RT SQ - Rotate and Shift - image, Quadratic interpolation ||

PURPOSE

Changes the scale, rotates, and shifts image circularly. Rotates counter-clockwise around the center (NSAM/2 + 1, NROW/2 + 1). (Negative angles = clockwise. Note that the terms "clockwise" and "counter-clockwise" refer to the mirrored x-y system used for image display).

SEE ALSO

RT	[RoTate - image or volume, use average as background]
RT B	[RoTate - image or volume, supply Background]
RT C	[RoTate - image, around arbitrary center, for small files]
RT M	[RoTate - image or volume, use minimum as background]

USAGE

.OPERATION: RT SQ

.INPUT FILE NAME OR TEMPLATE (E.G. STK@****): INSTACK03@
[Enter the name of the file to be rotated. This file can be a whole stack (ending in @), alternatively it can be a template for a set of stacked images (e.g stack3@******).]

If the input file is a whole stack the following questions appear:

.OUTPUT FILE: STACK03@
[Enter the name of the file where the rotated and shifted images are to be placed. This output file will be a whole stack.]

.ENTER REG. NUMBERS FOR ANGLE, SCALE, X, & Y SHIFT: 1 2 3 4
[Enter the column positions in the document file where these parameters are stored. If scale register is zero the scale defaults to 1.0.]

.ANGLE/SCALE DOCUMENT FILE: ANGDOC
[Name of document file that contains angle in degrees, scale factor (>0), X, and Y shifts.

If the input file is a set of stacked images the following questions appear:

.ENTER FILE NUMBERS OR SELECTION DOC. FILE NAME: select_03
[Enter the file numbers to be substituted into the file name template or name of a selection document file that contains the file numbers in the first register.]

.ENTER REG. NUMBERS FOR ANGLE, SCALE, X, & Y SHIFT: 6,0,7,8
[Enter the column positions in the document file where these parameters are stored. If scale register is zero the scale defaults to 1.0.]

.ANGLE/SCALE DOCUMENT FILE: ANGDOC
[Name of document file that contains angle in degrees, scale factor (>0), X, and Y shifts.

.OUTPUT FILE: STACK03@
[Enter the name of the stack file where the rotated and shifted images are to be placed. This stack will contain the whole set of images.

If the input file is a single image the following questions appear:

.OUTPUT FILE: H_IMG048
[Enter the name of the file where the rotated and shifted image is to be placed.]

.ROTATION ANGLE, SCALE: 90.0, .75
[Enter the rotation angle in degrees, and scale factor (>0). Default scale is set to 1.0 (see Note 2).]

.X, Y SHIFT : 12.34, -1.987
[Enter the X and Y shift values.]

NOTES

1. The whole task is done using only one interpolation of the input image; thus, the problem of accumulation of interpolation errors during alignment can be entirely overcome.

2. A change of scale will not change the image dimensions. All the parameters agree with the output of the marker program (operation 'MK').

3. The input file may be three-dimensional. In this case, each of the slices is separately rotated and shifted with respect to the z-axis, and stored in the output file, which will be created with the same dimensions.

4. The dimensions of the image need not be powers of two, and shifts can be any real numbers.

5. The accuracy of interpolation is much higher than that of the bilinear interpolation used in the 'RT' operation, but it is lower than the accuracy of bi-spline interpolation. In particular, the derivatives of the interpolated image are not continuous. The speed, however, is much higher than bi-spline interpolation.

6. Memory requirements: NSAM*NROW+NSAM

7. Since quadratic interpolation is used, it is possible for the output image min. & max. intensities to be outside the range of the input image.

8. Implemented by: P. Penczek.

SUBROUTINES

ROTQS, ROT2QS, QUADRI, GETDOCDAT

CALLER

UTIL3