    • The algorithm successfully computes inner distances for 3D shapes represented by volumetric models.
    • The proposed visibility checking is fast, robust, and effective for volumetric data.
    • Inner distances derived from this method are robust to articulation and reflect shape deformation accurately.

    Conclusions:

    • The developed algorithm offers a superior method for computing inner distances in 3D shapes, especially those with articulated parts.
    • This approach provides a more accurate shape description compared to traditional distance measures.
    • The method's direct operation on volumetric models simplifies the process and enhances applicability.