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Reliable estimation of membrane curvature for cryo-electron tomography

Fig 6

Curvature sign, principal direction and curvature estimation accuracy for a torus.

Panels (A-D) show visualizations of κ₂ (voxel^-1, triangles are color-coded by curvature, see color bar on the right) and (every fourth vector is shown as an arrow from a triangle center): (A) true values calculated analytically for a smooth torus surface with ring radius (rr) = 25 voxels and cross-section radius (csr) = 10 voxels, (B) estimated values using NVV, (C) RVV (both with rh = 8 voxels) and (D) Mindboggle (MB, with n = 4 voxels). Panels (E-G) show cumulative relative frequency histograms of the principal direction and curvature errors: (E) , (F) κ₁, (G) κ₂ on the torus surface using different algorithms: RVV, AVV, SSVV, VTK, MB and FreeSurfer (FS); the latter three algorithms only for curvatures in (F-G), since they do not estimate principle directions; the optimal rh or n (in voxels) were used for each algorithm and are indicated in the legends.

doi: https://doi.org/10.1371/journal.pcbi.1007962.g006