tiltalign(1) General Commands Manual tiltalign(1)NAMEtiltalign - Solve for alignment of tilted views using fiducialsSYNOPSIStiltalignDESCRIPTIONThis program will solve for the displacements, rotations, tilts, and magnification differences relating a set of tilted views of an object. It uses a set of fiducial points that have been identified in a series of views. These input data are read from a model in which each fiducial point is a separate contour. This program has several notable features: 1) Any given fiducial point need not be present in every view. Thus, one can track each fiducial point only through the set of views in which it can be reliably identified, and one can even skip views in the middle of that set. 2) The program can solve for distortion (stretching) in the plane of the section. It does so with two additional variables: "dmag", an increment to the magnification along the X axis; and "skew", the dif- ference in rotation between the X and Y axis. If there is stretch in the plane of the sections, then in general the aligned images will backproject correctly only at one plane in Z. This solution thus includes a set of adjustment factors that can be passed to the Tilt program to correct for this effect. 3) It is possible to constrain several views to have the same unknown value of rotation, tilt angle, magnification, compression, or distor- tion. This can reduce the number of unknowns and can give more accu- rate overall solutions. 4) If the fiducial points are supposed to lie in one or two planes, then after the minimization procedure is complete, the program can ana- lyze the solved point positions and determine the slope of this plane. It uses this slope to estimate how to adjust tilt angles so as to make the planes be horizontal in a reconstruction. 5) The program can solve for a series of local alignments using subsets of the fiducial points. This can be useful when aligning a large area which does not behave uniformly during the tilt series. The local alignments can then be used to obtain a single large reconstruction whose resolution is as good as would be attained in a smaller volume. 6) The program can use a robust fitting method to give different weights to different modeled points based on their individual fitting errors. Points with the most extreme errors are eliminated from the fit, and ones with high but less extreme errors are down-weighted. This fitting provides a substitute for fixing many modeled point posi- tions based on their errors. 7) The program includes an option for cross-validation, which measures how well a solution can predict the positions of points that are left out of the fitting. The method is useful for optimizing the selection of parameters to be fit and avoiding overfitting with too many parame- ters.MappingofVariablesThe constraining of different views to have related values of some unknown variable is called "mapping"; it works differently for tilt than for other variables. For variables other than tilt, if two or more views are mapped to the same variable, then all of those views will have the same value. For tilt angle, if two views are mapped to the same tilt variable, then the DIFFERENCE between their tilt angles is constrained to be a constant equal to the difference between their initial tilt angles. So, if they have the same initial tilt angle, they will always have the same tilt; and if their initial tilt angles differ by 10, their tilt angles will always differ by 10. Mapping can be set up relatively easily with "automapping". When you select automapping, the program will map views in a group of adjacent views to the same variable, and it will determine a set of groups of a specified size. You control the mapping by specifying the default size of the groups. In addition, if some views need to be grouped differ- ently, you can specify one or more ranges of views to have different sized groups. With automapping, the program can also set up variables that change linearly from one group to the next, rather than being constrained to the same value for all views in a group. In other words, the values for all of the views in a group will be a linear combination of the same two actual variables (typically the first one in the group and the first one in the next group). This feature usually gives a solution with less error. The distinction between actual variables and combina- tions can be seen in the "Variable mappings" table. Actual variables would appear as, e.g., "tilt 15" and "tilt 25", while combinations of the two appear as "t 15+ 20". There are also linear combinations between a variable and a fixed value, which appear in the table as "t 70+fix". Currently, the linear mapping is available only with automap- ping, not with manually specified mappings. With automapping, the size of the groups will be adjusted dynamically for two variables, tilt angle and x-axis stretch, so that groups become smaller at higher tilt angles. This is done because it is easier to solve accurately for tilt angle at higher tilt, and because the solu- tion for x-axis stretch tends to change rapidly at high tilts. The group size that you specify for these variables will be the average size of the whole range of tilts. If this dynamic automapping gives problems with tilt angle, use mapping in blocks rather than linear map- ping to have stricter control over the mapping process. The dynamic automapping is used for both kinds of mapping of x-axis stretch because the mapping in blocks is the preferred method for grouping this vari- able. (Linear mapping does not always work properly.) The size of groups when automapping will also be adjusted to provide more grouping when some views have only one or two points. Specifi- cally, views with fewer than 3 points will not be counted toward the total number of views to be included