Uniform cubic spline curve.

(a) Diagram showing the core components of a cubic B-spline curve, such as knots, control points, and the uniform knot positions ti. (b) Diagram showing the free-end boundary condition for a cubic B-spline.

3D spline model knot grid construction and shift field generation.

(a) Diagram showing the position of knots along the exposure accumulation direction and the shift amount along x for each movie frame. (b) A 3D diagram showing the cubic B-spline along the exposure accumulation direction, with red arrows representing the shifts where the knots are located (black dots on the gray line), and the cyan curve showing the spline curve for interpolating the shifts for each frame. (c, d) Shift field along x and y showing the shift amount of each pixel obtained from the bicubic B-splines on a 10 × 10 pixels frame (for demonstration only). (e) Schematic image grid before (gray grids) and after (cyan grid) applying the shift fields in (c, d). The red arrows represent the shift of patches. Black dots represent knot positions.

A micrograph of whole-cell Mycoplasma pneumoniae.

(a) Motion trajectory panel in the cisTEM GUI. (b) The cropped area shown in (a) without local distortion correction, experiencing blurring due to the local distortion (upper) and the power spectrum (lower). (c) The cropped area (upper) and the power spectrum of the local distortion-corrected micrograph (lower). (d) Detected particles (white) using 2DTM on the full-frame aligned micrograph. (e) Detected particles (white) using 2DTM on the local-distortion corrected micrograph.

Patch shift in different types of samples.

(a) Box plots of the standard deviation of patch motions calculated for micrographs of different types of samples. (b) The mean patch shifts for each micrograph, colored by sample type.

Magnitude of deformation correction of the micrograph shown in Figure 3a.

(a) Von Mises equivalent strain and (b) total equivalent strain.

Evaluation of local motion correction using Unbend across different sample types.

(a) Box plots displaying the distribution of the number of 2DTM detections per micrograph. (b) Histograms of the 2DTM SNR of detected 2DTM targets. Unbend improves the overall distribution of SNR values for all sample types. (c) 2DTM SNR difference between Unbend and Unblur. Across all sample types, Unbend led to improvements in either the number of detected targets or 2DTM SNR values, or both.

Impact of patch-based motion correction on detection of 60S subunits in focused ion beam-milled lamellae analyzed in a large dataset.

(a) Histogram showing the percentage of increase of 60S detection in montages processed using Unbend, compared to Unblur. (b) Scatterplot of the number of detected 60S per exposure in a representative montage that did not show a substantial increase of detection after processing with Unbend, compared to Unblur. (c) Similar to panel (b), but for a representative montage with a more substantial increase of detected targets after processing with Unbend, compared to Unblur.