| Title: | Geometric Morphometric Tools for Paleobiology |
|---|---|
| Description: | Fill missing symmetrical data with mirroring, calculate Procrustes alignments with or without scaling, and compute standard or vector correlation and covariance matrices (congruence coefficients) of 3D landmarks. Tolerates missing data for all analyses. |
| Authors: | Tim Lucas, Anjali Goswami |
| Maintainer: | Tim Lucas <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 0.1.4 |
| Built: | 2025-01-26 05:41:36 UTC |
| Source: | https://github.com/timcdlucas/paleomorph |
Count the number of missing landmarks in an array
countMissing(A)countMissing(A)
A |
An N x 3 x M array where N is the number of landmarks, 3 is the number of dimensions, and M is the number of specimens. |
A length n vector giving the number of missing landmarks for each specimen.
A <- array(1:(3*6*7), dim = c(7, 3, 6)) A[2, , 1] <- NA countMissing(A)A <- array(1:(3*6*7), dim = c(7, 3, 6)) A[2, , 1] <- NA countMissing(A)
Calculate covariance matrix between individual landmark coordinates. Skips any missing values in computation of covariance matrix.
covar(A)covar(A)
A |
An N x 3 x M array where N is the number of landmarks, 3 is the number of dimensions, and M is the number of specimens. |
This function does not guarantee that the returned matrix is
positive definite. If the covariance matrix is not positive definite
a warning is given and the matrix can be bent to create the closest
positive definite matrix with as.matrix(Matrix::nearPD(mat)$mat).
3N x 3N covariance matrix
A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) A.cov <- covar(A)A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) A.cov <- covar(A)
Calculate 3D vector correlation matrix using the congruence coefficient. Skips any missing values in computation of correlation matrix. Gives an N x N correlation matrix.
dotcorr(A)dotcorr(A)
A |
An N x 3 x M array where N is the number of landmarks, 3 is the number of dimensions, and M is the number of specimens. |
Correlation matrix
A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) A.corr <- dotcorr(A)A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) A.corr <- dotcorr(A)
Calculate 3D covariance matrix using unscaled congruence coefficient. Skips any missing values in computation of covariance matrix
dotcvm(A)dotcvm(A)
A |
An N x 3 x M array where N is the number of landmarks, 3 is the number of dimensions, and M is the number of specimens. |
This function does not guarantee that the returned matrix is
positive definite. If the covariance matrix is not positive definite
a warning is given and the matrix can be bent to create the closest
positive definite matrix with as.matrix(Matrix::nearPD(mat)$mat).
N x N covariance matrix
A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) A.cvm <- dotcvm(A)A <- array(rnorm(4 * 2 * 3), dim = c(2, 3, 4)) A.cvm <- dotcvm(A)
Given an N x 3 x M matrix, where N is the number of landmarks, 3 is the number of dimensions, and M is the number of specimens, fill in missing landmarks using their mirrored counterpart.
mirrorfill(A, l1, l2)mirrorfill(A, l1, l2)
A |
An N x 3 x M matrix where N is the number of landmarks, 3 is the number of dimensions, and M is the number of specimens. |
l1 |
Vector of indices for which landmarks to use to make a specimen midline |
l2 |
Vector or matrix of pairs of symmetrical landmarks |
l2 should be either
An even length vector containing pairs of landmarks on either side of the specimen. i.e. l2[1] and l2[2] are paired, l2[3] and l2[4] are paired etc.
A two column matrix with each row giving a pair of symmetrical landmarks.
l2 should be an even number length containing pairs of landmarks
on either side of the specimen.
# Create array A <- array(rep(1:36, by = 4), dim = c(12, 3, 4)) # Make it symmetrical A[7:12, 1:2, ] <- A[1:6, 1:2, ] A[7:12, 3, ] <- -A[1:6, 3, ] # Remove some data points missinga <- A missinga[1:2, , 1:3] <- NA mirrorA <- mirrorfill(missinga, l1 = c(3:6, 9:12), l2 = c(1, 7, 2, 8))# Create array A <- array(rep(1:36, by = 4), dim = c(12, 3, 4)) # Make it symmetrical A[7:12, 1:2, ] <- A[1:6, 1:2, ] A[7:12, 3, ] <- -A[1:6, 3, ] # Remove some data points missinga <- A missinga[1:2, , 1:3] <- NA mirrorA <- mirrorfill(missinga, l1 = c(3:6, 9:12), l2 = c(1, 7, 2, 8))
Given an n x 3 matrix, replace a set of landmarks using their mirrored counterpart.
mirrorfill1(s, l1, l2)mirrorfill1(s, l1, l2)
s |
An n x 3 matrix containing 3D landmark data of n landmarks. |
l1 |
Vector of indices for which landmarks to use to make a specimen midline. |
l2 |
Vector or matrix of pairs of symmetrical landmarks. |
l2 should be either
An even length vector containing pairs of landmarks on either side of the specimen. i.e. l2[1] and l2[2] are paired, l2[3] and l2[4] are paired etc.
