```xfsimplex(1)                General Commands Manual               xfsimplex(1)

NAME
xfsimplex - Searches for best transformation between two images

SYNOPSIS
xfsimplex  [options]  input_file_a  input_file_b  output_file

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 trans-
form, 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 With the -variables
option, 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, the cross-correla-
tion coefficient, or a measure of the distance between points of simi-
lar 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 cer-
tain fractional tolerance of the point with the minimum measure; or 2)
the most recent points had transformation parameters all within a cer-
tain tolerance of the point with the minimum measure. The latter toler-
ances 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 magni-
fication 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 or maximum correlation value found, and
the transformation parameters.  If semi-natural parameters were
searched for, first those parameters are output, then the formal param-
eter 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.  If correlation coefficients are used, then the mea-
sure of difference being minimized is one minus the correlation coeffi-
cient.  The distance measure is expressed as the mean distance per com-
parison point.

OPTIONS
Xfsimplex uses the PIP package for input (see the manual page for
pip) and can still take sequential input interactively, to maintain
compatibility with old command scripts.  The following options can be
specified either as command line arguments (with the -) or one per line
in a command file or parameter file (without the -).  Options can be
abbreviated to unique letters; the currently valid abbreviations for
short names are shown in parentheses.

-aimage (-ai) OR -AImageFile   File name
Input image file with reference image to be aligned to.  If this
option is not entered, the first non-option argument will be
used for this input file.

-bimage (-bim) OR -BImageFile       File name
Name of image file with image to align to reference.  If this
option is not entered, the second non-option argument will be
used for this input file.

-output (-o) OR -OutputFile    File name
Output file for transformation.  If this option is not entered,
the third non-option argument will be used for this output file.

-initial (-i) OR -InitialTransformFile   File name
Input file with transformation to start search with.  The final
reported transformation will include the initial one rather than
being incremental to it.

-useline (-use) OR -UseTransformLine     Integer
Line number of initial transform in file, numbered from 0
(default 0)

-sections (-se) OR -SectionsToUse   Two integers
Sections to use from the first and second file (default 0,0)

-variables (-v) OR -VariablesToSearch    Integer
Number of semi-natural variables to search, or 0 to search for
formal parameters.  See above for the meaning and order of the
variables selected by this option.

-limits (-lim) OR -LimitsOnSearch   Multiple floats
Limits for each of the variables being searched.  Each number
entered specifies the maximum amount that the respective vari-
able can change from its initial value.  Enter a 0 to avoid lim-
iting a parameter.  If the search is being done on formal param-
eters, then only the first two (shift in X and Y) can be lim-
ited, so only 1 or 2 values can be entered.  If the search is on
semi-natural parameters, then you can enter more or fewer values
than the number of variables being searched.  Extra values are
ignored, missing values are assumed to be zero.

-edge (-e) OR -EdgeToIgnore    Floating point
Fraction or number of pixels to ignore on edges of image.  Enter
a value less than 0.5 for a fraction, or a value greater than 1
for a number of pixels.  The default is 0.05.

-xminmax (-x) OR -XMinAndMax   Two integers
Starting and ending coordinates to analyze in X (numbered from
1).  This entry overrides the X coordinates implied by the -edge
entry or default.

-yminmax (-y) OR -YMinAndMax   Two integers
Starting and ending coordinates to analyze in Y (numbered from
1).  This entry overrides the Y coordinates implied by the -edge
entry or default.

-binning (-bin) OR -BinningToApply       Integer
Binning to apply to the images.  The default is 2.

-antialias (-an) OR -AntialiasFilter     Integer
Type of antialiasing filter to use for image reduction instead
of binning.  Antialiasing becomes important when the images are
highly reduced in size.  Ordinary binning reduces aliasing, but
not as much as these filters do.  This option makes any filter-
ing be applied after the image reduction (thus it implies the
-after option).  As in Newstack, the available types here
are:
2: Blackman - fast but not as good at antialiasing as slower
filters
3: Triangle - fast but smooths more than Blackman
4: Mitchell - good at antialiasing, smooths a bit
5: Lanczos 2 lobes - good at antialiasing, less smoothing
than Mitchell
6: Lanczos 3 lobes - slower, even less smoothing but more
risk of ringing
-1: Use the default filter, currently Lanczos 2

-sig1 OR -FilterSigma1    Floating point
Sigma value to filter low frequencies in both images with a
curve that is an inverted Gaussian.  This filter is 0 at 0 fre-
quency and decays up to 1 with the given sigma value.  However,
if a negative value of radius1 is entered, this filter will be
zero from 0 to |radius1| then decay up to 1.

