restrictalign(1) General Commands Manual restrictalign(1)NAMErestrictalign - Restrict tilt alignment parameters for low number of fiducialsSYNOPSISrestrictalign options tiltalign_command_fileDESCRIPTIONRestrictalign will modify the parameter settings in a command file for running Tiltalign so that they are appropriate for the number of fiducials available. It uses two fundamentally different methods for reducing the number of variables being solved for. The original method, currently the default, is based on the ratio of measured values to unknown variables. Variables are reduced until this ratio rises to a target or minimum level. Although this ratio provides some guidance for how to avoid over-fitting, this method cannot take into account the signal-to-noise ratio of the data, namely how much random error there is in the measurements.Cross-validationThe newer method is cross-validation: running Tiltalign numerous times with a small fraction of points left out, measuring how well each solution predicts the positions of the points left out, and computing an average "leave-out error". This error, not the mean residual error, accurately reflects whether a different selection of parameters gives a better solution or not. The mean residual will always go down when more variables are solved for (e.g, by adding a parameter to solve for or reducing its grouping), whereas the leave-out error will go down when the added variables improve the fit and go up when they over-fit to the data. The downside of this superior method of avoiding overfit- ting is that it takes much more time for the many runs of Tiltalign; this becomes a major consideration with local alignments and many fidu- cials. The variables tested are completely different depending on whether local alignments are to be tested. Without local alignments, the pro- gram tests a sequence of the global variables being solved for. For each variable, it tests with default grouping if there is no grouping, with intermediate grouping, with very large grouping, and with the variable fixed (or, for rotation, with solving for only one rotation angle), stopping when the leave-out error rises. The order of the tests is X-stretch and skew together, tilt angle, rotation, magnifica- tion, beam tilt, X axis tilt, and projection stetch. With local align- ments, the program can test either by restricting alignment variables in a similiar sequence, or by increasing the size of local areas together with the required number of fiducials in each, or with both kinds of tests. Here the sequence of variables is X-stretch and skew together, tilt angle, rotation, and magnification. It is recommended that the area requirements be tested first because the same requirement tends to be chosen regardless of which order they are done in, whereas the variables tend to be restricted more when tested before the area requirement has been increased. If robust fitting is being done, the program may first disable it per- manently if the ratio of measurements to unknowns is too low. If not, the program uses a weighted leave-out error computed with and without robust fitting to assess the benefit from robust fitting, and if the benefit is not above a criterion, it turns off robust fitting temporar- ily for all further tests simply in order to save time.RestrictionsBasedontheRatioofMeasurementstoUnknownsIn the old method, the program proceeds by applying a series of restrictions - grouping a variable instead of solving at every tilt, or fixing it instead of grouping - in a specified order until an appropri- ate ratio of measured values to unknown variables is reached. That ratio is picked based on two parameters, the minimum required ratio, and a target ratio. When two restrictions both give more than the min- imum ratio, the one closest to the target is chosen. To have the pro- gram always pick the first restriction where the ratio is above the minimum, set the target ratio equal to the minimum ratio. The-orderoption controls the order in which restrictions will be applied by changes in the magnification, rotation, and tilt solutions, but these are not the only changes that can occur. Before applying any of these restrictions, the stretching solution (X-stretch and skew), local alignments, and variable X-axis tilt (except between two halves of a tilt series) will be turned off. If these restrictions are suffi- cient, no further changes are made. When there are fewer than 4 beads, the beam tilt solution, projection stretch, and variable X-axis tilt between two halves of a tilt series are turned off; all of these involve solving for a single variable. The solution for one rotation angle is turned off with only one bead. When the ratio of measurements to unknowns falls below the minimum, robust fitting is turned off. The program always changes parameters so as to solve for fewer vari- ables than in the current file. If the ratio is already greater than the minimum and closer to the target than with any restriction applied, no change will be made. To use the program with the default settings with a single-axis tilt series, simply enter: restrictalign align.com to use the original method, or restrictalign -cross 1 align.com to do cross-validation when local alignments are not being used, or restrictalign -cross 1 -local 3 align.com to test the local area requirements then the local variables. The existing file will be renamed to align.com~ and the file with the changed parameters will be written as align.com, unless the-trialoption is entered.OPTIONSRestrictalign uses the PIP package for input (see the manual page for pip). Options can be specified either as command line arguments (with the -) or one per line in a command file (without the -). Options can be abbreviated to unique letters; the currently valid abbreviations for short names are shown in parentheses.-align(-a)OR-AlignCommandFileFilenameCommand file for running Tiltalign. If this option is not entered, the first non-option argument will be used for the name of the command file.-fiducials(-f)OR-NumberOfFiducialsIntegerNumbers of fiducial markers (beads) in the alignment model. With this entry, he program will assume that each bead is marked on every view. If this option is not entered, the program will use the number of contours in the fiducial model with more than one point, and count up the number of points in those contours. The latter will give more accurate estimates of the ratio of measurements to unknowns when there beads marked on only a sub- set of views.