Create Matrices necessary for Thin-Plate Spline
Create (Bending Engergy) Matrices necessary for Thin-Plate Spline, and sliding of Semilandmarks
CreateL(matrix, lambda = 1e-08, output = c("K", "L", "Linv", "Lsubk",
"Lsubk3"), threads = 1)matrix |
k x 3 or k x 2 matrix containing landmark coordinates. |
lambda |
numeric: regularization factor |
output |
character vector: select which matrices to create. Can be a vector containing any combination of the strings: |
threads |
threads to be used for parallel execution calculating K. sliding of semilandmarks. |
depending on the choices in output:
.
This function is not intended to be called directly - except for playing around to grasp the mechansims of the Thin-Plate Spline.
Gunz, P., P. Mitteroecker, and F. L. Bookstein. 2005. Semilandmarks in Three Dimensions, in Modern Morphometrics in Physical Anthropology. Edited by D. E. Slice, pp. 73-98. New York: Kluwer Academic/Plenum Publishers.
Bookstein FL. 1989. Principal Warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on pattern analysis and machine intelligence 11(6).
data(boneData) L <- CreateL(boneLM[,,1]) ## calculate Bending energy between first and second specimen: be <- t(boneLM[,,2])%*%L$Lsubk%*%boneLM[,,2] ## calculate Frobenius norm sqrt(sum(be^2)) ## the amount is dependant on on the squared scaling factor # scale landmarks by factor 5 and compute bending energy matrix be2 <- t(boneLM[,,2]*5)%*%L$Lsubk%*%(boneLM[,,2]*5) sqrt(sum(be2^2)) # exactly 25 times the result from above ## also this value is not symmetric: L2 <- CreateL(boneLM[,,2]) be3 <- t(boneLM[,,1])%*%L2$Lsubk%*%boneLM[,,1] sqrt(sum(be3^2))
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