in a group. This feature is most important with the local alignments described next, where there may be relatively few points in a local area.LocalAlignmentsThe program can embark on local alignments after obtaining the standard global solution with all of the fiducials. The program divides the image area, or the area occupied by fiducials, into a regular array of overlapping subareas. Fiducials whose X and Y coordinates fall within a subarea are included in the computations for that subarea. A subarea is expanded about its center, if necessary, to include a certain mini- mum number of fiducials. The program then seeks a solution for the subset of fiducials that is, for all variables, "incremental" to the global solution; that is, it solves for variables that are added to the parameters from the global solution. This method allows a dramatic reduction in the number of variables to be solved for, mostly because rotation and magnification can be mapped to a much smaller number of variables than in the global solution. The usual need for each view to have its own rotation and magnification variable is already accommo- dated in the global solution. One option in the local alignment is whether to solve for the X-Y-Z coordinates of the subset of fiducials, or to fix them at their values from the global solution. Solving for the coordinates may give a more accurate solution but it does require more fiducials to get a reliable result. Fixing the coordinates reduces the number of variables to be solved for and allows a reliable solution with only a relatively few fiducials; it also avoids distortions in the resulting reconstruction that could be difficult to account for when trying to combine recon- structions from tilts around two axes.RobustFittingThe goal in robust fitting is to reduce the effect of incorrectly placed model points on the fitted solution by giving less weight to points which appear to be outliers. Because it is not possible to be certain about which points are indeed incorrect, each point is given a weight that depends on how large its error is relative to that of other points. When the option to use robust fitting is selected, the program first obtains a global alignment solution, or one for a local area, which gives a residual error value for each projection point. The residual values are analyzed to derive a weight between 0 and 1 for each one, and the fitting routine is call again to refine the solution with these weights. This solution provides new residuals, and this process is repeated until the weights do not change significantly or until the fitting routine only runs for one iteration several times in a row. At the end, the program prints out the final F value from the fit, which is the square root of the mean squared weighted errors, and it also prints a weighted mean residual value immediately after the ordinary mean. It also prints a line showing the number of weights that were set to 0, less than 0.1, less than 0.2, and less than 0.5. The latter number is usually about 5% of the total points. The numbers of down-weighted points can be increased or decreased by entering the KFactorScaling with a value less than or greater than 1, respectively. The weights are derived by the following method. The median residual is first obtained for each view from the errors of the unweighted fit, and these values are smoothed to obtain a curve for the dependence of median residual on view number. The projection points are divided into groups of about 100 by forming groups of adjacent views, and, for the global solution, by sorting the points into concentric rings based on distance from the center. These two measures are used to reduce the influence of systematic variations in residual error with tilt angle and with distance from the center on the detection of incorrectly posi- tioned points. For a group of points, each point's residual is divided by the smoothed median residual for that point's views. The median of the values is found, as well as the normalized median absolute devia- tion from the median (the MADN). For each point with residual greater than the median, the value x = (residual - median) / (K * MADN) is computed, where K is the K factor (4.685 by default), and the weight is (1 - x**2)**2 for x < 1, or 0 for x > 1.TheAlignmentModelThe program implements the following model for the imaging of the spec- imen in each individual view: 1) The specimen itself changes by a) an isotropic size change (magnification variable); b) additional thinning in the Z dimension (compression variable); and c) linear stretch along one axis in the specimen plane, implemented by variables representing stretch along the X axis and skew between the X and Y axes; 2) The specimen is tilted slightly around the X axis (X tilt variable) 3) The specimen is tilted around the X axis by the negative of the beam tilt, if any (one variable for all views) 4) The specimen is tilted around the Y axis (tilt variable) 5) The specimen is tilted back around the X axis by the beam tilt, if any 6) The projected image rotates in the plane of the camera (rotation variable) 7) The projected image may stretch along an axis midway between the original X and Y axes (one variable for all views) 8) The image shifts on the camera Only a subset of this complete model can be solved for in any given case. In particular, thinning cannot be solved for together with tilt angle and stretch along the X axis; it is very difficult to solve for X axis tilt together with rotation angle; and it is almost impossible to solve for beam tilt together with rotation and skew. The complete model is summarized in: Mastronarde, D. N. 2008. Correction for non-perpendicularity of beam and tilt axis in tomographic reconstructions with the IMOD package. J. Microsc. 