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AP MQ - Alignment Program - 3D projection / Multi reference alignment

(01/21/97)

PURPOSE

Calculate distances between projections in polar coordinates. Determine the three Eulerian angles and translation parameters. This operation forms the main part of the 3D Projection Alignment Method (see the example appended below).

SEE ALSO

VO EA [Even Angles docfile]
VO MD [angular docfile from AP MD/Q]
AP CA [classification alignment]
AP RA [rotational alignment]
AP SA [shift alignment]
AP SR [shift and rotational alignment]

USAGE

.OPERATION: AP MQ

.Enter template for 2-D reference image name: REF***
[Give the template name of the existing file series of 2D reference projections.]

.Selection doc FILE: : SELECTREF
[Enter selection document file name containing the numbers of the input images in the first column.]

.Expected size of the object: 25
[The search for translation parameters will be restricted to +/- (NSAM-object_size)/2. For expected object size => actual object size there will be no search for translation parameters.]

.FIRST AND LAST RING: 5,15
[Only rings with radii in the range 5-15 will be analyzed.]

.ENTER TEMPLATE FOR 2-D EXPERIMENTAL PROJECTIONS NAME: DAT***
[Give the template name of the existing file series of 2D data projections.]

.Selection doc FILE: : SELECT
[Enter selection document file name containing the numbers of the input images in the first column.]

.DOCUMENT FILE NAME: ANGLES101
[This is the only output produced by this program. It contains 6 columns:

1. Number of the most similar reference projection.
When this number is larger than the number of reference projections, the most similar is the mirrored projection (see note 1).

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

3. Psi angle.
In-plane rotation angle determined.

4. X-shift.
X translation determined.

5. Y-shift.
Y translation determined.

6. Experimental projection number.]

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 first column of the document file is equal to the number of corresponding mirrored reference projection increased by the largest reference projection number (see included batch program).

  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 commands. 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. The output document file created by 'AP MQ' can be converted to the angular document file using 'VO MD' command. Please note that in this case the angular document file created by VO EA is required.

  5. Alignment parameters (angle and translation included in columns 3-5 of the output document file) can be used in command RT SQ to align images.

  6. An example of the Spider batch program which can be used to produce an angular document file from the output document file of this command is included in the manual chapter for the command 'VO MD'.

  7. Implemented by: Paul Penczek.

SUBROUTINES

MRQLI, MRQLI_P, CROSRNG_M, CROSRNG_D, CROSRMG_D, ALRQ_M, FOURING, FOURING, ALPRBS, PRB1D, FFTR_D, FFTC_D, ANGMR, NORMAS, LOG2_P

CALLER

UTIL4
Example of the Spider batch program implementing 3D alignment of projections
procedure:

;b11.alq

;rotate and shift images according to the parameters from AP MQ alignment

md
vb off
md
set mp
2
; Number of reference image is 87
x87=87
do lb1 i=1,900
x55=x0
ud ic,x55,x21,x22,x23,x24,x25,x26
docapmq
if(x21.gt.x87) goto lb2
rt sq
win/ser00x26
ali/sar00x26
x23
x24,x25
goto lb1
lb2
rt sq
win/ser00x26
_1
x23
x24,x25
mr
_1
ali/sar00x26
Y
lb1
en 

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