Estimate Shifts w/ Symmetry#1397
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This PR incorporates the multiple common-lines between images of symmetric molecules into the shift estimation algorithm.
Specifically for each pair of images, instead of generating a single shift equation using the common-line induced by the estimated rotations Ri and Rj, we generate a set of shift equations using the multiple common-lines induced by the estimate Ri and the estimates g @ Rj, for each g in the symmetry group associated with the symmetric molecule.
For simulated data (with and without noise) incorporating the symmetry reduced shift estimation by about 5% on average when using the projected relative error which is used in the matlab code and in the associated publication. This error accounts for a global 3d translational ambiguity that is inherent in the solution.
More dramatically, when we make a direct euclidean distance comparison (ie. not accounting for the global translational ambiguity) between the estimated shifts and the ground truth offsets of the simulation, we get on average a 50% reduction in error. This is because in the case of higher order symmetries (Dn, T, O, I) the global translation ambiguity is constrained away by the additional common-line information. This mean we are getting shift estimates that correspond to a volume whose center is more aligned to the volume which produced the simulated images.
There are 3 main additions in this PR:
There is still some work to do regarding the max memory check that occurs on larger problems.