230: 212-217. The version of the model prior to the addition of beam tilt is described in more detail in: Mastronarde, D. N. 2007. Fiducial marker and hybrid alignment methods for single- and double-axis tomography. In: Electron Tomography, Ed. J. Frank, 2nd edition, pp 163-185. Springer, New York.Cross-validationFor cross-validation, the program does many fits, each with a subset of points left out, and predicts the position of each of the left-out points from the solution obtained without them. The errors in these predictions are averaged and reported as the "leave-out error". This error is a valid indicator of whether solving for additional parameters truly improves the solution. In contrast, the mean residual error of a fit will always go down when parameters are added, and there is no good indication of whether the solution is indeed better or is just overfit- ting to accommodate random errors. The program Restrictalign can test systematically for whether more restricted parameters will improve the leave-out error. The default parameters will leave out segments of 5 points on adjacent views, and evaluate prediction errors on the 3 middle points of each segment. About 10% of points are left out on each fit, and enough fits are done with different sets of points to accumulate an error value accurate enough to compare between parameter selections. The padding by one point is intended to reduce the influence on the solution of a possible dependency between adjacent points. This strategy is used to avoid several problems with leaving out whole contours, the most impor- tant two being: 1) When there are fewer than 10 fiducials, more than 10% of points have to be left out, which could destabilize the solu- tion. 2) When there are fewer than 20 fiducials, only one will be left out of each fit and there will be only as many unique runs as the num- ber of fiducials, limiting the accuracy of the result. The disadvantage of cross-validation is that it does require multiple fits, so the computational time could be 20-50 times higher than for a single fit. This is particularly problematic if robust fitting is used as well, and one strategy (used by Restrictalign) is to turn off robust fitting during the validations unless it is beneficial enough. When cross-validation is used with robust fitting, the output of leave- out errors is more complex. It has this form: Global non-robust leave-out error (10888 pts): 0.3111 nm weighted 0.2720 nm Global robust leave-out error (10888 pts): 0.3026 nm weighted 0.2638 nm Benefit from robust fitting: unweighted 0.0084 weighted 0.0082 nm On the first line, the first value (0.3111) is the error of the left- out points in the unweighted solution before robust fitting. Results from robust solution are on the second line: first the mean error with no weights applied, then the error after applying the weights from the full robust solution that included all the points. The first value includes all the points that have been downweighted or eliminated in the robust solution with all points and is thus the result of two coun- tervailing factors: the errors of those points should have increased while the error of the remaining points decreased. The second value from robust fitting appropriately discounts the outlying points. It can be compared with the second value on the first line, in which the errors of points left out of the non-robust solution have been multi- plied by the same weights used for the weighted errors from the robust solution. Since potentially outlying points have been discounted in the identical way in the two weighted values, their difference (the second value on the "Benefit" line) is the best measure of how much benefit robust fitting gave. A negative value indicates that the robust solution is actually worse.OPTIONSTiltalign uses the PIP package for input (see the manual page for pip) and can no longer take sequential input interactively. The following options can be specified either as command line arguments (with the -) or one per line in a command file or parameter file (with- out the -). Options can be abbreviated to unique letters; the cur- rently valid abbreviations for short names are shown in parentheses. In all entries of view numbers, the views are numbered from 1.INPUTANDOUTPUTFILEOPTIONSThese options give information about input and output files.-ModelFileFilenameInput fiducial model file-ImageFileFilenameImage file that fiducial model was built on, used to obtain information for scaling the model. If this entry is omitted, the program will use values entered with ImageSizeXandY, ImageO- riginXandY, and ImagePixelSizeXandY, or values from the model itself if those options are omitted. In general, the informa- tion from the model header should be sufficient and none of these entries should be needed.-ImageSizeXandYTwointegersDimensions of image file (optional)-ImageOriginXandYTwofloatsX and Y origin values from image file header (optional)-ImagePixelSizeXandYTwofloatsX and Y Pixel spacing from image file header, in Angstroms (optional)-UnbinnedPixelSizeFloatingpointPixel size of unbinned data in nanometers-ImagesAreBinnedIntegerThe current binning of the images relative to the original data. This factor is used to scale the values entered with AxisZShift and AxisXShift from unbinned to binned coordinates. The default is 1.-OutputModelFileFilenameFile in which to place 3-D model of the fiducials based on their solved positions-OutputResidualFileFilenameOutput file for a list of the residuals at all projection points, which can be converted to a model with Patch2imod.-OutputModelAndResidualFilenameRoot name for output of both a 3-D model and residuals; the files will have extensions .3dmod and .resid, respectively.