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Related Concept Videos

Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

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In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
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The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
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Depth perception is the ability to perceive objects three-dimensionally. It relies on two types of cues: binocular and monocular. Binocular cues depend on the combination of images from both eyes and how the eyes work together. Since the eyes are in slightly different positions, each eye captures a slightly different image. This disparity between images, known as binocular disparity, helps the brain interpret depth. When the brain compares these images, it determines the distance to an object.
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Precession can be demonstrated effectively through a spinning top. If a spinning top is placed on a flat surface near the surface of the Earth at a vertical angle and is not spinning, it will fall over due to the force of gravity producing a torque acting on its center of mass. However, if the top is spinning on its axis, it precesses about the vertical direction, rather than topple over due to this torque. Precessional motion is a combination of a steady circular motion of the axis and the...
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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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Polarimetric Helmholtz Stereopsis.

Yuqi Ding, Yu Ji, Zhang Chen

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |January 25, 2024
    PubMed
    Summary
    This summary is machine-generated.

    Polarimetric Helmholtz stereopsis (polar-HS) enhances 3D surface reconstruction by incorporating light polarization. This novel method uses polarization information for accurate depth and normal estimation with fewer images.

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    Area of Science:

    • Computer Vision
    • Optics
    • Computational Imaging

    Background:

    • Helmholtz stereopsis (HS) enables 3D surface reconstruction using the Helmholtz reciprocity principle.
    • Classical HS requires multiple image pairs and struggles with diverse surface reflectances.

    Purpose of the Study:

    • To introduce polarimetric Helmholtz stereopsis (polar-HS) for improved 3D reconstruction.
    • To leverage polarization information for enhanced surface depth and normal estimation.

    Main Methods:

    • Derived Mueller matrix reciprocity relationship and formulated new polarization-aware constraints.
    • Unified reciprocity and polarimetric constraints (diffuse/specular) within an optimization framework.
    • Utilized diffuse angle of polarization consistency for depth and degree of linear polarization for normal refinement.

    Main Results:

    • Demonstrated high-quality 3D reconstruction using a hardware prototype.
    • Successfully reconstructed surfaces with varying reflectance properties, from diffuse to specular.
    • Achieved accurate depth and normal estimation with a single reciprocal image pair.

    Conclusions:

    • Polar-HS significantly advances 3D reconstruction by integrating polarization.
    • The method offers a robust and efficient approach for complex surfaces.
    • Polarization provides crucial phase information for enhanced stereopsis.