A two column matrix with each row giving a pair of symmetrical landmarks.
# Make data that is reflected in x plane s <- matrix(rep(1:21, 2), byrow = TRUE, ncol = 3) s[1:7, 1] <- -s[1:7, 1] # Now remove some data s[1, ] <- NA # Mirror point 1 using it's complimentary landmark, point 8. mirrorS <- mirrorfill1(s, l1 = c(2:7, 9:14), l2 = c(1, 8))# Make data that is reflected in x plane s <- matrix(rep(1:21, 2), byrow = TRUE, ncol = 3) s[1:7, 1] <- -s[1:7, 1] # Now remove some data s[1, ] <- NA # Mirror point 1 using it's complimentary landmark, point 8. mirrorS <- mirrorfill1(s, l1 = c(2:7, 9:14), l2 = c(1, 8))
This function requires the rgl package. Given a N x 3 x M array (where M is the number of specimens and N is the number of landmarks), as used elsewhere in this package, plot each specimen in a different colour in an intereactive 3D frame.
plotSpecimens(A, l1 = NULL, midlineSpecimens = NULL, cols = NULL, bySpecimen = TRUE, planeOptions = NULL, ...)plotSpecimens(A, l1 = NULL, midlineSpecimens = NULL, cols = NULL, bySpecimen = TRUE, planeOptions = NULL, ...)
A |
An N x 3 x M array. |
l1 |
Optional vector of indices for which landmarks to use to make a specimen midline. If NULL, no midline plane is plotted. |
midlineSpecimens |
Numeric vector indicating which specimens should be used to built the midline plane. If NULL, but l1 is defined, all specimens are used. |
cols |
A vector of colours. |
bySpecimen |
Logical that determined whether points should be coloured by specimen (default) or by landmark. |
planeOptions |
Named list of parameters passed to |
... |
Further parameters passed to |
plot3d mirrorfill planes3d rgl.material
A <- array(rep(rnorm(3 * 20, sd = 30), by = 6) + rnorm(6 * 20 * 3), dim = c(20, 3, 6)) plotSpecimens(A) plotSpecimens(A, bySpecimen = FALSE) plotSpecimens(A, cols = grey(seq(0, 1, length.out = 6))) plotSpecimens(A, l1 = c(1:4), planeOptions = list(alpha = 0.4, color = 'red'))A <- array(rep(rnorm(3 * 20, sd = 30), by = 6) + rnorm(6 * 20 * 3), dim = c(20, 3, 6)) plotSpecimens(A) plotSpecimens(A, bySpecimen = FALSE) plotSpecimens(A, cols = grey(seq(0, 1, length.out = 6))) plotSpecimens(A, l1 = c(1:4), planeOptions = list(alpha = 0.4, color = 'red'))
Conducts Procrustes superimposition to align 3D shapes with or without scaling to centroid size. Skips any missing values in computation of Procrustes coordinates.
procrustes(A, scale = TRUE, scaleDelta = FALSE, maxiter = 1000, tolerance = 1e-05)procrustes(A, scale = TRUE, scaleDelta = FALSE, maxiter = 1000, tolerance = 1e-05)
A |
N x 3 x M matrix where N is the number of landmarks, 3 is the number of dimensions, and M is the number of specimens |
scale |
Logical indicating whether objects should be scaled to unit centroid size |
scaleDelta |
Logical determining whether deltaa should be scaled by the total number of landmarks. |
maxiter |
Maximum number of iterations to attempt |
tolerance |
Difference between two iterations that will cause the search to stop. |
A number of computations are run until the difference between two iterations is less than tolerance.
The more specimens and landmarks you have, the less each landmark is allowed to move before this tolerance
is reached. Setting scaleDelta = TRUE will make the alignment run faster but have potentially less
well aligned results. But the alignment between a large and small array of shapes should be more comparable
with scaleDelta = TRUE. However, preliminary tests imply that run time scales linearly with
scaleDelta set to TRUE or FALSE.
A new (N x 3 x M) array, where each 3d vector has been rotated and translated to minimize distances among specimens, and scaled to unit centroid size if requested.
# Make an array with 6 specimens and 20 landmarks A <- array(rep(rnorm(6 * 20, sd = 20), each = 6) + rnorm(20 * 3 * 6 ), dim = c(20, 3, 6)) # Align the data (although it is already largely aligned) aligned <- procrustes(A) plotSpecimens(aligned)# Make an array with 6 specimens and 20 landmarks A <- array(rep(rnorm(6 * 20, sd = 20), each = 6) + rnorm(20 * 3 * 6 ), dim = c(20, 3, 6)) # Align the data (although it is already largely aligned) aligned <- procrustes(A) plotSpecimens(aligned)