Job: Rebalance Orientations

At a Glance

Remove particles from over-represented viewing directions.


Rebalance Orientations sorts particles into two sets: ‘rebalanced’ and ‘excluded’. The rebalanced particle set will have a more uniform viewing direction distribution (as compared to the input particles) which can help improve downstream refinements.

Excluded particles are taken from over-populated viewing direction bins. Viewing direction bins are defined by a set of direction vectors on the unit sphere (generated via Fibonacci sampling). Each particle is sorted into the bin nearest to the particle’s viewing direction. Once the bins are populated, they are sorted by particle count and all bins with a population above the Kth percentile are deemed overpopulated. Each overpopulated bin has particles excluded until it reaches the population of the Kth percentile bin.

N.B., the Rebalance Orientations job is idempotent, in the sense that if two Rebalance Orientations jobs are run in sequence (with the same parameters), the second job will make no change to its inputs.



Particles to be rebalanced. These particles must have 3D pose estimates, and so should come from a 3D refinement such as Homogeneous or Non-Uniform Refinement.

Commonly Adjusted Parameters

Number of orientation bins

Particles will be grouped into this number of bins. When views are rebalanced, they are considered per-bin. Put another way, Rebalance Orientations does not consider a single view as overrepresented, but rather a bin of similar views.

In general we have found the default setting to be sufficient. If orientation bias is focused on a single, narrow region of orientation space, using more bins may focus Rebalance Orientations on only particles in that view.

Rebalance percentile

This number (between 0 and 100) sets the percentile above which bins are rebalanced.

Note that this parameter operates on bins, not particles. Put another way, setting this parameter to 80 will result in bins in the 80th percentile and higher (that is, bins with more particles in them than the bottom 80 percent) having particles removed until they have the same number as the 80th percentile. Note that setting this parameter to 80 does not mean that precisely 20% of particles would be removed by this operation; the number of particles removed depends on the orientation distribution of the particles.

Intra-bin exclusion criterion

Once a bin is marked as overrepresented, particles in that bin must be discarded. This parameter provides several choices of how particles are to be selected for exclusion.


Particles are selected at random and discarded until the bin is at the threshold.


Particles with the worst Normalized Cross Correlation score are removed. The Normalized Cross Correlation is calculated during particle picking and measures how well the particle image matches the template, blob, or ring used to select the particle.


Particles with the greatest error between the volume projection and the particle image, computed during upstream refinement, are removed. Note that if the volume is highly anisotropic due to orientation bias, the error value may be unreliable.


Particles with the lowest per-particle scale are discarded. Per-particle scale accounts for local variations in greyscale and is typically taken as a proxy for ice thickness, but would also be affected by overall particle quality and other factors. Note that if the volume is highly anisotropic due to orientation bias, the per-particle scale may be unreliable.


Particles with the greatest error between the 2D class average and the particle image are discarded. Note that this error value will capture a combination of pose error and residual error in the refinement of the class average itself. If relatively few classes were requested during 2D classification, good particles may have high error if their true pose is far from the nearest available class average.


Rebalanced particles

Particles that fell in bins which were below the threshold and particles that fell in overpopulated bins but were selected by the Intra-bin exclusion criterion are collected together in this output. They are otherwise unchanged from the input.

Excluded particles

Particles that fell in overpopulated bins and were excluded by the Intra-bin exclusion criterion are collected in this output. They are otherwise unchanged from the input.


Rebalance Orientations produces Viewing Direction Distribution plots from before and after the rebalancing operation is performed. These plots are simple heatmaps of particle viewing directions, explained more in the Common Plots guide page.

Rebalance Orientations also produces similar plots showing the bin locations and particle counts before and after the rebalancing operation.

Finally, a plot of the rebalancing operation itself is produced. Bins are arranged in increasing order of initial particle count. Bins with a number of particles less than or equal to the threshold are marked with a blue point. Bins with particles in excess of the threshold are represented with two points: a blue point at the threshold, and a red point indicating the number of particles removed from that bin.

Note that each position along the X-axis in this plot represents the number of particles in an individual bin, not the cumulative sum of particles in that number of bins.

Common Next Steps

Removal of overrepresented views may help reduce map anisotropy in some cases. However, the overall quality of the map may also be degraded when removing good information in any orientation. Thus, a potentially useful workflow involves using this job and a subsequent refinement to produce a more isotropic map, then using this map to repeat particle picking (e.g., using Create Templates and the Template Picker jobs, or in a neural-network particle picker such as TOPAZ) to attempt to find more of the rare views in the existing data.


  1. Campbell, M. G., Veesler, D., Cheng, A., Potter, C. S. & Carragher, B. 2.8 Å resolution reconstruction of the Thermoplasma acidophilum 20S proteasome using cryo-electron microscopy. eLife 4, e06380 (2015).

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