AP SH - Alignment - multi-reference, exhaustive rotation & shift ||*

PURPOSE

Compares a series of experimental images with a series of reference images. For each experimental image, it finds the in-plane Euler rotation angle, and X, Y translational shifts which align the image with the most-similar reference image. Exhaustively checks all requested rotations and shifts. Can restrict angular range of projections. Can restrict checking of mirror image.
(See align_overview.html for comparison of 'AP' operations.)

SEE ALSO

VO EA	[Vector Operation - Create Evenly Spaced Angles Document file]
VO MD	[Vector Operation - angular Document file from 'AP MD' output]
AP REF	[Alignment - multi-reference, rotation & shift ||*]
OR MQ	[ORientation search - 2D, rotation & shift, uses polar coords., checks mirror ||]
OR NQ	[ORientation search - 2D, rotation & shift, uses polar coords. ||]

USAGE

.OPERATION: AP SH

.ENTER TEMPLATE FOR REFERENCE IMAGES: REF***
[Give the template for the name of the existing file series of 2D reference images (typically projections).]

.ENTER FILE NUMBERS OR SELECTION DOC. FILE NAME: SELECTREF
[Enter numbers of reference files. The file numbers can also be read from a selection document file where file numbers are contained in the first register (not the keys).]

.TRANSLATION SEARCH RANGE, STEP SIZE: 6,2
[The search for translation parameters will be restricted to +/- search range, performed every "step size" pixel.
Restrictions:
1. Search range + last ring <=NSAM/2-2
2. Search range has to be divisible by step size.]
Speed will depend on square of the number of posistions searched.] Use of 'step size' greater than one can speed up alignment determination with minimal effect on final reconstruction resolution. ]

.FIRST, LAST RING, RING STEP & RAY STEP: 5,15,1,1
[The search for rotational alignment will be restricted to pixels with radii in the specified range (here: 5-15), performed every 'ring step' radius and on every 'ray step' radial ray.
Restrictions on 'ray' search, every: 1,2,4,8,16 'th radial ray can be included in search.
Use of 'ring step' and 'ray step' greater than one can speed up alignment determination on large images with minimal effect on final reconstruction resolution. ]

.REFERENCE IMAGES ANGLES DOCUMENT FILE: Refangles
[Enter the name of the angular document file containing Eulerian angles of reference images (projections): psi, theta, phi.]

.ENTER TEMPLATE FOR IMAGE SERIES TO BE ALIGNED: DAT***
[Give the template name of the existing file series of experimental images. These images will be checked for alignment versus the reference images.]

.ENTER FILE NUMBERS OR SELECTION DOC. FILE NAME: 1-2100
[Enter numbers of experimental files. The file numbers can also be read from a selection document file where file numbers are contained in the first register (not the keys).]

.EXPERIMENTAL IMAGES ALIGNMENT DOCUMENT FILE: angles001
[Optional input file. If '*' is given then this operation is similar to old 'AP MQ'. If you desire to restrict the range of angular search for projections then this file is necessary. It must contain the current Eulerian angles of experimental images (projections: psi, theta, phi) and optionally the current inplane rotation, shifts and other alignment parameters. The output files from 'AP SH' and 'AP REF' contain this info.]

.RANGE OF PROJECTION ANGLE SEARCH & ANGLE CHANGE THRESHOLD: 20.0, 14.0
[Experimental images will be compared with only these reference images whose normal is within specified range (in degrees). If a 0.0 is input, then there is NO restriction on which of the projections are compared. The "angle change threshold" is only used to report what percentage of the rotational changes exceed this specified threshold. This value can later be used to halt the iterations. The value is placed in a comment key at the end of the operations output file. It is not used for any other purpose.]

.CHECK MIRRORED POSITIONS (0=NOCHECK / 1=CHECK)?: 1
[Optional check of the mirrored reference image. By using this check and only providing reference images from one hemisphere of projection directions speed can be doubled.]

