Boulder Laboratory for 3-Dimensional Electron Microscopy of Cells
XFSIMPLEX(1) XFSIMPLEX(1)
NAME
xfsimplex - Searches for best transformation between two images
SYNOPSIS
xfsimplex
DESCRIPTION
This program searches for the best general linear transform between
a pair of images by varying either the six formal parameters of the
transform, the six "semi-natural" parameters underlying such a
transform, or restricted subsets of those semi-natural parameters.
These semi-natural parameters are, in the order in which the program
will consider them:
Delta X
Delta Y
Global rotation (average rotation of X & Y axes)
Global magnification (average stretch of X & Y axes)
Difference between stretch along Y- & X-axis
Difference between rotation of Y- & X-axis
In the fifth line of input, one enters either zero to search for
formal parameters, or a number specifying how many of the natural
parameters are to be varied. If one selects 2, only Delta X and
Delta Y will be varied; if one selects 4, global rotation and
magnification will be varied also. At the end, the program outputs a
six-parameter transformation (the 2x2 A matrix and DX and DY) in the
standard format.
Because the search method used by this program works iteratively from
a given starting point, it is unlikely to find the proper alignment
if it requires a large displacement. To overcome this problem,
the program can be given an initial transformation to work from.
This allows a large displacement to be found by cross-correlation and
passed to this program.
To find the best fit between images, the search can optimize either
a simple point-by-point difference between the images, or a measure
of the distance between points of similar intensities in the
images. The resulting transformation is applied to the second image
to align it to the first.
The search uses a so-called simplex minimization routine which starts
searching with an initial step size and refines the step size near a
minimum. It terminates the minimization when either 1) the most
recent points under consideration gave difference measures all
within a certain fractional tolerance of the point with the minimum
measure; or 2) the most recent points had transformation parameters
all within a certain tolerance of the point with the minimum measure.
The latter tolerances are expressed as fractions of the following
basic step sizes: 1 for delta X and Y; 0.025 for the 4 parameters of
the transformation matrix, if using formal parameters; or 2 degrees
for global rotation and differences between X and Y rotations, and
0.025 for global magnification and difference between X and Y
magnifications, if using semi-natural parameters.
By default, the program will perform an initial minimization with
a coarse tolerance for termination, then it will restart the
minimization at the best point, and terminate with a finer tolerance.
If the overall alignment method involves two stages, coarse and
fine, then you should omit the initial minimization by specifying
tolerances of zero for it.
At the end of the search, the program outputs the number of iterations,
the minimum difference/distance value found, and the transformation
parameters. If semi-natural parameters were searched for, first those
parameters are output, then the formal parameter matrix is output. The
difference measure is normalized to be the mean difference per pixel as a
multiple of the standard deviation of the first image. The distance measure
is expressed as the mean distance per comparison point.
The program prompts for all inputs, but all of the parameters have
defaults which may be selected with , or / (the values in [] below
and contained in [] in the prompts)
***lines 1-4
first image file
second image file
data file into which to place the best fitting transformation
name of file file with starting transformation, or Return if none
*** line 5 (6 values):
Fractional tolerances in the difference/distance measure and in the
transformation parameter values, to allow termination of final or
only minimization [.0005 and 0.02, or .001 and 0.04 for
images no bigger than 128 by 128]
Fractional tolerances in the difference/distance measure and in the
transformation parameter values, to allow termination of initial
minimization [.005 and 0.2]. Enter 0,0 to skip initial search.
Factor to apply to basic step sizes to get initial step sizes [2]
1 for trial-by-trial output, 2 for output of trials that yield new
minima only.
***line 6
0 for search on formal parameters, or # of natural parameters to
vary [0]
***lines 7-10
Fraction of images to ignore at edges [0.05]; or number of pixels
if the number entered is 1 or greater
float images to have same range (0) or same mean and S.D. (1), or
do not float images (-1) [1]
binning factor for reducing images in x and y [2]
use difference (0) or distance (1) measure [0]
If difference measure is chosen, one more line of input:
***line 11
1 to use bilinear interpolation during the search [0]
If distance measure is chosen, 5 more lines of input:
*** lines 11-14
distance to search to eliminate redundant points with similar
densities from comparison [default depends on image size after
reduction, if any: 0 for # of pixels < 240*180, 1 if # of pixels
between 240*180 and 480*360, 2 if # of pixels > 480*360
distance to search for matching densities [4 if reduce by 2, 5 if
not]
maximum density difference constituting a match [0.05]
Number of ranges of densities to make comparisons with [2]
*** line 15
lower and upper PERCENTILES for these ranges. The default is 0,8,92,
100 for small images. This means that the darkest 8% and brightest
8% of pixels will be used for comparison (minus ones eliminated
because of redundancy). The default depends on image size after
reduction, if any; the range is scaled from 8% down to 5% as image
size increases from 320*240 to 640*480
These defaults are based on limited experimentation. When the
distance measure is used, the defaults are set in an attempt to
limit the number of "points for comparison" to several thousand. If
there are more than about "5000 points for comparison", you should
depart from the defaults in order to reduce this number.
HISTORY
Written by David Mastronarde, 4/5/91 (adapted from XFSEARCH)