Fig. 3: Results of HAWKMAN analysis on experimental microtubule data from the Localisation Microscopy Challenge comparing SE and ME fitting.

The reconstructions for SE and ME fitting without HAWK are shown in a and b, respectively along with their equivalents c and d when HAWK is used. The results of HAWKMAN analysis are shown in the sharpening maps (e, f), the structure maps (g, h) and the confidence maps (i, j) for selected length scales. The SE reconstruction (a) shows substantial density-induced sharpening artefacts. The differences in structure between this reconstruction and the results of applying HAWK with SE fitting are highlighted by the sharpening map (e) shown at an example scale of 3 reconstruction pixels (60 nm using 20 nm size pixels). Substantial bias in the SE reconstruction where microtubules are in close proximity/crossing is highlighted in the structure map (g) even at a scale of 160 nm. Reliable regions in the reconstruction where both methods agree are highlighted in the confidence map (i), shown at the 100 nm scale. ME fitting (b) gives a more accurate reconstruction, however, as can be seen in (f, h, j) it still contains numerous artefacts. The confidence map (100 nm scale) (j) for this reconstruction shows a reduction in the severity of artefacts but some remain. The white arrows highlight some of the structure accurately reported (at this length scale) in the ME result (j) that were inaccurate in the SE case (i). A summary of the HAWKMAN results at all length scales is shown in the artefact scale maps (k, l) which indicate the maximum scale of artefacts at each area of the sample (colour indicates length scale in pixels (20–300 nm). Comparison of the SE (k) and ME (l) results shows that for ME fitting the maximum scale of artefacts is reduced in areas of high microtubule density. Scale bar 1 µm.