-------- Original Message -------- Subject: Re: 3D Covariance Matrix computing Date: Wed, 11 Jan 2012 15:04:02 -0500 From: Chris Klingenberg <[email protected]> Reply-To: [email protected] Organization: University of Manchester To: [email protected] Dear Bash It's all done the standard way. There is one choice that differs between various software packages: MorphoJ is using the full (rather than partial) Procrustes fit (with real biological data, the difference is usually very small). The best place to get formulas is this book: Dryden IL, Mardia KV. 1998. Statistical shape analysis. Chichester: Wiley. So for your formulas: 1. The covariance matrix is computed as usual in multivariate statistics, just with the Procrustes tangent coordinates in the data matrix (formula (4.35) in Dryden & Mardia 1998). For the covariance matrix itself, you can get the formulas from any textbook on multivariate statistics, e.g. Mardia et al. (1979), formulas (1.4.7) and (1.4.9) -- the latter is to use (n-1) in the denominator. There is no differemce in principle between 2D or 3D data -- just the data matrix differs, as there are 2 or 3 columns per landmark. (Reference: Mardia KV, Kent JT, Bibby JM. 1979. Multivariate analysis. London: Academic Press.) 2. Procrustes sum of squares: see expression (5.18) in Dryden & Mardia (1998). This is the same as the sum of squared Procrustes distances of all configuration from the full Procrustes mean. 3. Tangent sum of squares -- I can't find the formula at the moment. It's the sum of squared Euclidean distances of the tangent coordinates of all configurations to the full Procrustes mean. Best wishes, Chris On 1/11/2012 5:56 PM, morphmet wrote:
-------- Original Message -------- Subject: 3D Covariance Matrix computing Date: Wed, 11 Jan 2012 12:13:47 -0500 From: Bachar Cheaib <[email protected]> To: [email protected] Dear Morphometricians, I am user of MORPHOJ Please could you tell me how this software compute : 1- Covariance matrix in MorphoJ in case of three dimensions (X Y Z) ? 2- Procrustes sums of squares ? 3- Tangent sums of squares ? In other words which formulas are being used ? Best wishes for this year Bash On Thu, Dec 15, 2011 at 9:35 PM, morphmet <[email protected] <mailto:[email protected]>> wrote: -------- Original Message -------- Subject: color vs. shape group coding using morphoJ Date: Thu, 15 Dec 2011 13:22:21 -0500 From: Daniel Arranaga <[email protected] <mailto:[email protected]>> To: [email protected] <mailto:[email protected]> Dear Morphmetricians, I am currently using MorphoJ to analyze my dataset. My dietary groups are color coded but I need them coded by shape (triangle, square, circle) so that I can print out my graphs in black and white. Can this be done in MorphoJ or is there another shape analysis software that allows for this? Thank you, Daniel Arrañaga
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