There exist many algorithms that, given a starting 3D structure, are able to refine that structure on the basis of a set of negative-stain or cryo-EM images, which are taken to be projections of the 3D object. Data sets typically range from 104 to 105 particle images, and refinements require tens to thousands of CPU-hours.

The refinement procedure is an iterative procedure that until convergence alternates between: 

  1. orientation assignment for the raw images based on the current guess of the 3D structure, typically by projecting the current structure in many different directions and 2D alignment between the raw images and the projected images;
  2. tomographic inversion that produces a new 3D structure from the raw images and their previously assigned orientations.


As the starting point for the refinement process, however, some sort of ab initio estimate of the 3D structure must be made. The initial structure can be obtained by running one of our orientation assignment algorithms on the class averages. Starting from a good initial model can also significantly reduce the number of iterations needed for convergence, therefore lead to substantial savings in computational running time.