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Recently I heard about the term volumetric data. The definition for volumetric data is as follows

#1: Definition

Volumetric data is typically a set S of samples $(x, y, z, v)$, representing the value v of some property of the data, at a 3D location $(x, y, z)$. If the value is simply a 0 or a 1, with a value of 0 indicating background and a value of 1 indicating the object, then the data is referred to as binary data. The data may instead be multivalued, with the value representing some measurable property of the data, including, for example, color, density, heat, or pressure.

#2: Some more details

A volumetric dataset consists of information at sample locations in some space. The information may be a scalar (such as density in a computed tomography (CT) scan), a vector (such as velocity in a flow field), or a higher-order tensor (such as energy, density, and momentum in computational fluid dynamics (CFD)). The space is usually 3D, consisting of either three spatial dimensions or another combination of spatial and frequency dimensions.

In simple words, I can say that volumetric data is nothing but a three-dimensional collection of tensors.

The articles linked above contain some examples of volumetric data in the medical (and probably physics) domain.

Are there any other simple real-world examples for volumetric data other than the medical and physics domain and physics?

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  • $\begingroup$ "Physics" is quite broad... That eliminates several engineering applications I can think of. However, you mention medicine, where it's mostly used by biophysicists, so by physics, do you mean pure/theoretical physics? $\endgroup$
    – Avatrin
    Nov 21, 2021 at 11:00
  • $\begingroup$ @Avatrin Yeah, I do mean pure/theoretical physics. $\endgroup$
    – hanugm
    Nov 21, 2021 at 14:09

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Whenever a system is being modelled in three dimensions, you can be sure that tensors either can or are being used. Most of the systems I can think of are either simulated volumetric data, or a combination of real measurements and interpolated values.

CAD and BIM

Computer-Aided Design, or CAD, if quite commonly used in engineering. It's quite natural that, if they are modelling a mechanical system, that they need information regarding the materials they are considering to use to make the device; A little bit of googling showed that Autodesks Inventor computes inertia tensors and their mechanical simulation software computes stress tensors.

BIM is essentially CAD for the construction industry, but again, a lot of the same kind of information regarding the materials used is needed; Else, the building may collapse.

Geology

Modelling the stability of soil to construct a skyscraper may require 3D data. There is an old question at gis.stackexchange discussing software used to model geological systems. Of those, this one and this other one still seems to be up.

Meteorology

Most meteorological data, to the best of my knowledge, is two-dimensional. However, weather radar can be used to extract 3D data with information about precipitation and motion.

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