Model Evaluation

Access: CP::3D Model::Evaluation (Tab)

A 3D model reconstruction can be evaluated (though may not necessarily be validated) by a set of simple matrices:

1. Model Projection : this function generates model re-projections according to individual particle alignment parameters, then builds a stack interleaving the model projection and the raw particle image for direct comparison.
2. Euler Distribution : 2D-plot of the Euler-angle distribution from an aligned particle stack.
3. Alignment Statistics : a simple chart-plot showing the distribution of particle alignment shift and image-model correlation score.
4. Fourier Shell Corr. : the conventional Fourier Shell Correlation statistics.

Tilt Validation

More objectively and reliably, the correctness and handedness of a model reconstruction can be validated via particle tilt-pairs when such data is available.  In fact, in every single-particle EM project, it is always recommended to collect at least a few hundred tilted particle-pairs for model cross-validation.  As an example, assume that a stack of 6,000 particles come from single-exposure data acquisition.  In addition, there are 1,000 pairs (at 60-degree tilt in between) from double-exposure data acquisition.  Then, in PARTICLE, the validation procedure proceeds as follows:

1. Combine all the particles into one stack in the order of: 6,000 particles from single-exposure, 1,000 particles in the tilt-pair from the first exposure (named the Base-set), followed by the other 1,000 particles in the tilt-pair from the second exposure (named the Tilt-set).  Totally there are 8,000 particles in the stack.
2. Apply single-particle data analysis to the 8,000-particle stack: particle classification, model reconstruction and refinement, regarding each particle as independent image data.  In theory, for a correct model reconstruction and sufficient number of tilt-pairs, when the Base-set particles are all oriented in the same way (e.g., to the North-pole), the Tilt-set particles should scatter in a circle at the latitude corresponding to the tilt angle.
3. Operationally, go to the 3D Model::Validation::Tilt Validation group, define the starting particle ID in the Base-set (6001) and the Tilt-set (7001), the number of particles in the validation set (1000), and the nominal reading of the tilt geometry (60.0) in the data collection.  Upon activating the Validate button, the distribution of the tilted particles will be displayed on the Euler sphere according to the established particle alignment.

For a correct model reconstruction, the majority of the data points should appear at (or close to) the latitude corresponding to the nominal tilt geometry.  When a large number of particles deviate from the standard latitude, either the alignment has not converged, or the model correctness is in question.

Data "Purification"

Following the above validation procedure, particle pairs with substantial discrepancy in their relative orientation from the experimental tilt must have been miss-aligned (in one or both particle images), therefore they should be removed from the 3D reconstruction.  For a user-defined Tolerance of deviation, activating the Purify button will highlight the accepted particle pairs in the stack editor, from which a better density model can be reconstructed.