### FINDOFF

Performs pattern-matching between position lists related by simple offsets

#### Description:

This routine is designed to determine which positions in many unaligned and unlabelled lists match, subject to the condition that the transformations between the lists are well modelled by simple translations. Although the position lists are written in pixel coordinates, the objects can be related by translations in the Current coordinate system of the associated images.

The results from this routine are labelled position lists (one for each input list) which may be used to complete image registration using the REGISTER routine. The estimated offsets are reported, but REGISTER should be used to get accurate values.

#### Usage:

findoff inlist error outlist

#### Parameters:

A completeness threshold for rejecting matched position list pairs. A completeness factor is estimated by counting the number of objects in the overlap region of two lists, taking the minimum of these two values (this adjusts for incompleteness due to a different object detection threshold) and comparing this with the number of objects actually matched. Ideally a completeness of 1 should be found, the lower this value the lower the quality of the match. [0.5]
The error, in pixels, in the X and Y positions. This value is used to determine which positions match within an error box (SLOW) or as a bin size (FAST). An inaccurate value may result in excessive false or null matches. [1.0]
If FAST is TRUE then this parameter indicates whether the SLOW algorithm is to be used when FAST fails. [TRUE]
If TRUE then the FAST matching algorithm is used, otherwise just the SLOW algorithm is used. [TRUE]
This parameter is used to access the names of the lists which contain the positions and, if NDFNAMES is TRUE, the names of the associated images. If NDFNAMES is TRUE the names of the position lists are assumed to be stored in the extension of the images (in the CCDPACK extension item CURRENT_LIST) and the names of the images themselves should be given in response (and may include wildcards).

If NDFNAMES is FALSE then the actual names of the position lists should be given. These may not use wildcards but may be specified using indirection (other CCDPACK position list processing routines will write the names of their results file into files suitable for use in this manner) the indirection character is "^".

Name of the CCDPACK logfile. If a null (!) value is given for this parameter then no logfile will be written, regardless of the value of the LOGTO parameter.

If the logging system has been initialised using CCDSETUP then the value specified there will be used. Otherwise, the default is "CCDPACK.LOG". [CCDPACK.LOG]

Every CCDPACK application has the ability to log its output for future reference as well as for display on the terminal. This parameter controls this process, and may be set to any unique abbreviation of the following:
• TERMINAL – Send output to the terminal only

• LOGFILE – Send output to the logfile only (see the LOGFILE parameter)

• BOTH – Send output to both the terminal and the logfile

• NEITHER – Produce no output at all

If the logging system has been initialised using CCDSETUP then the value specified there will be used. Otherwise, the default is "BOTH". [BOTH]

This parameter gives the maximum acceptable displacement (in pixels) between the original alignment of the images and the alignment in which the objects are matched. If frames have to be displaced more than this value to obtain a match, the match is rejected. This will be of use when USEWCS is set and the images are already fairly well aligned in their Current coordinate systems. It should be set to the maximum expected inaccuracy in that alignment. If null, arbitrarily large displacements are allowed, although note that a similar restriction is effectively imposed by setting the RESTRICT parameter. [!]
This parameter specifies the minimum number of positions which must be matched for a comparison of two lists to be deemed successful. Small values (especially less than 3) of this parameter can lead to a high probability of false matches, and are only advisable for very sparsely populated lists and/or small values of the MAXDISP parameter (presumably in conjunction with USEWCS). [3]
Positions which are very close may cause false matches by being within the error box of other positions. The value of this parameter controls how close objects may be before they are both rejected (this occurs before pattern-matching). [Dynamic – 5.0$\ast$ERROR]
The name of a file to contain the names of the output position lists. The names written to this file are those generated using the expression given to the OUTLIST parameter. This file may be used in an indirection expression to input all the position lists output from this routine into another routine (say REGISTER), if the associating position lists with images option is not being used. [FINDOFF.LIS]
If TRUE then the routine will assume that the names of the position lists are stored in the NDF CCDPACK extensions under the item "CURRENT_LIST". The names will be present in the extension if the positions were located using a CCDPACK application (such as FINDOBJ). Using this facility allows the transparent propagation of position lists through processing chains.

