IMP: Superposer Itegrated Morphometrics Package Superpositio Tool Programmig by: David Lieber ( 03) Caisius College 200 Mai St. Buffalo, NY 4208 Cocept by: H. David Sheets, Dept. of Physics, Caisius College sheets@caisius.edu Itroductio Superposer is a part of a suite of software (IMP) meat for use i morphometric aalysis. Superposer is iteded primarily as a tool for trasformig raw morphometric data ito oe of four superpositio types: () Bookstei registratio, (2) Procrustes superpositio, (3) Slidig Baselie Registratio, or (4) RFTRA. How to Use Superposer: Loadig Data This program is desiged to load data files i the xyx2y2 CS (*.txt) format or TPS (*.tps) format. If cetroid sizes have ot bee appeded to the data set, the program will automatically calculate them ad apped them to the data. To load a file, select File o the meu bar ad click o Load Data Set. Choose the file you would like to load. If the file is i the appropriate format, the data will be plotted o the axes, ad the fileame will appear both i the listbox etitled Available Data Sets ad udereath the graphical image. The blue asterisks o the graph represet the mea shape for the loaded data. More tha oe data set ca be loaded i the program at a time. Simply load additioal data sets followig the same format as above. The fileames for the loaded data sets will appear i the listbox etitled Available Data Sets. Please ote that the active data set is the oe that is highlighted i the listbox, ot ecessarily the oe that is displayed o the graph. To switch betwee active data sets, click o the fileame of the desired data set to highlight it. This will allow the program to carry out superpositios with that particular data set.
Carryig out a Superpositio Oce the appropriate data set has bee loaded ad selected, a superpositio ca be carried out. A umber of differet optios are offered: ) Select Superpositio Type Select from amog four differet superpositio types: Procrustes, Bookstei, Slidig Baselie, or RFTRA. Depedig o which superpositio type is chose, it will limit which of the remaiig optios ca be selected. Procrustes Superpositio: Idividual shapes i the data set are superimposed o a referece shape. The superpositio is optimized by miimizig a appropriately chose error fuctio that icorporates the distaces betwee ladmarks o the image ad their respective ladmarks o the superimposed shape. Images may be costraied to be cetroid size ad/or cetered about the origi. Bookstei Registratio: Two ladmarks are selected to serve as achorig poits for the image. Oe ladmark is fixed at the origi (0,0). The secod ladmark is fixed at the poit (,0). Slidig Baselie Registratio: Oce agai, two ladmarks serve as achors for the image. Here, the two ladmarks are costraied to lie alog the x-axis. The image is ofte costraied to be cetroid size ad cetered about the y- axis. If it is ot fully costraied i this maer, a Procrustes-type error fuctio may be miimized to optimize the fit. Slidig baselie registratio is especially useful whe the images beig superimposed have a well-defied axis of symmetry. RFTRA: This is a stadardized robust superpositio. Iitially, the shape data is superimposed usig a least-squares Procrustes superpositio i which the shapes are costraied to be cetroid size ad cetered about the origi. Subsequetly, a series of repeated medias is carried out to determie the media coefficiets for scalig, rotatio, ad traslatio. The result is a robust superpositio that is resistat to outlyig data poits. Oe disadvatage to the techique, however, is that the fial superpositio i somewhat depedet o the iitial orietatio of the referece object. 2) Select Ladmarks that Form the Baselie (Bookstei ad Slidig Baselie, oly) Eter the umbers of the ladmarks that will be the achors for the superpositio. Ladmark umbers are based o the order that each ladmark is etered i the data set. (If the data file that is goig to be used i the
superpositio is curretly graphed o the axes, see View Optios to see how ladmark umbers ca be displayed o the graph.) 3) Select Error Fuctio (Procrustes ad Slidig Baselie, oly) A variety of error fuctios are offered for Procrustes ad Slidig Baselie superpositios. Most error fuctios are costructed usig the followig stadard format: k i= j= Here, deotes the umber of distict images stored i the data file, while k deotes the umber of ladmarks cotaied withi each image. The term d ij is used to deote the geometric distace betwee ladmark j o the i th object ad ladmark j o the referece object. The error fuctio f is subject to user specificatio. Curretly, there are five error fuctios available to choose from. Least-squares is stadard for most purposes; however, it may ot be ideal whe variatios i shape are highly localized, or whe there are outliers. I these cases, oe should cosider oe of the four other error fuctios, which are more robust i these situatios. f ( d ij ) Error Fuctio Least squares Absolute value Adrew s sie Natural logarithm Least media i= Format k 2 d ij i= j= k d ij i= j= k i= j= k i= j= si( l( media({ d d ij d ij ) + ) i, di2,..., d ik }) It should also be oted that the mea that is calculated durig the superpositio routie for both Procrustes ad Slidig Baselie is depedet o the choice of error fuctio. Followig the completio of the superpositio, the mea is calculated by miimizig the selected error fuctio with d ij ow used to represet the distace betwee ladmark j o the i th object ad ladmark j o the mea. The mea is also costraied to be both cetroid size ad cetered. (This techique is used i order to force the mea to lie withi the same dimesioal space as the superimposed images. Also, it is importat to ote that if the true mea were used istead, it would be
