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Related Concept Videos

Calculation of Volume of Solids by Integration01:27

Calculation of Volume of Solids by Integration

Volume calculation often begins with simple geometric solids. For example, the volume of a rectangular box is obtained by multiplying the area of its base by its height. This straightforward approach relies on the fact that the cross-sectional area of the box remains constant throughout its length. Many real-world objects, however, do not have uniform cross-sections, and their volumes cannot be determined using elementary geometric formulas.To address this limitation, the Slicing Method...
Triple Integrals in Rectangular Coordinates01:23

Triple Integrals in Rectangular Coordinates

Triple integrals provide a method for calculating the accumulated value of a function over a three-dimensional region. Common applications include computing volume, mass, and other physical quantities that vary with position. The fundamental idea is to partition a solid region into small rectangular boxes, evaluate the function at sample points within each box, and sum the contributions. As the partitions become finer, this triple Riemann sum approaches the exact value of the triple integral.In...
Triple Integrals in Cylindrical Coordinates01:28

Triple Integrals in Cylindrical Coordinates

Cylindrical coordinates describe a point in three-dimensional space using three values: radial distance, angle, and height. The height gives the position above the xy-plane, the radial distance measures how far the point is from the z-axis, and the angle describes the point’s direction from the positive x-axis in the xy-plane. This system is especially useful for regions with circular symmetry because it matches the natural geometry of cylinders, disks, and circular tanks.To calculate volume,...
Triple Integrals over General Regions01:28

Triple Integrals over General Regions

Triple integrals over general bounded regions extend the concept of double integrals from planar domains to three-dimensional solids. A solid region E in space is commonly enclosed within a rectangular box B, and a continuous function f(x, y, z) is integrated over the region by defining F such that it coincides with f on E and is zero outside the solid. The triple integral is therefore expressed as\begin{equation*}\iiint_E f(x,y,z) dV \end{equation*}The existence of the integral requires that f...
Real-Life Applications of Multiple Integrals01:18

Real-Life Applications of Multiple Integrals

Multiple integrals provide a powerful mathematical framework for calculating physical quantities distributed throughout two- and three-dimensional regions. One important application is the determination of volume in objects with curved geometries, such as storage tanks, pipes, and reservoirs. Cylindrical coordinates are especially useful for systems with rotational symmetry because they simplify the description of circular and paraboloid-shaped regions.Consider a paraboloid-shaped water tank...
Imaging Studies III: Computed Tomography01:27

Imaging Studies III: Computed Tomography

DefinitionComputed Tomography (CT) of the genitourinary (GU) tract is a non-invasive imaging modality that utilizes X-rays and computer processing to generate detailed cross-sectional images of the urinary system, encompassing the kidneys, ureters, bladder, and adjacent structures such as the adrenal glands.PurposeCT scans of the GU tract serve several diagnostic and therapeutic purposes, including:Diagnosis of Urinary Tract Diseases: Detects kidney stones, tumors, cysts, and congenital...

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Related Experiment Video

Updated: Jun 22, 2026

Determining 3D Flow Fields via Multi-camera Light Field Imaging
14:25

Determining 3D Flow Fields via Multi-camera Light Field Imaging

Published on: March 6, 2013

Three-dimensional volumetric object reconstruction using computational integral imaging.

Seung-Hyun Hong, Ju-Seog Jang, Bahram Javidi

    Optics Express
    |May 29, 2009
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel three-dimensional (3D) imaging technique for sensing and reconstructing 3D scenes into volumetric images using microlens arrays and computational optics.

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    Area of Science:

    • Optics and Photonics
    • Computer Vision
    • Image Processing

    Background:

    • Traditional 3D imaging methods face limitations in capturing volumetric data.
    • Accurate reconstruction of 3D scenes is crucial for various applications.

    Purpose of the Study:

    • To propose and verify a novel 3D imaging technique for volumetric image reconstruction.
    • To demonstrate the capability of sensing and computationally reconstructing 3D scenes.

    Main Methods:

    • Utilizing a microlens array and detector array for optical sensing of elemental images.
    • Employing computational simulation based on ray optics for 3D volumetric reconstruction.
    • Back-propagating elemental images through a synthesized pinhole array for arbitrary plane reconstruction.

    Main Results:

    • Successful experimental demonstration of 3D image sensing and volumetric reconstruction.
    • Verification of the algorithm and imaging system's performance.
    • Demonstrated utility of volume pixel values for 3D surface reconstruction.

    Conclusions:

    • The proposed technique effectively senses 3D scenes and reconstructs them as volumetric images.
    • The computational reconstruction method based on ray optics is validated experimentally.
    • This approach enables 3D image surface reconstruction from volumetric data.