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Fourier shell correlation : ウィキペディア英語版
Fourier shell correlation
In structural biology, the three-dimensional Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes over corresponding shells in Fourier space (i.e., as a function of spatial frequency〔Harauz & van Heel, 1986〕). The FSC is the three-dimensional extension of the two-dimensional Fourier ring correlation (FRC);〔van Heel, 1982〕 also known as: spatial frequency correlation function.〔Saxton & Baumeister, 1982〕
== Calculation ==
:
FSC(r) =
\frac }}
\cdot \sum_}}

where F_1 is the complex structure Factor for volume 1, F_2^ is the complex conjugate of the structure Factor for volume 2, and r_i is the individual voxel element at radius r.〔van Heel & Schatz, 2005〕 In this form, the FSC takes two three-dimensional data sets and converts them into a one-dimensional array.
The FSC originated in cryo-electron microscopy and gradually proliferated to other fields. To measure the FSC, two independently determined 3D volumes are required. In cryo-electron microscopy, the two volumes are the result of two three-dimensional reconstructions, each based on half of the available data set. Typically, the even particle images form one half and the odd particles the other half of the data set. Most publications quote the FSC 0.5 resolution cutoff, which ''ad hoc'' criterion refers to when the correlation coefficient of the Fourier shells is equal to 0.5.〔Böttcher et al., 1997〕〔Frank, 2006, p250-251〕 However, determining the resolution threshold remains a controversial issue: fixed-value thresholds were argued to be based on incorrect statistical assumptions.〔 Many other criteria using the FSC curve exist, including 3-σ criterion, 5-σ criterion, and the 0.143 cutoff. The half-bit criterion indicates at which resolution we have collected enough information to reliably interpret the 3-dimensional volume, and the (modified) 3-sigma criterion indicates where the FSC systematically emerges above the expected random correlations of the background noise.〔

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