-OutputFilledInModelFilenameOutput file for fiducial model with missing points filled in on the views included in the solution. This model can be used for erasing fiducial markers. A missing point is first computed from the projection position of the solved 3-D position of the fiducial. Then, a line is fit to the residuals of points on the 6 nearest views and an estimated residual is subtracted from the projection position, in order to incorporate a consistent dis- parity between the fiducial positions and the solution. Projec- tion positions from a global solution are replaced by ones from local solutions, if any, and ones from multiple local areas are averaged. This option is ignored for a model from patch track- ing.-OutputTopBotResidualsFilenameRoot name for output of residuals for fiducials on the top and bottom surfaces into separate files, with extensions .topres and .botres.-OutputFidXYZFileFilenameFile for text output of the solved X-Y-Z coordinates-FixedXYZInputFileFilenameFile with fixed X-Y-Z coordinates to use in local alignments. The values will be used when initializing the coordinates for the search in each local area, but they will have little effect unless-FixXYZCoordinatesis entered. Each line of this file should start with the three coordinates; numbers after that are ignored. There must be the same number of lines in the file as the number of fiducials.-OutputTiltFileFilenameOutput file for the solved tilt angles after adjustment for beam tilt, if any-OutputUnadjustedTiltFileFilenameOutput file for the solved tilt angles before adjustment for beam tilt, if any-OutputXAxisTiltFileFilenameOutput file for tilts around the X axis.-OutputTransformFileFilenameOutput file for 2-D transformations needed to align images-OutputZFactorFileFilenameOutput file for factors to adjust X and Y as function of Z in backprojection. When there is specimen stretch along an axis, a 2-D transformation of the projections cannot fully correct for this effect, and these factors are needed to adjust the backpro- jection position for different Z heights in the reconstructed slice.ANGLEANDVIEWRELATEDOPTIONSThese options provide information about tilt angles and the views to be included in the analysis.-IncludeStartEndIncThreeintegersStarting and ending view numbers, and increment between views, to include in analysis. This option, IncludeList, and ExcludeList are mutually exclusive. The default is to include all views that have points in the model.-IncludeListListofintegerrangesList of views to include in the analysis (ranges allowed)-ExcludeListListofintegerrangesList of views to exclude from the analysis (ranges allowed)-RotationAngleFloatingpointInitial angle of rotation in the plane of projection. This is the rotation (CCW positive) from the Y-axis (the tilt axis after the views are aligned) to the suspected tilt axis in the unaligned views.-SeparateGroupListofintegerrangesList of views that should be grouped separately in automapping. Multiple entries can be used to specify more than one set of separate views. (Successive entries accumulate)-NoSeparateTiltGroupsIntegerAllow tilt angles to be grouped across separate view groups in order to prevent large jumps in the solved tilt angles. Enter 1 to allow this grouping with a patch tracking model, or 2 to allow it for any fiducial model.-first(-f)OR-FirstTiltAngleFloatingpointTilt angle of first view, in degrees. Use this option together with TiltIncrement.-increment(-i)OR-TiltIncrementFloatingpointIncrement between tilt angles, in degrees. Use this option together with FirstTiltAngle.-tiltfile(-t)OR-TiltFileFilenameUse this option if tilt angles are in a file, one per line.-angles(-a)OR-TiltAnglesMultiplefloatsUse this option to enter the tilt angles for each view individu- ally, in degrees. (Successive entries accumulate)-AngleOffsetFloatingpointAmount to add to all entered tilt angles.GLOBALVARIABLESELECTIONOPTIONSThese options specify the variables to be included in the global fit to all of the points and information about them, such as group sizes.-ProjectionStretchSolve for a parameter representing a skew between the microscope X and Y axes that occurs during projection of all images. This is equivalent to a stretch along a 45-degree line between the axes. A component of stretch parallel to the axes cannot be distinguished from a stretch of the 3D fiducial coordinates par- allel to the axes, so as of IMOD 3.10.7 only this skew component is solved for. The initial rotation angle of the tilt axis is used to determine the approximate axis along which this stretch would occur after the final image rotation.-BeamTiltOptionIntegerType of solution for non-perpendicularity between tilt axis and beam axis, referred to as beam tilt: 0 for beam tilt fixed at the initial value, 1 to include beam tilt as a variable in the minimization procedure, 2 to perform the minimization at a series of fixed beam tilt values and search for the value that gives the smallest error. Because some variables can covary with the beam tilt to give nearly equivalent solutions, the second option for finding the beam tilt gives more reliable results. Some combinations of variable simply cannot be solved for, in particular the stretch variables and rotation together with beam tilt; either omit the stretch variables or solve for a single rotation angle. Note that only the component of the beam tilt around the X axis is solved for; the component around the Y axis is indistinguishable from a change in tilt angle. When the beam tilt is non-zero, either as a result of a search or because a fixed value was entered, its effect is expressed as a varying tilt around the X axis and a modification of the tilt angles and in-plane image rotations. Thus, a file of X-tilt angles should be output when beam tilt is included in the solution.-FixedOrInitialBeamTiltFloatingpointThe entry provides either an initial value for the beam tilt, when it is being solved for, or a fixed value when it is not.