Fig. 1. Tilt series alignment, 3D reconstruction and 3D image analysis.

Fig. 2. Tilt geometry: (x, y, z): coordinate system fixed with respect to the microscope. z is the optical axis, A (the x–y-plane) is the image plane. (x′, y′, z′): coordinate system fixed with respect to the specimen. The direction of the tilt axis t is measured anticlockwise from the x-axis by the angle ψ, the tilt azimuth. The transformation from (x, y, z) to (x′, y′, z′) consists of a rotation by an angle θ about the tilt axis t, and an additional rotation (ψ′, θ′, ′) which defines the orientation of the specimen C with respect to the specimen holder B. Reprinted from (Winkler and Taylor, 2006), Copyright (2005), with permission from Elsevier B.V.

Fig. 3. Coarse alignment of an insect flight muscle sample. The inset (top right) shows the situation before alignment. Two images of a tilt series are superimposed, a fixed reference and a movable image that is being aligned. The images are displayed with two complementary colors. If the two images are brought into register, blending of the two colors produces a grayscale image in the ideal case. In practice, a perfect match cannot always be achieved, since two neighboring images of a tilt series are not identical, even when the foreshortening at different tilt angles is taken into account. In addition, if the estimated geometric parameters deviate from the true values, the images cannot be brought into register in general with translations and rotations alone over the whole field of view.

Fig. 4. Two sections of a tomogram of ice-embedded HIV virions. The sections are extracted at different z-coordinates and cut through the virions at different heights. For selection of the glycoprotein positions on the surface, the user scrolls through the map in z-direction. Selected positions at the current z-level are marked in yellow, previously selected ones below the current level in red, and above in green. After the selection is completed, an ellipsoidal surface is fitted to the measurements. The pink shaded areas represent cross-sections of the ellipsoid at the respective z-level.

Fig. 5. Rafts of actin crosslinked with α-actinin, formed on a lipid monolayer. Left, enlarged area of a micrograph; right, reassembled image after alignment, classification, and averaging. The motifs in this exercise consisted of one crossover of an actin filament in the center with the bound α-actinin molecules on either side. After aligning all motifs to the central actin filament, crosslinks on the left and right hand side of actin were classified separately (rectangular areas). The appropriate class averages for the left and right half-motifs were then recombined and the combined average mapped back to the original position (oval areas). The classification and recombination procedure restores crosslinks in the average with an accuracy of 60% when compared with the raw motif. With a different classification run (not shown here), where left and right halves combined formed the motif used for classification, the expectation would be a restoration accuracy of 36%, the actual value found was 30%.

Shell scripts and executables for marker-free alignment

Basic image manipulation programs (executables)

Layout for the native FFF image format