.OUTPUT ALIGNMENT DOCUMENT FILE: PARM101
[This is the only output produced by this operation. (Appends to existing output file of same name). It contains 15 register columns:

1. Eulerian angle (psi) of nearest reference image.
When no matching projection was found within the angular range specified, this column will contain the experimental image's previous Eulerian angle (if any) or 0.0.

2. Eulerian angle (theta) of nearest reference image.
When no matching projection was found within the angular range specified, this column will contain the experimental image's previous Eulerian angle (if any) or 0.0.

3. Eulerian angle (phi) of nearest reference image.
When no matching projection was found within the angular range specified, this column will contain the experimental image's previous Eulerian angle (if any) or 0.0.

4. Number of the most similar reference projection.
When no matching projection was found within the angular range specified, this column will contain 0.

5. Experimental projection number.

6. Cumulative In-plane rotation angle (psi).

To use in 3D reconstruction programs invert the sign. This is the sum of any rotation from the 'experimental images align. document file' and the current rotation.

7. Cumulative X shift
This is the sum of any shift from the 'experimental images align. document file' and any current shift.

8. Cumulative Y shift
This is the sum of any shift from the 'experimental images align. document file' and any current shift.

9. Number of projections searched.
Number of projections searched can vary when an angular restriction on search is used.

10. Angular change for projection.
Angular difference between previous and current projection. This will be -1.0 if the previous projection angles was not specified.

11. Not-normalized alignment correlation coefficient.
Can be used as a similarity measure.

Following values are seldom used by existing procedures:

12. Current In-plane rotation angle (psi).
This is the rotation necessary to align the experimental image with the current reference projection.

13. Current X shift
This is the X shift necessary to align the experimental image with the current referenceprojection.

14. Current Y shift
This is the Y shift necessary to align the experimental image with the current reference projection.

15. Current Mirroring
If mirroring was necessary to align the experimental image with the reference projection in use, this value is negative.

NOTES

1. In 3D space the projection with the direction: (psi, theta, phi) has its mirrored (around X-axis) counterpart in the direction:
   (-psi, 180-theta, phi+180).
   To save time, the program takes this into account, and each data projection is compared with the reference projection and its mirrored version at the same time. Thus, only half of the total number of reference projections are required; namely, only those with 0<theta<90.
   If the best match was with the mirrored reference projection, then the number stored in the 15th column of the document file is negative.
   

2. Images need not have power-of-two dimensions.

3. The reference projections (of the existing structure) can be created using 'VO EA' and 'PJ 3Q' operations. 'VO EA' creates an angular document file with quasi-evenly spaced projection directions and 'PJ 3Q' creates projections of the volume according to this doc file.

4. Alignment parameters (angle and translation included in columns 6-8 of the output document file) can be used with operation 'RT SQ' to align images.

5. Alignment parameters can be used as input to further 'AP SH' or 'AP REF' operations during refinement.

6. This operation parallelized for use with MPI.

7. Sequence of steps in the alignment using this operation:
   Load gallery of reference images created by projection of the reference volume.
   Extract radial rings from a window of each reference image, converting image to a polar representation.
   Take fourier transform of the ring data and weight the data corresponding to length and radius.
   Load a sample image.
   Extract radial rings from a window of sample image, coverting image to a polar representation.
   Take Fourier transform of the ring data and weight the data corresponding to length and radius.
   Perform a cross correlation in Fourier space of the reference and sample data.
   Find location of highest peak from cross correlation and map it to a rotation angle for the sample image.
   Repeat for all requested X & Y shifts of the sample image. You now have sample shift and rotation.
   Repeat for next sample image.
   

SUBROUTINES

APMASTER, MRQLI_PS, MRQLI_SS, APRINGS, NORMASC, NORMASS, ALRQ_MS, CROSRNG_MS, CROSRNG_E, FRNGS, AP_END, AP_STAT, RINGWE, APPLYWS, PARABLD, AP_GETANGA, AP_GETDATS, AP_GETDAT

CALLER

UTIL4