-RotOptionIntegerType of rotation solution: 0 for all rotations fixed at the initial angle, 1 for each view having an independent rotation, 2 to enter general mapping of rotation variables, 3 or 4 for automapping of rotation variables (3 for linearly changing values or 4 for values all the same within a group), or -1 to solve for a single rotation variable.-RotDefaultGroupingIntegerDefault group size when automapping rotation variables-RotNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose rotation variables should be grouped differently from the default. Multiple entries can be used to specify more than one set of views with nondefault grouping. (Successive entries accumulate)-RotationFixedViewIntegerNumber of view whose rotation should be fixed at the initial rotation angle. This entry is relevant with any of the positive RotOption entries.-TiltOptionIntegerType of tilt angle solution: 0 to fix all tilt angles at their initial values, 1 to solve for all tilt angles except for a specified view, 2 to solve for all tilt angles except for the view at minimum tilt, 3 to solve for all tilt angles except for a specified view and the view at minimum tilt, 4 to specify a mapping of tilt angle variables, 5 or 6 to automap groups of tilt angles (5 for linearly changing values or 6 for values all the same within a group), or 7 or 8 to automap and fix two tilt angles (7 for linearly changing values or 8 for values all the same within a group)-TiltFixedViewIntegerNumber of view at which to fix the tilt angle (required with TiltOption 1, 3, 7, or 8)-TiltSecondFixedViewIntegerNumber of second view at which to fix the tilt angle (required with TiltOption 7 or 8)-TiltDefaultGroupingIntegerAverage default group size when automapping tilt variables-TiltNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose tilt variables should be grouped differently from the default. (Successive entries accumulate)-MagReferenceViewIntegerNumber of reference view whose magnification will be fixed at 1.0. The default is the view at minimum tilt.-MagOptionIntegerType of magnification solution: 0 to fix all magnifications at 1.0, 1 to vary all magnifications independently, 2 to specify a mapping of magnification variables, or 3 or 4 for automapping of variables (3 for linearly changing values or 4 for values all the same within a group).-MagDefaultGroupingIntegerDefault group size when automapping magnification variables-MagNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose magnification variables should be grouped differ- ently from the default. (Successive entries accumulate)-CompReferenceViewIntegerNumber of the view to fix at compression 1.0 (something other than a view whose tilt angle is fixed at zero.) Required if CompOption not 0.-CompOptionIntegerType of compression solution: 0 to fix all compressions at 1.0, 1 to vary all compressions independently, 2 to specify a mapping of compression variables, or 3 or 4 for automapping of variables (3 for linearly changing values or 4 for values all the same within a group).-CompDefaultGroupingIntegerDefault group size when automapping compression variables-CompNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose compression variables should be grouped differently from the default. (Successive entries accumulate)-XStretchOptionIntegerType of X-stretch solution: 0 to fix all X stretches at 0, 1 to vary all X stretches independently, 2 to specify a mapping of X-stretch variables, or 3 or 4 for automapping of variables (3 for values all the same within a group or 4 for linearly changing values).-XStretchDefaultGroupingIntegerDefault average group size when automapping X stretch variables.-XStretchNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose X stretch variables should be grouped differently from the default. (Successive entries accumulate)-SkewOptionIntegerType of skew solution: 0 to fix all skew angles at 0.0, 1 to vary all skew angles independently, 2 to specify a mapping of skew variables, or 3 or 4 for automapping of variables (3 for linearly changing values or 4 for values all the same within a group).-SkewDefaultGroupingIntegerDefault group size when automapping skew variables-SkewNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose skew variables should be grouped differently from the default. (Successive entries accumulate)-XTiltOptionIntegerType of X-axis tilt solution: 0 to fix all X tilts at 0., 1 to vary all X-tilts independently, 2 to specify a mapping of X-tilt variables, or 3 or 4 for automapping of variables (3 for linearly changing values or 4 for values all the same within a group).-XTiltDefaultGroupingIntegerDefault group size when automapping X-axis tilt variables-XTiltNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose X-axis tilt variables should be grouped differently from the default. (Successive entries accumulate)MINIMIZATIONANDOUTPUTOPTIONSThese options control the minimization procedure and the outputs of the program.-ResidualReportCriterionFloatingpointCriterion number of standard deviations above mean residual error that should be reported. This can be based on either the overall mean and S.d. of the residual errors, or on a mean and S.d. computed from points in nearby views. Enter a positive value for a report based on overall mean, or a negative value for a report based on the mean residual in the same and nearby views.-SurfacesToAnalyzeInteger0 to omit surface analysis, or 1 or 2 to fit points to one or two surfaces and derive a surface angles and recommended tilt angle offset. This entry has no effect on the global alignment solution.-MetroFactorFloatingpointThis entry determines how large a step the variable metric mini- mization procedure (METRO) tries to take. The default is 0.25, which typically works even for large data sets. When METRO fails for various reasons, the program will retry with several other nearby values of the factor.