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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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The Earth's shape is best described as an ellipsoid, a slightly flattened sphere created by rotating an ellipse around its minor axis. This flattening results in the polar axis being about 21 kilometers shorter than the equatorial axis. In contrast, the geoid represents the Earth's gravitational shape and aligns with the mean sea level (MSL). The geoid is an irregular equipotential surface where gravity is perpendicular at every point. Variations in Earth's mass distribution cause geoid...
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Updated: Nov 5, 2025

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SMSIR: Spherical Measure Based Spherical Image Representation.

Gang Wu, Yunhui Shi, Xiaoyan Sun

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    |May 18, 2021
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    Summary
    This summary is machine-generated.

    This study introduces a novel spherical image representation (SMSIR) and resampling techniques. Our methods offer higher accuracy and quality for spherical images compared to existing representations and interpolation methods.

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    Area of Science:

    • Computer Vision
    • Image Processing
    • Spherical Geometry

    Background:

    • Spherical images are increasingly used in VR/AR and 360° media.
    • Existing representations like Equirectangular Projection (ERP) have limitations in accuracy and computational efficiency.
    • There is a need for advanced methods for spherical image processing and analysis.

    Purpose of the Study:

    • To propose a new spherical image representation called Spherical Measure based Spherical Image Representation (SMSIR).
    • To develop sphere-based resampling methods for generating SMSIR from ERP.
    • To introduce a spherical wavelet transform for Multi-Resolution Analysis (MRA) of spherical images.

    Main Methods:

    • Formal recursive definition of SMSIR elements and a dyadic index scheme for efficient global random access.
    • Two resampling methods: spherical measure-based and Radial Basis Function (RBF)-based.
    • Design of high-pass and low-pass filters using lifting schemes for spherical isotropy.

    Main Results:

    • SMSIR recovers original image signals with higher accuracy than ERP and Cubemap (CMP) representations.
    • Proposed resampling methods outperform bilinear and bicubic interpolation, achieving up to 2dB S-PSNR gain.
    • Spherical wavelet transform captures more geometric features than traditional wavelet transforms.

    Conclusions:

    • SMSIR provides an efficient and accurate representation for spherical images.
    • The developed resampling techniques offer superior quality and computational efficiency.
    • The proposed spherical wavelet transform enables effective Multi-Resolution Analysis for spherical image data.