impossible to carry out a superpositio aroud that mea usig ostadard error fuctios.) 4) Select a Referece Image (Procrustes, Slidig Baselie, ad RFTRA) For the above superpositio types, a referece image is required to carry out the superpositio. Two optios are preseted: Superimpose objects aroud mea of curret data set: As idicated above, the mea is ot a true mea, but it is a composite of the shapes i the data set as defied by the selected error fuctio. Superpositios aroud the mea are ofte used to show the extet of variace relative to certai ladmarks. Superimpose objects aroud referece form: I this case, the superpositio is carried out aroud a image that is separately loaded ito the program. This optio caot be selected uless a referece file has already bee loaded. To load a referece form, select File o the meu bar ad click o Load Referece Form. Choose the appropriate file (*.txt or *.tps format). Make sure that the file cotais oly a sigle shape image; otherwise, it will ot be loaded. Oce the file has bee loaded, the title of the file should appear i the popup box that is adjacet to the radio butto labeled Referece form. More tha oe referece form ca be stored i the program at a time. Simply repeat the above procedure. A superpositio will be carried out aroud a referece form oly if the appropriate radio butto is highlighted, ad oly if the referece form is displayed i the popup box. 5) Additioal Optios (Procrustes ad Slidig Baselie, oly) Two additioal optios are preseted for Procrustes ad Slidig Baselie superpositios. Alig all cetroids: For a Procrustes superpositio, this forces the images to be cetered at the origi. For a Slidig Baselie registratio, the images are cetered aroud the y-axis. Set cetroid size to uity: All images are forced to be uit cetroid size. For stadard least squares superpositios, it is faster ad more coveiet to select both of these optios. For ostadard error fuctios, the superpositio may be more optimal if oe or both of these optios are ot selected, sice this allows for greater freedom with outliers. Oce all of the optios have bee selected, the superpositio is ready to be carried out. Simply click o the pushbutto labeled, Do it! to start the superpositio. The poiter should chage to a timepiece to idicate that the software is workig. Whe the superpositio is fiished, the program will display the fiished superpositio o the
graph. The specifics of the superpositio will be listed below the graph, icludig (as relevat) the fileame, whether a idepedet referece form was used, ladmarks used i the baselie, error fuctio selected, time required to carry out the superpositio, average error per sample, ad ay other optios. Oce a superpositio has bee carried out, it is stored i the computer s RAM. To retrieve the results of a superpositio that was carried out earlier i a sessio, simply select the same optios as before, ad click o Do it! The results should be rapidly pulled up. View Optios A umber of differet viewig optios are preseted for the data uder the View meu: ) Autoscale, True Aspect: This optio is selected by default. This forces the axes o the graphical image to be scaled i equal icremets. If this optio is uchecked, the graphical image is displayed i the default format i.e. the axes tightly surroud the image o all sides. 2) Show Data Labels: This optio, by default, is uchecked. Whe it is selected, the program will automatically display the ladmark umbers ext to the appropriate data poits for the graphical object that is curretly displayed o the graph. 3) Hide Axes: Whe this optio is selected, the axes backgroud ad tick marks are ot displayed. Oly the graphical image appears. 4) Oly Show Mea: This optio was desiged to allow oly the average positio of the data set to be displayed. The idividual data poits themselves are hidde. 5) Show Referece: If a idepedet referece form was selected for the superpositio, it ca be displayed o the graph. Simply select this optio. The referece form will appear with gree asterisks. If o referece form was used i the superpositio, this optio is ot active. These optios are ofte most useful whe copyig or pritig images i order to tailor their appearace. Copyig Images I order to copy a image to the clipboard, click o Edit, the Copy to Clipboard. The image will be copied as a meta-file. I order to copy a image to a file, click o Edit, the Copy to File. Select a appropriate fileame ad click OK. The image will be copied as a Ecapsulated Post-
Script (*.eps) file. These images should load ormally ito most word-processig programs. Pritig Images To prit the image that is displayed o the scree, simply click o File ad select Prit. Click OK whe ready to prit. Savig Data Two save optios are preseted. I order to save the superpositioed images that are displayed o the graph, click o File ad select Save Curret Data. Choose a appropriate fileame, ad click o OK. This will save the superimposed data oly. It will ot save the referece or the calculated mea. All data is saved i the xyx2y2 CS format. I order to save the calculated mea for the data displayed o the graph, click o File ad select Save Curret Mea. Oce agai, choose a appropriate fileame, ad click o OK. This will save the calculated mea oly. Oce agai, the mea is saved i the xyx2y2 CS format. Coclusio Superposer is a fairly versatile tool i that it offers a variety of superpositio optios, both stadard ad robust. Hopefully, it ca help you i your edeavors at shape aalysis.