Fast and automatic identification of particle tilt pairs based on Delaunay triangulation

Random conical tilt (RCT) and orthogonal tilt reconstruction (OTR) are two remarkable methods for reconstructing the three-dimensional structure of macromolecules at low resolution. These techniques use two images at two different sample tilts. One of the most demanding steps in these methods at the image processing level is to identify corresponding particles on both micrographs, and manual or semiautomatic matching methods are usually used. Here we present an approach to solve this bottleneck with a fully automatic method for assigning particle tilt pairs. This new algorithm behaves correctly with a variety of samples, covering the range from small to large macromolecules and from sparse to densely populated fields of view. It is also more rapid than previous approaches. The roots of the method lie in a Delaunay triangulation of the set of independently picked coordinates on both the untilted and tilted micrographs. These triangulations are then used to search an affine transformation between the untilted and tilted triangles. The affine transformation that maximizes the number of correspondences between the two micrographs defines the coordinate matching.