If a global value for this parameter has been set using CCDSETUP then that value will be used. [TRUE]

##### OUTLIST = FILENAME (Write)
A list of names specifying the result files. These contain labelled positions which can be used in registration. The names of the lists may use modifications of the input names (image names if available otherwise the names of the position lists). So if you want to call the output lists the same name as the input images except to add a type use:

OUTLIST $>$ $\ast$.find

If no image names are given (NDFNAMES is FALSE) then if you want to change the extension of the files (from ".find" to ".off" in this case) use:

OUTLIST $>$ $\ast$$|$find$|$off$|$

Or alternatively you can use an explicit list of names. These may use indirection elements as well as names separated by commas.

This parameter controls whether to continue and create an incomplete solution. Such solutions will result when only a subset of the input position lists have been matched.

If the associating position lists with NDFs option has been chosen, an position list will still be written for each input NDF, but for NDFs which were not matched the output list will be empty (will consist only of comment lines).

Incomplete matching would ideally indicate that one, or more, of the input lists are from positions not coincident with the others, in which case it is perfectly legimate to proceed. However, it is equally possible that they have too few positions and have consequently been rejected. [TRUE]

This parameter determines whether the Current coordinate system is used to restrict the choice of objects to match with each other. If set TRUE, then the only objects which are considered for matching are those which would appear in the overlap of two frames given that they are correctly aligned in their Current coordinate system. If it is set FALSE, then all objects in both frames are considered for matching.

This parameter should therefore be set TRUE if the frames are quite well aligned in their Current coordinate systems (especially in the case that there are many objects and a small overlap), and FALSE if they are not.

This parameter is ignored if USEWCS is FALSE. [FALSE]

This parameter specifies whether the completeness value will be used to weight the number of matches between a pair, when determining the graph connecting all input datasets. Using a completeness weight increases the chance of selecting high quality matches, but may reduce the chance of selecting matches with the highest counts in favour of those with lower counts. [TRUE]
This parameter determines whether Set header information should be used in the object matching. If USESET is true, FINDOFF will try to group position lists according to the Set Name attribute of the image to which they are attached. All lists coming from images which share the same (non-blank) Set Name attribute, and which have a CCD_SET coordinate frame in their WCS component, will be grouped together and treated by the program as a single position list. Thus no attempt is made to match objects between members of the same Set; it is assumed that the relative alignment within a Set is already known and has been fixed.

If USESET is false, all Set header information is ignored. If NDFNAMES is false, USESET will be ignored. If the input images have no Set headers, or if they have no CCD_SET frame in their WCS components, the setting of USESET will make no difference.

If a global value for this parameter has been set using CCDSETUP then that value will be used. [FALSE]

This parameter specifies whether the coordinates in the position lists should be transformed from Pixel coordinates into the Current coordinate system of the associated image before use. If the Current coordinates are related to pixel coordinates by a translation, the setting of this parameter is usually unimportant (but see also the RESTRICT parameter).

This parameter is ignored if NDFNAMES is false. [TRUE]

#### Examples:

findoff inlist=$\ast$ error=1 outlist=$\ast$.off
In this example all the images in the current directory are accessed and their associated position lists are used. The coordinates used for object matching are those in the position lists transformed into the Current frames of the WCS components of the images. The matched position lists are named $\ast$.off. The method used is to try the FAST algorithm, switching to SLOW if FAST fails. The completeness measure is used when forming the spanning tree. Matches with completenesses less than 0.5 and or with less than three positions, are rejected.
findoff fast nofailsafe
In this example the only the FAST algorithm is used.
findoff usecomp=false
In this example the completeness factor is derived but not used to weight the edges of the spanning tree.
findoff error=8 minsep=100
In this example very fuzzy measurements (or small pixels) are being used. The intrinsic error in the measurements is around 8 pixels and positions within a box 100 pixels of each other are rejected.
findoff inlist=data$\ast$ outlist=$\ast$.off restrict=true
This form would be used if the images data$\ast$ are already approximately aligned in their Current coordinates. Setting the RESTRICT parameter then tells FINDOFF to consider only objects in the region which overlaps in the Current coordinates of each pair of frames. This can save a lot of time if there are many objects and a small overlap, but will result in failure of the program if the images are not translationally aligned reasonably well in the first place.
findoff inlist=data$\ast$ outlist=$\ast$.off restrict minmatch=2 maxdisp=20 minsep=30
In this example the images are sparsely populated, and a pair will be considered to match if as few as two matching objects can be found. The images have been initially aligned in their Current coordinate systems to an accuracy of 20 or better. As an additional safeguard, no objects within 30 units (in coordinates of the Current frame) of each other in the same image are used for matching.