-MaximumCyclesIntegerLimit on number of cycles for minimization procedure (default 1000).-AxisZShiftFloatingpointAmount to shift the tilt axis in Z, relative to the centroid in Z of the fiducial points or relative to the original Z axis location if ShiftZFromOriginal is entered. It is also possible to enter 1000 to shift the tilt axis to the midpoint of the range of Z values. Enter this value in unbinned pixels.-ShiftZFromOriginalApply Z shift relative to original tilt axis location. If images were initially aligned by cross-correlation, this option will keep specimen material near the center of the reconstruc- tion even if fiducials are on one surface.-AxisXShiftFloatingpointAmount to shift the tilt axis in X away from the center of the image. Enter this value in unbinned pixels.ROBUSTFITTINGANDCROSS-VALIDATIONOPTIONSThese options control robust fitting to downweight outlying points and cross-validation by leaving out sets of points.-RobustFittingUse a robust fitting method that gives less weight to points with residuals higher than the median residual, and no weight to the most extreme points.-WeightWholeTracksWhen doing robust fitting with a model from patch tracking, assign the same weight to all the points in each contour. Con- tours with mean residuals higher than the median will thus be given less weight, and ones with the most extreme residuals will be given weights of 0.02.-KFactorScalingFloatingpointAmount to scale the K factor that controls how many points are down-weighted in the robust fitting. The default scaling of 1 gives a K factor of 4.685, the factor commonly used for the Tukey bisquare weighting. A smaller factor will down-weight and eliminate more points.-WarnOnRobustFailureGive just a warning instead of exiting with an error if the robust fitting fails and only a global alignment is being done. If local alignments are being done, a failure in either the global alignment or a local area will always result in just a warning. In all cases, the non-robust alignment is restored after a failure.-MinWeightGroupSizesTwointegersMinimum sizes of the groups of points used for computing weights, in global and local alignment runs. In order to apply the robust method to points that are relatively similar to each other, deviations from a median residual are computed within subsets of points that are located on adjacent views; and if there are enough points, the points in a global alignment run are also sorted into rings based on distance from the center. These entries set the minimum sizes of these groups. If the total number of points available for fitting falls below the minimum, the robust fitting is not done and a warning or error is issued. The defaults are 100 and 65 when adjusting weights for individual points. When assigning weights to whole contours with data from patch tracking, a similar approach is used to divide the contours into groups that are analyzed together. Here, the defaults are 30 and 20.-CrossValidateDo cross-validation by leaving out sets of points in multiple runs. In each run, the positions of points left out are pre- dicted from the solution and a "leave-out" error is computed. This error is averaged over enough runs with different points left to give an estimate of leave-out error that is accurate enough for comparing the merit of different variable selections. The details of cross-validation are governed by the following options, which all have reasonable defaults.-FractionToLeaveOutTwofloatsFraction of points to leave out of each cross-validation run. An entered value will be limited to be between 0.01 and 0.2. The default is 0.1 for 10 or more fiducials, or 0.1 times the number of fiducials for fewer than 10 fiducials, down to 0.04.-LeaveOutPredictAndPadTwointegersNumber of points on contiguous views to leave out as a group and from which to use predicted positions to measure the leave-out error; and number of additional points on each side of this group to leave out as padding. More padding will require more runs to reach a given accuracy level. If the first value is 0, whole contours (fiducials) will be left out in each run and the second value does not matter. The default is 3,1.-CVCoverageTargetOrFactorThis entry determines how many cross-validation runs will be done with different sets of points left out and thus how accu- rate the estimated error will be. The value can be either a target number of points to get leave-out errors from, or a fac- tor whose product with the number of fiducials would be the desired number of points to get errors from. If whole contours are being left out, the total number left out may be limited. Specifically, if the number of fiducials times the fraction of points to leave out rounds down to 1 or less, then only one con- tour would be left out at once, and the number of runs would be the limited to the number of fiducials. When more than one con- tour is left out per run, there is no redundancy with a coverage above 1 because different combinations of fiducials will be used. The default is 12000 points.-CVMinAndMaxCoverageFactorMinimum and maximum values for the actual coverage factor, or average number of times each point is left out. The default is 0.3 and 5.-RandomSeedIntegerA value for the seed of the random number generator used in cross-validation, or 0 for a seed computed from the current time. Using a fixed seed value for multiple runs is important when looking at the effects of changing alignment parameters because it minimizes variability between runs due to different sets of points being chosen. The default is to used a fixed seed.