Different symmetric component from bilat.symmetry (geomorph) and procSym (Morpho)

[YW]

Dear all,

I want to extract symmetric component from GPA of an object with object symmetry. I tried both bilat.symmetr in geomorph and procSym in Morpho. I get some confusing results.

library(Morpho)

library(geomorph)

data(boneData)

left <- c(4,6,8)

right <- c(3,5,7)

pairedLM <- cbind(left,right)

gpa <- bilat.symmetry(boneLM, object.sym = T, land.pairs = pairedLM, ind = 1:dim(boneLM)[3])

gpa$symm.shape[,,1]

             [,1]          [,2]         [,3]

 [1,]  0.34732242  2.407271e-17 -0.016892962

 [2,]  0.39146334  4.599880e-17 -0.005335477

 [3,]  0.35596324 -4.638598e-02  0.033862782

 [4,]  0.35596324  4.638598e-02  0.033862782

 [5,] -0.27746925 -7.299494e-02  0.018315568

 [6,] -0.27746925  7.299494e-02  0.018315568

 [7,] -0.24952878 -1.218970e-01  0.037420485

 [8,] -0.24952878  1.218970e-01  0.037420485

 [9,] -0.35308247 -6.961152e-17 -0.018107224

[10,] -0.04363372 -1.809286e-16 -0.138862006

As expected, gpa$symm.shape[3,,1] and gpa$symm.shape[4,,1] differ in sign of just one of the x, y, and z values. The same holds for gpa$symm.shape[5,,1] and gpa$symm.shape[6,,1] and gpa$symm.shape[7,,1] and gpa$symm.shape[8,,1]. However, I tried Morpho as follows:

symproc <- procSym(boneLM, pairedLM=pairedLM)

symcomp <- symproc$Sym

symproc$Sym[,,1]

             [,1]         [,2]         [,3]

 [1,]  0.34726918  0.003217396 -0.016493259

 [2,]  0.39143154  0.001908742 -0.005116181

 [3,]  0.35584408  0.042833306  0.039658115

 [4,]  0.35613939 -0.049164282  0.027929753

 [5,] -0.27767625  0.069233709  0.027278709

 [6,] -0.27721126 -0.075616014  0.008812477

 [7,] -0.24989503  0.115440171  0.052299968

 [8,] -0.24911854 -0.126445769  0.021463038

 [9,] -0.35325588  0.001177840 -0.018133798

[10,] -0.04352722  0.017414901 -0.137698822

This time, symproc$Sym[3,,1] and symproc$Sym[4,,1] no longer differ just by sign of one of x, y, and z values. I would like to ask what on earth is being extracted from symproc$Sym (symmetric component after GPA in Morpho) and how does it differ from gpa$symm.shape (symmetric component after GPA in geomorph)?

Thank you!

YW

[Murat Maga]

The sign flip would only hold if the axis of symmetry coincides with primary axis of image.
Perhaps when procSym is superimposing the samples, the arbitrary rotations results in a different coordinate system that doesn't coincide with axis of symmetry. That's really a Morpho question.

You may want to try setting pcAlign option to False and retry.