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 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-correlation coefficient, 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 or maximum correlation 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. If correlation coefficients are used, then the measure of difference being minimized is one minus the correlation coefficient. The distance measure is expressed as the mean distance per comparison point. 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 -): -aimage 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 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 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 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 OR -UseTransformLine Integer Line number of initial transform in file, numbered from 0 (default 0) -sections OR -SectionsToUse Two integers Sections to use from the first and second file (default 0,0) -variables 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 OR -LimitsOnSearch Multiple floats Limits for each of the variables being searched. Each number entered specifies the maximum amount that the respective variable can change from its initial value. Enter a 0 to avoid limiting a parameter. If the search is being done on formal parameters, then only the first two (shift in X and Y) can be limited, 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 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 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 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 OR -BinningToApply Integer Binning to apply to the images. The default is 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 frequency 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. -rad1 OR -FilterRadius1 Floating point 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 FilterSigma2. Spatial frequency units range from 0 to 0.5. Use FilterSigma1 instead of this entry for more predictable attenuation of low frequencies. -rad2 OR -FilterRadius2 Floating point 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 FilterSigma2. -sig2 OR -FilterSigma2 Floating point Sigma value for the Gaussian rolloff below and above the cutoff frequencies specified by FilterRadius1 and FilterRadius2 -after OR -FilterAfterBinning Apply the Fourier filter after binning data. This will be much faster, but it may introduce aliased noise from the higher frequencies in the original data. The radius and sigma values represent frequencies in the binned image, not the original image. The default is to filter before binning, in which case the high frequencies can be removed before binning. -sobel OR -SobelFilter Apply edge-detecting Sobel filter to both images. This filter will be applied after binning and filtering if any. -float 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 intensities alone. Only pixels within the range being analyzed will be considered when determining the scaling. The default is 1. -ccc OR -CorrelationCoefficient Compute the standard cross-correlation coefficient instead of difference between images. The difference measure that is minimized 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 OR -LocalPatchSize Integer Size of square subareas (patches) within which to compute a measure 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 actually available for comparison within each patch. If image difference is being computed, the measure will be the standard deviation of the difference; otherwise the correlation coefficient 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 frequency 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 OR -LinearInterpolation Use linear interpolation instead of nearest pixel interpolation when computing image differences or correlation coefficients. -distance OR -DistanceMeasure Use distance instead of difference or correlation measure -near 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 OR -RadiusToSearch Floating point Radius to search for matching pixels when using the distance measure. The default is 4 if binning by 2, or 5 if not. -density 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 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 OR -CoarseTolerances Two floats Fractional tolerances in difference and parameters for the initial search. Enter 0,0 to skip the initial search. The default values are 0.005 and 0.2 of the basic step size. -final 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 OR -StepSizeFactor Floating point Factor to multiply basic step size by to get initial step size. The default is 2. -trace OR -TraceOutput Integer 1 for output at each step, 2 for output at new minima -param OR -ParameterFile Parameter file Read parameter entries as keyword-value pairs from a parameter file. -help OR -usage Print help output -StandardInput Read parameter entries from standard input. A subset of entries can still be made by running the program interactively. 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