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Related Concept Videos

Fischer Projections02:18

Fischer Projections

Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines. While...
Newman Projections02:06

Newman Projections

Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as conformers.
Coordinates and Map Projections01:29

Coordinates and Map Projections

Coordinates and map projections are essential tools in accurately representing the Earth's surface for various applications, ranging from navigation to spatial analysis. The latitude and longitude coordinate system is a universally recognized framework for defining locations. Latitude specifies the distance of a point north or south of the equator, measured in degrees from 0° at the equator to 90° at the poles. Longitude indicates a location's position east or west of the prime meridian,...
Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...
Divergence Theorem in 3D Space01:20

Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...
Spherical Coordinates01:23

Spherical Coordinates

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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Related Experiment Video

Updated: Jul 7, 2026

Photorealistic Learned Landscapes for Augmented Reality
06:54

Photorealistic Learned Landscapes for Augmented Reality

Published on: June 27, 2025

Projection space iteration reconstruction-reprojection.

J H Kim, K Y Kwak, S B Park

    IEEE Transactions on Medical Imaging
    |January 1, 1985
    PubMed
    Summary
    This summary is machine-generated.

    A new Projection Space Iterative Reconstruction-Reprojection (PSIRR) algorithm improves computed tomography (CT) image quality by eliminating interpolation errors inherent in the original iterative reconstruction-reprojection (IRR) method.

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    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

    Published on: December 3, 2013

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    Photorealistic Learned Landscapes for Augmented Reality
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    Published on: June 27, 2025

    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
    11:34

    High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

    Published on: December 3, 2013

    Area of Science:

    • Medical Imaging
    • Computational Imaging
    • Image Reconstruction

    Background:

    • Limited view computed tomography (CT) often faces image quality degradation due to interpolation errors in iterative reconstruction-reprojection (IRR) algorithms.
    • These errors can lead to image artifacts and potential divergence, necessitating a large number of rays for acceptable results.

    Purpose of the Study:

    • To introduce a novel Projection Space Iterative Reconstruction-Reprojection (PSIRR) algorithm.
    • To address the limitations of existing IRR methods in limited view CT by eliminating interpolation in the object space.

    Main Methods:

    • Developed a PSIRR algorithm that performs backprojection-reprojection in the projection space.
    • Iteration is achieved using a single equation, thereby removing the need for interpolation operations.
    • Evaluated the algorithm using computer simulations and experimental data from ultrasonic attenuation CT with a sponge phantom.

    Main Results:

    • The PSIRR algorithm demonstrated substantial improvements in image quality compared to the conventional IRR algorithm.
    • Elimination of object space interpolation significantly reduced image artifacts and improved reconstruction accuracy.
    • Successful application to ultrasonic attenuation CT imaging was confirmed.

    Conclusions:

    • The PSIRR algorithm offers a significant advancement for limited view CT reconstruction.
    • It provides superior image quality by avoiding interpolation-induced errors.
    • This method holds promise for various CT applications, including ultrasonic imaging.