-TestSetIntervalOrFracFloatingpointWhen running cross-validation by leaving out points or contours on multiple runs, a fraction of fiducials can be reserved as a test set as well. Solutions will be obtained using just the remaining points, including the multiple solutions with some of those points left out. The errors for the test set will be reported both for the full solution with the remaining points and for the cross-validation runs. This option is useful for validating the cross-validation itself but not for tuning param- eters in actual data sets without a large excess in the number of fiducials.LOCALALIGNMENTOPTIONSThese options control local alignments.-LocalAlignmentsDo alignments with subsets of points in local areas. When this option is selected, the appropriate Local...Option values must be entered to control what variables are solved for; the default is 0 for all of the local option values.-OutputLocalFileFilenameOutput file for transformations for local alignments-NumberOfLocalPatchesXandYTwointegersNumber of local patches in X and in Y in which to obtain a solu- tion from the fiducials located in that patch. If this option is entered, overlapping patches will be set up that fill the image area.-TargetPatchSizeXandYTwointegersTarget for the size of local patches in X and Y in which to obtain a solution from the fiducials located in that patch. The number of patches will be set so that patches smaller or up to 5% larger than this size and overlapping by a fixed amount will fill the range occupied by fiducials (not the image area). The patches on the edges should not have to expand as much as when the patch centers are set up to fill the image area. If this option is entered, NumberOfLocalPatchesXandY must not be entered, and MinSizeOrOverlapXandY must specify an overlap instead of a size.-MinSizeOrOverlapXandYTwofloatsEither the minimum size of each patch in X and Y (enter values > 1) or the minimum fractional overlap between patches (values < 1). The default is an overlap of 0.5.-MinFidsTotalAndEachSurfaceTwointegersMinimum total number of fiducials, and minimum number present on each surface if two surfaces were assumed in the analysis of surfaces. A patch will be expanded about its center until it contains enough points to meet both of these criteria.-FixXYZCoordinatesFix the X-Y-Z coordinates of the fiducials at their values from the global solution; the default is to solve for them indepen- dently in each local area. For more on the implications of this option, see the note above in the section on local alignments.-LocalOutputOptionsThreeintegersThese three entries control the output of results for each local alignment: 1 to output the values of the parameters for each view or 0 not to; 1 to output the X-Y-Z coordinates of fiducials or 0 not to; and 1 to output points with high residuals, or 0 not toLOCALVARIABLESELECTIONOPTIONSThese options specify the variables to be included in the local alignment fits and information about them, such as group sizes.-LocalRotOptionIntegerType of local rotation solution: 0 for local rotations fixed, 1 for each view having an independent rotation, 2 to enter general mapping of variables, 3 or 4 for automapping of rotation variables (3 for linearly changing values or 4 for values all the same within a group), or -1 to solve for a single rotation variable.-LocalRotDefaultGroupingIntegerDefault group size when automapping local rotation variables.-LocalRotNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose local rotation variables should be grouped differ- ently from the default. (Successive entries accumulate)-LocalTiltOptionIntegerType of local tilt angle solution; values 0-8 have same meaning as for global solution.-LocalTiltFixedViewIntegerNumber of view at which to fix the tilt angle in the local solu- tion (required with LocalTiltOption 1, 3, 7, or 8)-LocalTiltSecondFixedViewIntegerNumber of second view at which to fix the tilt angle in the local solution (required with LocalTiltOption 7 or 8)-LocalTiltDefaultGroupingIntegerAverage default group size when automapping local tilt variables-LocalTiltNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose local tilt variables should be grouped differently from the default. (Successive entries accumulate)-LocalMagReferenceViewIntegerNumber of reference view whose local magnification will be fixed at 1.0. The default is the view at minimum tilt.-LocalMagOptionIntegerType of local magnification solution; values 0-3 have same mean- ing as for global solution.-LocalMagDefaultGroupingIntegerDefault group size when automapping local magnification vari- ables-LocalMagNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose local magnification variables should be grouped dif- ferently from the default. (Successive entries accumulate)-LocalXStretchOptionIntegerType of local X-stretch solution; values 0-3 have same meaning as for global solution.-LocalXStretchDefaultGroupingIntegerDefault average group size when automapping local X stretch variables-LocalXStretchNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose local X stretch variables should be grouped differ- ently from the default. (Successive entries accumulate)-LocalSkewOptionIntegerType of local skew solution; values 0-3 have same meaning as for global solution.-LocalSkewDefaultGroupingIntegerDefault group size when automapping local skew variables-LocalSkewNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose local skew variables should be grouped differently from the default. (Successive entries accumulate)-LocalXTiltOptionIntegerType of local X-axis tilt solution; values 0-3 have same meaning as for global solution.-LocalXTiltDefaultGroupingIntegerDefault group size when automapping local X-axis tilt variables-LocalXTiltNondefaultGroupThreeintegersStarting and ending view numbers and group size for a set of views whose local X-axis tilt variables should be grouped dif- ferently from the default. (Successive entries accumulate)MAPPINGOPTIONSThese are obsolete options for ultimate control of variable mapping.