Methodology of 2D particle alignment


Approaches to 2D particle alignment can be subdivided into several categories. The main division is created by the availability of a reference image, and the secondary division by the degree of variability within the data set, i.e., in how many orientations the particle is observed to lie in a micrograph.

Types of alignment problems:
  1. One or a small known number of reference images are known or can be easily approximated, and particle orientations, i.e. the way the particle sits on a surface, are well defined (with possible small variations). This case will be referred to as Reference-based alignment.

  2. An approximation of a reference image is known and there is only one particle orientation (with possible small variations). This case will be referred to as Refined Alignment with a reference.

  3. Reference images are not known, but the data set can in principle be divided into a known number of homogeneous classes. This case will be referred to as Multireference classification alignment.

  4. Reference images are not known, but the data set can in principle be divided into a known number of homogeneous classes. The particles can be centered. This case will be referred to as Rotationally invariant K-means alignment.

  5. Reference images are not known, and there is no clear groupings in the data set. This case will be referred to as Reference-free alignment.



Reference-based alignment

We assume that a limited number of reference images are known or that a good approximation of them are available. We expect all the particles to be noisy versions of the reference, with possible small variations. In this case the alignment problem becomes a pattern matching problem. We have to place every particle in an orientation in which it will best match the reference image. In the case of multiple reference images, in addition, we have to decide which reference is the most similar one. We must also try the mirror orientation since the particle may be flipped.
We use the cross-correlation coefficient to measure the similarity between a particle and a reference.

The ref-mult-ali.spi procedure implements reference based alignment with multiple references. In this procedure alignment is done using 'AP SHC' where search for rotation is integrated with the search for translation resulting highly accurate but somewhat slow alignment determination. The operation: AP REF could be used for poorer but faster alignment determination.

Advantages of reference-based alignment: Disadvantages of reference-based alignment:

Refined Alignment with a reference

We assume that a set of particles from one motif is available. Particles are not identical, but they share the same motif (e.g. they are all oriented on their same side on a surface). A reference image may be available or can be calculated from the sample images. The refi-ref-ali.spi procedure begins with calculation of the global average to approximate the reference, then aligns all the images using the 'AP SHC' operation, and calculates new average to obtain an improved reference. These steps are iterated a prescribed number of times.

Advantages of refined Alignment with a reference:

Disadvantages of refined Alignment with a reference:

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Multireference classification alignment

We assume that a very large data set is available. It comprises particles in a few distinct orientations. The data set is sufficiently large that at least some of the similar views occur in similar in-plane orientations, and so can be averaged. Thus, if we can approximately center the particles, the subsequent classification step should reveal some of the classes. These classes are used as reference images in the next multireference alignment step, classification is repeated, and new classes are formed. This procedure is iterated until stable classes are obtained.

Such a multireference classification alignment is sometimes called alignment through classification. This name reflects the idea that alignment is done separately within groups produced by the classification step.

The ref-mul-class-ali.spi procedure implements multireference alignment using 'AP SH' operation to do the alignment. This operation employs exhaustive search to find rotation and translation simultaneously. In principle it should be more accurate than using 'AP REF', but it is much slower (particularly for large number of classes). This program uses the additional procedure: centr.spi

Since multireference alignment is a general idea rather than a detailed algorithm, ref-mul-class-ali.spi constitutes a particular implementation. It should be considered a blueprint upon which one can build one's own procedure optimized for the particular data set.

Advantages of multireference classification alignment:

Disadvantages of multireference classification alignment:

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Rotationally invariant K-means Alignment

We assume that the particles were centered and we can divide the data set into a specified number of orientation classes. In this case, operation 'AP CA' will perform classification and alignment. For each particle the rotation angle as well as the group assignment will be found. The procedure: rotkm-ali.spi demonstrates how to use 'AP CA' and how to calculate group averages.

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Reference-free alignment

The rationale of the reference-free alignment is explained in the Introduction to Reference-Free Alignment. The procedure will seek such orientations of all the particles in the data set that all the possible pairs of images from this set are in the 'best' relative orientation as determined by the maximum of the CCF.

The reference-free alignment procedures were designed for very noisy data, for particles in many different orientations, and in general for cases in which a reference image is unknown or in which its usage could result in a bias and incorrect results. There are three basic operations in SPIDER that implement this strategy:
'AP SA' is a shift alignment, 'AP RA' is a rotational alignment, and 'AP SR' is a combined shift and rotational alignment.

In addition, 'AP CA' performs both classification and rotational alignment for pre-centered data. Unlike previous procedures none of these procedures checks mirrored orientations; thus, any mirror-related views will appear as two different orientations. All the alignment operations can be either used separately or as a part of longer, more elaborate alignment schemes.

The procedure: ref-free-apra-ali.spi uses 'AP RA' to rotationally align an image series and applies parameters stored by the operation in a document file to rotate all the particles. Subsequently, aligned articles are subjected to PCA and classified using hierarchical classification .

The procedure: ref-free-apsara-ali.spi alternates between 'AP SA' and 'AP RA' to align an image series both translationally and rotationally.

The procedure: ref-free-apsr-ali.spi uses operation 'AP SR' to align an image series and applies parameters stored in a document file to rotate and shift all the particles. Subsequently, aligned particles are subjected to PCA and classified using Hierarchical Classification.

Another approach to alignment uses self-correlation functions. See 'PO', 'CC P', 'AC S', 'AC NS', 'AC MSS', 'EP TM', and 'CC MS' for info on usefull operations.

Advantages of reference-free alignment:

Disadvantages of reference-free alignment:

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Source: align.html     Last update: 21 Mar 2012    
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