Crowther criterion¶

The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion.

Version: v1 · 2026-09-28 · History
Domain-specific #: 8794
Domain group: Natural Sciences
Origin domain: Biology & Ecology
Subdomains: Structural Biology, Electron Tomography → Biology & Ecology

Core Idea¶

Crowther criterion is treated here as the recurring crossdomainmodelsstructuresrepresentations identity summarized by this source-grounded definition: The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion. The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion. The minimum number of views, m , to reconstruct a particle of diameter D to a resolution of d is given by. where d = 1/R , with R the reciprocal space radius corresponding to the maximum meaningfully filled frequency in Fourier space.

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How Many Pictures You Need

Imagine trying to figure out the shape of a toy you can't touch, only by taking pictures of it from different sides. The bigger the toy and the more tiny details you want to see, the more pictures you need. The Crowther criterion tells scientists the fewest pictures needed for the detail they want.

Views Needed for a Sharp 3D Picture

In tomography, scientists build a 3D picture of an object by combining many 2D views taken from different directions. The Crowther criterion is the usual way to figure out how sharp that 3D picture can be. It says how many views you need to rebuild a particle of a certain size with a certain level of detail. The bigger the particle, or the finer the details you want to see, the more views you need. If you don't have enough views, the fine details can't be filled in properly.

Views Needed for Tomographic Resolution

In tomography, a 3D reconstruction is built from 2D projection images taken at different viewing angles. Each view fills in part of the object's information in 'Fourier space,' a way of describing the object by its spatial frequencies, where higher frequencies correspond to finer detail. The Crowther criterion is the conventional way to judge the resolution a reconstruction can reach: it gives the minimum number of views m needed to reconstruct a particle of diameter D to a resolution d. Here d = 1/R, where R is the largest radius in Fourier space that is meaningfully filled by the data. More views are needed as the particle gets larger or the target resolution gets finer.

The Crowther criterion is the conventional method for evaluating the achievable resolution of a tomographic reconstruction. By the projection-slice theorem, each projection view samples a central section of the object's Fourier transform, so a finite number of views leaves gaps between sections at high spatial frequency. The criterion gives the minimum number of views m needed to reconstruct a particle of diameter D to resolution d, with m scaling in proportion to D/d; in its usual form m = πD/d. Here d = 1/R, where R is the reciprocal-space radius corresponding to the maximum meaningfully filled frequency in Fourier space. Conversely, given the number of views and the particle size, it bounds the resolution that the reconstruction can meaningfully claim.

Scope of Application¶

Documented setting. The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion.
Documented setting. The minimum number of views, m , to reconstruct a particle of diameter D to a resolution of d is given by.
Documented setting. where d = 1/R , with R the reciprocal space radius corresponding to the maximum meaningfully filled frequency in Fourier space.
Documented setting. The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion.
Documented setting. The minimum number of views, m , to reconstruct a particle of diameter D to a resolution of d is given by.

Clarity¶

A clear use of Crowther criterion names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion.

Manages Complexity¶

Crowther criterion compresses multiple crossdomainmodelsstructuresrepresentations details into a stable diagnostic relation. The source shows both the central mechanism—the minimum number of views, m , to reconstruct a particle of diameter D to a resolution of d is given by.—and the practical consequence—where d = 1/R , with R the reciprocal space radius corresponding to the maximum meaningfully filled frequency in Fourier space.

Abstract Reasoning¶

Type the carrier. Identify the crossdomainmodelsstructuresrepresentations entities to which the claim applies.
State the relation. Use the source-grounded identity: The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion.
Check operation and conditions. where d = 1/R , with R the reciprocal space radius corresponding to the maximum meaningfully filled frequency in Fourier space.
Demand recognition evidence. The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion.
Test variation.

Knowledge Transfer¶

Within the home domain. Knowledge about Crowther criterion transfers literally when a new case preserves the same carrier type, relation, and recognition test. The conventional method to evaluate the resolution of a tomography reconstruction is determined by the Crowther criterion. The minimum number of views, m , to reconstruct a particle of diameter D to a resolution of d is given by. Beyond the home domain. No canonical parent is asserted for Crowther criterion.

Neighborhood in Abstraction Space¶

Crowther criterion sits in a sparse region of the domain-specific corpus (85^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08