-views(-vi)OR-NumberOfViewsIntegerNumber of views in the tilt series. If this option is not entered, the program will use the number of views in the image file listed in the command file.-target(-ta)OR-TargetMeasurementRatioFloatingpointTarget ratio of measurements to unknown values. If two succes- sive restrictions give a ratio above the minimum required by the-minimumoption, the restriction that gives a ratio closest to this value will be chosen. The default is 3.6.-minimum(-m)OR-MinMeasurementRatioFloatingpointMinimum ratio of measurements to unknown values. Restrictions will be applied until at least one ratio rises above this value. The default is 3.2.-order(-or)OR-OrderOfRestrictionsMultipleintegersOrder in which possible restrictions should be applied to achieve the target. The restrictions are numbered as follows: 1: Group rotations 2: Solve for one rotation 3: Fix tilt angles 4: Group magnifications 5: Fix magnifications The default order is 1,4,3,2,5, which means rotations will be grouped, then magnifications grouped, tilt angles fixed, then one rotation solved for, then magnifications fixed. If fewer than 5 numbers are entered, they will replace just the first numbers in the order list, and they must be different from the remaining values-cross(-cr)OR-UseCrossValidationIntegerWith this option, the program will test for the value of restricting the alignment parameters using cross-validation. Namely, alignment is run repeatedly with ~10% of points left out, and the error in predicting the positions of the left-out points from the solution obtained with the remaining points is computed. A set of alignment parameters is considered to be better if it reduces this error, regardless of the effect on the mean residual of the fit with all points. If 1 is entered, sets of 5 points on adjacent views are left out, with error measured from the middle 3 points. If 2 is entered, contours will be left out instead. The latter approach is unsuitable if there are few contours.-local(-l)OR-LocalAlignValidationIntegerDo cross-validation on local alignment parameters: enter 1 to test the variable selections, increasing the grouping or turning off magnification, rotation, tilt, and x-stretch and skew together. Enter 2 to test the required number of fiducials in local areas while increasing their target size (or reducing the number if that is specified instead of target size). Enter 3 or 4 to do both tests, first areas then variables with a 3, or variables then areas with a 4. These tests can take several to many minutes. No tests will be done on global variable selec- tions. Local alignment must be selected in the command file.-benefit(-b)OR-MinRobustBenefitFloatingpointMinimum percentage benefit (reduction in leave-out error) with robust fitting needed to keep using robust fitting during cross- validation tests. The benefit is the difference between the non-robust and robust weighted errors of the points left out, i.e., the weights from robust fitting with no points left out are applied identically to the prediction errors of the points left out without and with robust fitting. When the benefit is less than the give amount, robust fitting will be omitted in order to speed up the tests. The default is 2%.-cvorder(-cv)OR-CrossValTestOrderMultipleintegersOrder in which different variables are tested with cross-valida- tion. variables are numbered as follows and the default is to test in this order 1: X stretch and skew 2: Variable tilt around the X axis 3: Tilt 4: Rotation 5: Magnification 6: Single variables: beam tilt, single X-tilt, projection stretch Fewer than 6 numbers may be entered; they will replace the first ones in order list and must be different from the remain- ing values. The same order will apply to local variable tests, although only 1, 3, 4, and 5 are relevant there.-onestep(-on)OR-OneStepPerVariableTestIntegerMake only one change for a variable before testing other vari- ables. With an entry of 0, the program will test all the possi- ble restrictions on the first variable in the testing order and adopt each restriction that improves the leave-out error, then do the same for the second variable, etc. With the default value of 1, the program will test restrictions on a variable until an improvement occurs, accept that restriction, then go on to the next variable. It will cycle through the variables repeatedly until there is nothing left to test. When testing both local variables and local areas, it will alternate between a change in variable and a change in local area. With an entry of 2 or 3, the program will test restrictions on a variable until the first improvement occurs, but not accept the restric- tion. After all variables have been tested, it will accept the restriction that gave the biggest or smallest improvement with an entry of 2 or 3 respectively. Then it will cycle through the variables again, until finished.-permute(-p)OR-TestPermutationsMultipleintegersList of variables for which to try all permutations in testing order when evaluating global variables. These variables will exchange positions with each other in the order and others will keep their defined positions. The whole sequence of tests is run for each permutation, so this will take 6 times as long to permute 3 variable, and 24 times as long to permute 4. Vari- ables are numbered as in-cvorderabove. If this option is entered, the default value of-onestepbecomes 0 and a non-zero entry for-onestepwill give an error. This option will be ignored if local alignments are being evaluated.-skipbeam(-s)OR-SkipBeamTiltWithOneRotBy default, the program will add a solution for beam tilt if and when it switches to solving for only one rotation angle. (If parameters are already set to solve for only one rotation angle, this switch does not occur and it will not add beam tilt.) With this option, it will not add the beam tilt solution along with this restriction.-trial(-tr)OR-TrialModeOutput modifications to a different command file instead of replacing the input file. The output file will be named as the root of the input file plus "_new.com"-verbose(-ve)OR-VerboseOutputOutput the errors at each step when doing cross-validation-PIDPrint process ID-help(-h)OR-usagePrint help output-StandardInputRead parameter entries from standard inputFILESThe input file is renamed by adding a ~ to the end of its name and replaced with the new file, or new file is produced in trial mode with the root of the input name followed by "_new.com".AUTHORDavid MastronardeSEEALSOtiltalignBUGSEmail bug reports to mast at colorado dot edu. IMOD 4.12.47 restrictalign(1)