Low spatial frequencies in both images will be attenuated by a
Gaussian curve that is 1 at this cutoff radius and falls off
below this radius with a standard deviation specified by Filter-
Sigma2.  Spatial frequency units range from 0 to 0.5.  Use Fil-
terSigma1 instead of this entry for more predictable attenuation
of low frequencies.

High spatial frequencies in both images will be attenuated by a
Gaussian curve that is 1 at this cutoff radius and falls off
above this radius with a standard deviation specified by Filter-
Sigma2.

-sig2 OR -FilterSigma2    Floating point
Sigma value for the Gaussian rolloff below and above the cutoff

-after (-af) OR -FilterAfterBinning
Apply the Fourier filter after binning data.  This will be much
faster, but it may introduce aliased noise from the higher fre-
quencies in the original data unless antialiased reduction is
used.  The radius and sigma values represent frequencies in the
binned image, not the original image.  If antialias reduction is
not used, the default is to filter before binning, in which case
the high frequencies can be removed before binning; if
antialiasing is used, the filtering always happens after reduc-
tion and this option is redundant.

-sobel (-so) OR -SobelFilter
Apply edge-detecting Sobel filter to both images.  This filter
will be applied after binning and filtering if any.

-float (-fl) OR -FloatOption   Integer
0 to float images to have the same range, 1 to float them to
have the same mean and standard deviation, or -1 to leave inten-
sities alone.  Only pixels within the range being analyzed will
be considered when determining the scaling.  The default is 1.

-ccc (-cc) OR -CorrelationCoefficient
Compute the standard cross-correlation coefficient instead of
difference between images.  The difference measure that is mini-
mized will be 1 minus the CCC, but the CCC itself is printed in
the trace and final output.  It takes < 5% more time to compute
the CCC.

-local (-lo) OR -LocalPatchSize     Integer
Size of square subareas (patches) within which to compute a mea-
sure of image difference, in pixels before binning, if any.  The
image will be divided into patches of this size and the measure
will be computed separately within each patch; then a weighted
average will be formed, weighted by the number of pixels actu-
ally available for comparison within each patch.  If image dif-
ference is being computed, the measure will be the standard
deviation of the difference; otherwise the correlation coeffi-
cient is computed.  Patches with less than half the full number
of pixels will be pooled with the nearest patches containing
enough pixels.  This option should prevent the need for low fre-
quency filtering, which would increase execution time by roughly
10%.  Patch sizes on the order of 1/20 to 1/10 of the image size
should be effective.

-linear (-lin) OR -LinearInterpolation
Use linear interpolation instead of nearest pixel interpolation
when computing image differences or correlation coefficients.

-distance (-di) OR -DistanceMeasure
Use distance instead of difference or correlation measure

-near (-n) OR -NearestDistance      Integer
Distance to search to eliminate redundant points, or 0 not to
search, when using the distance measure.  The default is 0 for #
of pixels < 240*180, 1 if # of pixels is between 240*180 and
480*360, 2 if # of pixels > 480*360.

Radius to search for matching pixels when using the distance
measure.  The default is 4 if binning by 2, or 5 if not.

-density (-de) OR -DensityDifference     Floating point
Maximum density difference that constitutes a match when using
the distance measure, as a fraction of the density range.  The
default is 0.05.

-percent (-pe) OR -PercentileRanges      Multiple floats
Lower and upper limits of percentile ranges to match.  The
default is to have two ranges, i.e., 0,8,92,100, for images less
than 320*240, scaling down to 5% ranges as image size increases
from 320*240 to 640*480.

-coarse (-co) OR -CoarseTolerances       Two floats
Fractional tolerances in difference and parameters for the ini-
tial search.  Enter 0,0 to skip the initial search.  The default
values are 0.005 and 0.2 of the basic step size.

-final (-fi) OR -FinalTolerances    Two floats
Fractional tolerances in difference and parameters for the final
or only search.  The default values are 0.0005 and 0.02 of the
basic step size, or 0.001 and 0.04 for images no bigger than 128
by 128.

-step (-st) OR -StepSizeFactor      Floating point
Factor to multiply basic step size by to get initial step size.
The default is 2.

-trace (-t) OR -TraceOutput    Integer
1 for output at each step, 2 for output at new minima

-param (-pa) OR -ParameterFile      Parameter file
Read parameter entries as keyword-value pairs from a parameter
file.

-help (-h) OR -usage
Print help output

-StandardInput
Read parameter entries from standard input.

INTERACTIVE INPUT
A subset of entries can still be made by running the program interac-
tively.  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

The distance measure has been little used and the defaults for it are
based on limited experimentation. These 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)
7/1/08: Converted to PIP, added search limits, filtering, CCC

BUGS
Email bug reports to mast at colorado dot edu.

IMOD                                4.10.18                       xfsimplex(1)
```