Figure 2:

Common Lines in cryo-EM. The left most images $I_i$ and $I_j$ are examples of projections of a molecule density $𝒳$; each projection is obtained from a different direction. At the center, are the Fourier transforms ${\hat{I}}_i$ and ${\hat{I}}_j$ of those images, overlaid with radial lines. The lower right sub-figure is a visualization of the two slices of the 3-D Fourier transform of the 3-D density $𝒳$, corresponding to ${\hat{I}}_i$ and ${\hat{I}}_j$; the two slices intersect each other, so that there is a line in ${\hat{I}}_i$ that is identical to a line in ${\hat{I}}_j$ (assuming no noise). Indeed, the point $\left(x_{ij},y_{ij}\right)$ which lies along this common line in ${\hat{I}}_i$ is identical to the point $\left(x_{ji},y_{ji}\right)$ which lies along this common line in ${\hat{I}}_j$. A more detailed discussion of common lines is available, for example, in [8, 9, 10, 11]