-RotMappingMultipleintegersIf RotOption is 2, this option must be used to enter a rotation variable number for each view. These variable numbers can be completely arbitrary, e.g. 1,1,1,3,3,3,5,5,5. The numbers are used to define block grouping. (Successive entries accumulate)-LocalRotMappingMultipleintegersIf LocalRotOption is 2, this option must be used to enter a local rotation variable number for each view. (Successive entries accumulate)-TiltMappingMultipleintegersIf TiltOption is 2, this option must be used to enter a tilt variable number for each view. (Successive entries accumulate)-LocalTiltMappingMultipleintegersIf LocalTiltOption is 4, this option must be used to enter a local tilt variable number for each view. (Successive entries accumulate)-MagMappingMultipleintegersIf MagOption is 2, this option must be used to enter a magnifi- cation variable number for each view. (Successive entries accu- mulate)-LocalMagMappingMultipleintegersIf LocalMagOption is 2, this option must be used to enter a local magnification variable number for each view. (Successive entries accumulate)-CompMappingMultipleintegersIf CompOption is 2, this option must be used to enter a compres- sion variable number for each view. (Successive entries accumu- late)-XStretchMappingMultipleintegersIf XStretchOption is 2, this option must be used to enter an X stretch variable number for each view. (Successive entries accumulate)-LocalXStretchMappingMultipleintegersIf LocalXStretchOption is 2, this option must be used to enter a local X stretch variable number for each view. (Successive entries accumulate)-SkewMappingMultipleintegersIf SkewOption is 2, this option must be used to enter a skew variable number for each view. (Successive entries accumulate)-LocalSkewMappingMultipleintegersIf LocalSkewOption is 2, this option must be used to enter a local skew variable number for each view. (Successive entries accumulate)-XTiltMappingMultipleintegersIf XTiltOption is 2, this option must be used to enter an X-axis tilt variable number for each view. (Successive entries accumu- late)-LocalXTiltMappingMultipleintegersIf LocalXTiltOption is 2, this option must be used to enter a local X-axis tilt variable number for each view. (Successive entries accumulate)UNIVERSALOPTIONS-param(-p)OR-ParameterFileParameterfileRead parameter entries as keyword-value pairs from a parameter file.-help(-h)OR-usagePrint help output-StandardInputRead parameter entries from standard input. Note: when compression is solved for, the program prints both the abso- lute and the incremental compression for each view. When no compres- sion is solved for, the program prints instead two additional columns: "deltilt" is the difference between the solved and original tilt angles, and "mean resid" is the mean residual error for each view.FILESFiles generated by Tiltalign for use by other programs have the follow- ing formats: The file with alignment transforms (option OutputTransformFile) con- tains one line per view, each with a linear transformation specified by six numbers: A11 A12 A21 A22 DX DY where the coordinate (X, Y) is transformed to (X', Y') by: X' = A11 * X + A12 * Y + DX Y' = A21 * X + A22 * Y + DY The file with solved tilt angles (option OutputTiltFile) has the angle in degrees for each view, one per line. The file with X-axis tilt angles (option OutputXAxisTiltFile) has the angle in degrees for each view, one per line. The file with Z factors (option OutputZFactorFile) has two numbers on one line for each view, the displacement in X and the displacement in Y per pixels of deviation in Z from the midplane. The file with all residuals (option OutputResidualFile) starts with a line with the number of residuals to follow, then has five values per line for each residual: X Y Z X_residual Y_residual It can be converted to a model by running Patch2imod with no special options. The file with solved X-Y-Z coordinates (option OutputFidXYZFile) has one line per 3D point: fiducial_# X Y Z object_# contour_# The first line has, after these values, the pixel size and the size of the image file that the alignment was run with: Pix: pixel_in_Angstroms Dim: X_size Y_Size The file of local alignments (option OutputLocalFile) has a header line with: #_X #_Y X_start Y_start dX dY if_Xtilts pixel_Angstroms if_Zfactors where #_X and #_Y are number of patches in X and Y, X/Y_start are the centers of the first patches in X and Y, dX and Y are the spacing between patches in X and Y, if_Xtilts is 1 if there are X-axis tilts, pixel_Angstroms is the pixel size of the image file, and if_Zfactors is 1 if there are Z factors. Following the header is a block of data for each local area, where areas progress in X then in Y. The data are all expressed as incre- ments to the global alignment information. The elements in each block are: Tilt angles, one per view, many per line X-axis tilt angles if they are included, one per view, many per line Z factors if they are included, a pair of X and Y factors for each view, several pairs per line Refinement transformations for each view in the same format as above, one per lineHISTORYWritten by David Mastronarde, March 1989, based on programs ALIGN and ALIGNXYZ (Mike Lawrence, 1982) obtained from R.A. Crowther at the MRC 5/19/89 added model output, changed format of output table 6/21/89 added mean residual output to find_surfaces, changed to get recommendation on maximum FIXED tilt angle 4/9/93 allow full mapping of compression variables 10/30/95 added distortion, automapping, point & angle output. 10/17/98 added linear combinations to automapping 2/12/98 added local alignments; changed find_surfaces to find and recommend an X-axis tilt.BUGSEmail bug reports to mast at colorado dot edu. IMOD 4.12.47 tiltalign(1)