Hi all, I just stumbled across this discussion a bit too late, so I am joining the party after everybody has left.
> 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. As Philipp wrote, this can really make the difference for problematic cases (and especially when minimizing ProcD: even with reprojection, this can lead to distorted shapes if the coordinates have slid away on the tangent planes to find a minimum) For those who want to test the effect: In Morpho::slider3d you can control this dampening by specifying stepsize (e.g. to 0.2 according to Philipps example). Best Stefan On 18/02/16 21:18, mitte...@univie.ac.at wrote: > > 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 >> <https://sites.google.com/site/alcardini/home/main> >> >> >> FREE Yellow BOOK on Geometric Morphometrics: >> http://www.italian-journal-of-mammalogy.it/issue/view/405 >> <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 >> >> <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 >> <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 >> <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/ >> <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. > To unsubscribe from this group and stop receiving emails from it, send > an email to morphmet+unsubscr...@morphometrics.org > <mailto:morphmet+unsubscr...@morphometrics.org>. -- 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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