Fig 1.
(a) Schematic diagram of the segmentation algorithm. To illustrate better the algorithm procedure steps, intermediate results from an example image of the real data (described in Section 2.5) are also demonstrated: starting from the original image (b), a local multiscale ridge detection step is first applied (c), followed by a ridge selection or pruning step (e) to keep only those compatible with an initial (manual) contour (d, blue) from a reference slice, the latter is then deformed to detect the current membrane contour (f, g, red) through an active contour based model that is driven by the found compatible ridges. 3D membrane segmentation is obtained via propagation along the optical axis (Z axis). Additionally, an optional refinement step along the YZ and XZ slices is proposed to cope with cryo-TXM imaging limitations. Inset view (white frame in a) with the contours sequence obtained from the segmentation process in 5 iterations, from initial guess (blue) to the solution (red), driven by compatible ridges only (h, i), or by all detected ridges (j, k).
Fig 2.
(a) Digital phantom simulating 4 organelles. The tilt axis is marked in red and the tilting angles (±65°) for the projections are marked in purple lines; (b) reconstruction from simulated X-ray microscope data.
Fig 3.
Schematic drawing of the profile area (grey region) based on membrane profile.
Fig 4.
Schematic drawing of the cryo-TXM optical settings.
Fig 5.
(Top row) Examples of the two contour models: single shells (e.g. to mimic plasma membranes) of various thickness values (three leftmost) and double shells (e.g. to mimic nuclear membranes) of various thickness values as well as with the space between the two bilayers (three rightmost). (Bottom row) The corresponding images after convoluted with the PSF of the X-ray microscope at the TXM-U41 beamline of BESSY-II. The scale bar equals 40nm.
Fig 6.
(a) Reconstruction from simulated X-ray microscope data and overlaid with known contours from the ideal geometry; (b) left: XY slice overlaid with the segmentation, using the found compatible ridges only (green) or using all ridges (red); middle and right: YZ and XZ slices overlaid with segmentation results before (white) and after (red) the refinement step for the membrane of organelle 1; (c) reconstruction overlaid with the final segmentation.
Fig 7.
left: Grouped bar plot of average segmentation error and standard deviation, calculated as surface distance, from the results with compatible ridges only and with all ridges; right: ideal geometry of the phantom, Color-coded segmentation errors from the results with compatible ridges only and with all ridges.
Fig 8.
Average membrane profiles with variable thickness obtained for single shell (a) and double shell (b) phantoms. Plots of three different features of the profiles against the theoretical thickness for both models: FWHM (c, f), profile minima (d, g) and upper area (e, h).
Fig 9.
Average profiles for the phantom with thickness 15 nm, with variable μm.
G: Upper profile area with variable μ.
Fig 10.
A segmentation example for a local region in a control cell, using both the manual segmentation and our algorithm.
left: Segmentation contours overlaid on a 2D slice; middle: The 3D surface models obtained from both segmentations; right And the average plasma and nuclear membrane profiles, as well as their FWHM and upper area values.
Fig 11.
Results of different boundary detection algorithms to extract compatible edges on slice of a cell (from top to bottom): multi-scale ridge detection [24] we used, gradient magnitude, and Canny edge detection. (from left to right): Obtained contour (red curve) overlaid on the slice image, together with the initial contour (green curve), and a white frame indicating the zoomed in views on the next columns; All detected edges (grey curves) and those compatible ones (blue curves); Zoomed view of all detected edges (grey curves), compatible ones (blue curves), the initial contour (green curve) with its normal direction (green arrows), and the obtained contour (red curve); Same zoomed view with contours overlaid on the slice image. Same initial contour was used for all results from different boundary detection algorithms.
Table 1.
Parameters used for membrane segmentation.
Fig 12.
A: Membrane average profiles computed in local regions from 2 control and 2 incubated cells. Negative values indicate interior of the nucleus/cell; B: membrane surface models used for the 3D profiles computation (blue: plasma membranes; red: nuclear membranes); C: membrane average profiles computed in 2D for a single slice of C1.
Fig 13.
Top rows: Examples of control cells (C1, C2) and treated cells (T1, T2) of the original reconstruction and the segmentation as contour overlay in XY and XZ views: plasma membrane (blue), nuclear membrane (red) and other organelles (yellow). Rectangles indicate the local regions used for the plasma and nuclear membrane profile analysis shown in Fig 12. Bottom row: 3D surface view of the segmentation. The circular sub-cellular organelles (shown as yellow spheres) were segmented using a variant of the Circular Hough Transform [37].