Related Experiment Video

Updated: Jul 19, 2026

Three-Dimensional Reconstruction for the Whole Lung with Early Multiple Pulmonary Nodules
07:53

Three-Dimensional Reconstruction for the Whole Lung with Early Multiple Pulmonary Nodules

Published on: October 13, 2023

Analytical calculation of volumes-of-intersection for iterative, fully 3-D PET reconstruction

Jürgen J Scheins1, Fritz Boschen, Hans Herzog

  • 1Institute of Medicine, Research Center Jülich, Jülich 52425, Germany. j.scheins@fz-juelich.de

IEEE Transactions on Medical Imaging
|October 10, 2006
PubMed

More Related Videos

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data09:37

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

Published on: April 26, 2016

Cryo-EM and Single-Particle Analysis with Scipion09:06

Cryo-EM and Single-Particle Analysis with Scipion

Published on: May 29, 2021

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...
Finding Volume Using Cross-Sectional Area01:25

Finding Volume Using Cross-Sectional Area

For solids whose cross-sectional areas vary in a predictable way, volume can be determined by integrating these areas along an axis perpendicular to the slices. This approach is particularly useful for polyhedral solids, where classical geometric formulas may not be immediately applicable. A tetrahedron provides a clear example of how cross-sectional integration can be applied to a three-dimensional object with continuously changing geometry.Consider a tetrahedron with height h and a base that...
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
Volumes of Solids of Revolution01:29

Volumes of Solids of Revolution

Volumes of irregularly shaped objects can be systematically determined using the concept of solids of revolution. This approach begins with a region defined by a curve in a two-dimensional plane. When this region is rotated about a fixed line, known as the axis of revolution, it generates a three-dimensional object with rotational symmetry. Such objects frequently arise in mathematical modeling, physics, and engineering applications.When the region being rotated lies directly against the axis...
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,...
Iterated Integrals and Fubini's Theorem01:28

Iterated Integrals and Fubini's Theorem

A double integral generalizes the concept of a single-variable integral to functions of two variables, enabling the computation of the volume beneath a surface z = f(x, y) over a planar region R . For a rectangular region defined by a ≤ x ≤ b and c ≤ y ≤ d, and for functions continuous on this domain, the double integral can be evaluated as an iterated integral. This approach simplifies computation by reducing the problem to successive integrations with respect to one variable at a...