As Michael described, the average shape configuration affects the sliding when used as reference for the TPS; the final configurations thus are sample-dependent. However, if the curves/surfaces are covered densely enough by the semilandmarks (e.g., to avoid that a semilandmark can slide away from a relevant region), Procrustes distances are quite stable. Dense sampling can also improve the estimation of the tangents.
If the semilandmarks slide a lot relative to the local curvature, they get off the curve. Of course, they can be projected back, but the following trick often is sufficient: Instead of the full amount of sliding, let all the semilandmarks slide just a fraction of the computed distance, say 20% (multiply T by 0.2 in equation of 4 of Gunz et al. 2005). Then update the tangents and let the semilandmarks slide again a fraction of the computed distance, etc. This requires more iterations but keeps the semilandmarks closer to the curve or surface. Also when minimizing Procrustes distance instead of BE, these distances are reduced relative to the sample average. But as for the superimposition itself, the sample configuration has only limited effect on the final configurations for small to moderate shape variation. (If variation is very large, the analysis is problematic anyway.) Note that the full sample must be slid together for a joint analysis (i.e., don't slide each population separately and then analyze them together). The choice of the minimization criterion (Proc dist versus BE) can lead to different configurations. For most datasets, this difference is negligible, but in some situations it can matter. For example, when minimizing Proc dist semilandmarks can change their order or slide across a real landmark, whereas this is almost impossible for minimizing BE (changing order would have a very high BE). On the other hand, minimizing BE does not minimize affine shape variation (because it has zero BE). If affine shape variation is not constrained by real landmarks, this can lead to strange results. For instance, I had a dataset of mandibular cross-sections, which were U-shaped with real landmarks only at the two upper ends and semilandmarks in-between. Affine variation thus was not properly controlled. After BE sliding, the group differences comprised a lot of (meaningless) affine differences. I thus decided for minimizing Proc dist. Usually, though, I prefer minimizing BE because its is closer to our biological understanding of homology, including the preservation of landmark order and large scale shape features. Minimizing BE leads to smoother TPS deformation grids, whereas miminizing Proc dists leads to smaller sum of squares. Note that when updating the reference configuration in each iteration, the algorithm can converge to quite undesired minima (e.g. all semilandmarks collapse to a single point). This can be avoided by iterating just a few times, which is usually enough, or by keeping the reference constant at some point in the algorithm. In general, the more the semilandmarks are constrained by real landmarks and the smoother the curves, the more stable is the algorithm. Because of these issues, it is important to apply the semilandmark algorithm carefully, especially for 3D surfaces. Always check the tangents and how the semilandmarks slide along these tangents. Check how the total sliding reduces from one iteration to the next, and interpret the final pattern of shape variation in the light of the property being minimized. Best wishes, Philipp Mitteroecker Am Donnerstag, 18. Februar 2016 18:41:44 UTC+1 schrieb Collyer, Michael: > > Andrea, > > I like to think of semilandmark sliding as iteratively finding fitted > (predicted) values for the generalized linear model fit described by Gunz > et al. (2005) (equation 4), and updating coordinates by these values until > there is no more meaningful change (with regard to an acceptable > criterion). If Bending energy is not used, the bending energy matrix is > replaced by an identity matrix (i.e., independence), which produces the > minimized Procrustes distance version of the sliding algorithm. (This is > is the same as ordinary least squares being a simplification of generalized > least squares by using an identity matrix for the covariance matrix in GLS > estimation of parameters.) Calculating the bending energy matrix requires > using the reference configuration. The hat matrix calculated in the > process is typically post-multiplied by the target coordinates centered by > the reference configuration. Changing the reference should, therefore, > change the solution. Also, let’s not forget that with surface points, if > we follow the Gunz et al. (2005) recommendation, 5 nearest neighbors are > used to estimate the principal components for defining a tangent plane. > One could use more nearest neighbors, which would change the tangent > planes. One could also choose to project points after sliding back onto > the surface (by finding the nearest neighbor) or not. One could choose to > recursively update the reference configuration as the Procrustes average in > each iteration, or use a constant reference. One could also choose > different convergence criteria, depending on how precise the finished > product should be. This is all to say that there are several - perhaps > arbitrary - choices that can be made that will affect the results. > > Whether these nuances have an appreciable empirical effect, I’m not sure. > I doubt that shape distances would change “remarkably” (depending on one’s > definition of remarkable), but I think one cannot expect that subsampling > will produce the same Procrustes residuals that would be found from using > one inclusive sample. > > As you have indicated, the same thing happens with GPA performed on > “fixed” landmarks. The extent to which surface semilandmarks would be > similar or more susceptible to change is hard to argue without considering > whether bending energy is used, how many nearest neighbors are used, the > relative density of surface points, etc. This is probably a question to > answer empirically with specific data. (Get Procrustes residuals from the > full data, do it again with subsetted data, and maybe do a two-block PLS > analysis between two sets of matching specimens to see if there is any > appreciable change.) > > I would be curious to know what others think. I have been thinking about > this topic a lot, especially after dealing with the programming in > geomorph. I’m sure there are other perspectives. > > Mike > > Michael Collyer > > Associate Professor > Biostatistics > Department of Biology > Western Kentucky University > 1906 College Heights Blvd. #11080 > Bowling Green, KY 42101-1080 > Phone: 270-745-8765; Fax: 270-745-6856 > Email: michael...@wku.edu <javascript:> > > On Feb 18, 2016, at 11:03 AM, andrea cardini <alca...@gmail.com > <javascript:>> wrote: > > Mike, does this mean that, in general, the position of the semilandmarks > is strongly sample dependent, which would mean that also the shape > distances might change remarkably despite the fact one has the same number > of points on exactly the same surface? > Say that I have two samples, A and B. I first (1) superimpose (and slide) > within A. Then I do the same with both A and B together (2). Could I get > appreciable differences between A1 and A2 just because of the sliding? > > All Procrustes shape distances depend on the sample composition. However, > in my experience, differences between A1 and A2 tend to be negligible with > 'standard' landmarks. Is this different with semilandmarks? Are there > sensitivity analyses that explore the issue (if it's an issue)? > > Thanks in advance. > Cheers > > Andrea > > At 17:06 18/02/2016, Collyer, Michael wrote: > > Contrary to your logic, subsetting your sample could have an effect. Your > mean configuration would change in each of the subsamples, from the mean of > your original sample, thus changing the reference configuration used in the > separate GPAs performed. The reference configuration has a prominent role > in the sliding of landmarks. > > > > Dr. Andrea Cardini > Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di > Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy > tel. 0039 059 2058472 > > Adjunct Associate Professor, Centre for Forensic Science , The University > of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia > > E-mail address: alca...@gmail.com <javascript:>, andrea....@unimore.it > <javascript:> > WEBPAGE: https://sites.google.com/site/alcardini/home/main > > > FREE Yellow BOOK on Geometric Morphometrics: > http://www.italian-journal-of-mammalogy.it/issue/view/405 > or full volume at: > http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf > > Editorial board for: > Zoomorphology: > http://www.springer.com/life+sciences/animal+sciences/journal/435 > Journal of Zoological Systematics and Evolutionary Research: > http://www.wiley.com/bw/journal.asp?ref=0947-5745&site=1 > Hystrix, the Italian Journal of Mammalogy: > http://www.italian-journal-of-mammalogy.it/ > > > -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. 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