#### Notes:

• Position list formats.

CCDPACK supports data in two formats.

CCDPACK format - the first three columns are interpreted as the following.

• Column 1: an integer identifier

• Column 2: the X position

• Column 3: the Y position

The column one value must be an integer and is used to identify positions. In the output position lists from one run of FINDOFF, lines with the same column-1 value in different files represent the same object. In the input position lists column-1 values are ignored. If additional columns are present they must be numeric, and there must be the same number of them in every line. These have no effect on the calculations, but FINDOFF will propagate them to the corresponding lines in the output list.

EXTERNAL format - positions are specified using just an X and a Y entry and no other entries.

In all cases, the coordinates in position lists are pixel coordinates.

• Column 1: the X position

• Column 2: the Y position

This format is used by KAPPA applications such as CURSOR.

Comments may be included in a file using the characters "#" and "!". Columns may be separated by the use of commas or spaces.

• NDF extension items.

If NDFNAMEs is TRUE then the names of the input position lists will be gotten from the item "CURRENT_LIST" of the CCDPACK extension of the input NDFs. On exit this item will be updated to contain the name of the appropriate output lists.

#### Notes on Algorithms

The pattern-matching process uses two main algorithms, one which matches all the point pair-offsets between any two input lists, looking for the matches with the most common positions, and one which uses a statistical method based on a histogram of the differences in the offsets (where the peak in the histogram is assumed the most likely difference). In each case an estimate of the positional error must be given as it is used when deciding which positions match (given an offset) or is used as the bin size when forming histograms.

Which algorithm you should use depends on the number of points your position lists contain and the expected size of the overlaps between the datasets. Obviously it is much easier to detect two lists with most of their positions in common. With small overlaps a serious concern is the likelihood of finding a ‘false match. False matches must be more likely the larger the datasets and the smaller the overlap.

The first algorithm (referred to as SLOW) is more careful and is capable of selecting out positions when small overlaps in the data are present (although a level of false detections will always be present) but the process is inherently slow (scaling as n$\ast$$\ast$3log2(n)). The second algorithm (referred to as FAST) is an n$\ast$n process so is much quicker, but requires much better overlapping.

Because the FAST process takes so little CPU time it is better to try this first (without the SLOW process as a backup), only use the SLOW algorithm when you have small datasets and do not expect large areas (numbers of positions) of overlap.

A third algorithm, referred to as SNGL, is used automatically if one or both of the lists in a pair contains only a single object. In this case object matching is trivial and, of course, may easily be in error. SNGL can only be used if the MINMATCH parameter has been set to 1, which should be done with care. The SNGL algorithm may be useful if there really is only one object, correctly identified, in all the frames. If this is not the case, it should only be used when USEWCS is true and MAXDISP is set to a low value, indicating that the alignment of the images in their Current coordinate systems is already fairly accurate.

The global registration process works by forming a graph with each position list at a node and with connecting edges of weight the number of matched position-pairs. The edge weights may be modified by a completeness factor which attempts to assess the quality of the match (this is based on the ratio of the expected number of matches in the overlap region to the actual number, random matches shouldnt return good statistics when compared with genuine ones). This still leaves a possibility of false matches disrupting any attempt to register the datasets so a single "spanning tree" is chosen (this is a graph which just visits each node the minimum number of times required to get complete connectivity, no loops allowed) which has the highest possible number of matched positions (rejecting edges with few matched positions/low completenesses where possible). This gives a most likely solution to the offsets between the position lists, rather than the "best" solution which could well include false matches; compare this solution with a median as opposed to a mean. The final registration is then used to identify all the objects which are the same in all datasets (using a relaxation method), resulting in labelled position lists which are output for use by REGISTER.

#### Behaviour of parameters

Most parameters retain their current value as default. The "current" value is the value assigned on the last run of the application. If the application has not been run then the "intrinsic" defaults, as shown in the parameter help, apply.

Retaining parameter values has the advantage of allowing you to define the default behaviour of the application but does mean that additional care needs to be taken when re-using the application after a break of sometime. The intrinsic default behaviour of the application may be restored by using the RESET keyword on the command line.

Certain parameters (LOGTO, LOGFILE, NDFNAMES and USESET) have global values. These global values will always take precedence, except when an assignment is made on the command line. Global values may be set and reset using the CCDSETUP and CCDCLEAR commands.