Fig. 3.

Extraction of helix coordinates from the cross-correlation map. (A) Position mapping of helix traces into micrograph by combining tile rotation θ, shift Δ and cc-score. (B) Histogram of correlation map values contains predominantly low random correlations and some high correlation values from helices. The integral of the histogram bins is normalized to 1. The histogram can be fit by an exponential distribution (red line) corresponding to the background of low correlations. The α-threshold can be used as a cutoff value (green line) to separate the tail (green bins) from the background (grey bins). Pixel values beyond the α-threshold correspond to helical traces (right). (C) Binarized map is skeletonized to one-pixel wide traces for further processing. (D) Areas of overlapping traces are found by branch point detection (dashed circles) and erased. (E) Traces shorter than the minimum helix length (dashed circles and blue) are excluded resulting in effective contamination removal. (F) Remaining traces are extracted and fitted by polynomials to present helical traces in coordinates. Persistence length for traces is computed. (G) Histogram of persistence lengths (log scale) from helix population of entire micrograph set. Determination of median enables pruning of highly bent outliers for helices that have persistence lengths of two standard deviations (computed as median absolute deviation) below the mean.