Description Usage Arguments Details Value Author(s) References See Also Examples

relax one specific landmark configuration against a reference (e.g. a sample mean)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | ```
relaxLM(lm, ...)
## S3 method for class 'matrix'
relaxLM(
lm,
reference,
SMvector,
outlines = NULL,
surp = NULL,
sur.name = NULL,
mesh = NULL,
tol = 1e-05,
deselect = FALSE,
inc.check = TRUE,
iterations = 0,
fixRepro = TRUE,
missing = NULL,
bending = TRUE,
stepsize = ifelse(bending, 1, 0.5),
use.lm = NULL,
silent = FALSE,
...
)
## S3 method for class 'mesh3d'
relaxLM(
lm,
reference,
tol = 1e-05,
deselect = FALSE,
inc.check = TRUE,
iterations = 0,
fixRepro = TRUE,
missing = NULL,
bending = FALSE,
stepsize = ifelse(bending, 1, 0.5),
use.lm = NULL,
silent = FALSE,
...
)
``` |

`lm` |
k x 3 or k x 2 matrix containing landmark data to be slidden - or a triangular mesh of class "mesh3d". See details |

`...` |
additonal arguments - currently unused |

`reference` |
k x 3 or k x 2 matrix containing landmark of the reference, or a mesh with the same amount of vertices as there are landmarks in |

`SMvector` |
A vector containing the row indices of (semi-) landmarks on the curve(s) that are allowed to slide |

`outlines` |
A vector (or if threre are several curves) a list of vectors (containing the rowindices) of the (Semi-)landmarks forming the curve(s) in the successive position on the curve - including the beginning and end points, that are not allowed to slide. |

`surp` |
integer vector containing the row indices of semi-landmarks positioned on surfaces. |

`sur.name` |
character: containing the filename of the corresponding
surface.When specified, mesh has to be NULL. If |

`mesh` |
triangular mesh of class "mesh3d" loaded into the R workspace, when specified, "sur.name" has to be NULL. |

`tol` |
numeric: Threshold for convergence in the sliding proces. Full Procrustes distance between actual result and previous iteration. |

`deselect` |
Logical: if TRUE, the SMvector is interpreted as those landmarks, that are not allowed to slide. |

`inc.check` |
Logical: if TRUE, the program stops when convergence criterion starts increasing and reports result from last iteration. |

`iterations` |
integer: maximum amounts the algorithm runs - even when 'tol' is not reached. When iterations=0, the algorithm runs until convergence. |

`fixRepro` |
logical: if |

`missing` |
vector of integers, specifying row indices of missing (semi-)landmarks. They will be relaxed freely in 3D and not projected onto the target (works only for 2D data). |

`bending` |
if TRUE, bending energy will be minimized, Procrustes distance otherwise (not suggested with large shape differences) |

`stepsize` |
integer: dampening factor for the amount of sliding.
Useful to keep semi-landmarks from sliding too far off the surface.
The displacement is calculated as |

`use.lm` |
indices specifying a subset of (semi-)landmarks to be used in the rotation step - only used if |

`silent` |
logical: if TRUE, console output is suppressed. |

if `lm`

is a surface mesh, all vertices will be treated as semilandmarks and a allowed to freely slide along the surface.

returns kx3 matrix of slidden landmarks

Stefan Schlager

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 | ```
require(rgl)
data(nose)
### relax shornose against longnose
# define fix landmarks
fix <- c(1:5,20:21)
# define surface patch by specifying row indices of matrices
# all except those defined as fix
surp <- c(1:dim(shortnose.lm)[1])[-fix]
relax <- relaxLM(shortnose.lm,
longnose.lm, mesh=shortnose.mesh, iterations=1,
SMvector=fix, deselect=TRUE, surp=surp)
## example minimizing Procrustes distance when displacement is not
## dampened by stepsize
relaxProcD <- relaxLM(shortnose.lm,
longnose.lm, mesh=shortnose.mesh, iterations=1,
SMvector=fix, deselect=TRUE, surp=c(1:623)[-fix],bending=FALSE,stepsize=1)
## Not run:
# visualize differences red=before and green=after sliding
deformGrid3d(shortnose.lm, relax, ngrid=0)
# visualize differences minimizing Procrusted distances red=before and green=after sliding
deformGrid3d(shortnose.lm, relaxProcD, ngrid=0)
## no smooth displacement, now let's check the distances:
rot2ref <- rotonto(relaxProcD,longnose.lm)
angle.calc(rot2ref$X,rot2ref$Y)
# 0.2492027 Procrustes distance between reference and slided shape
# (minimizing Procrustes distance)
rot2refBend <- rotonto(relax,longnose.lm)
angle.calc(rot2refBend$X,rot2refBend$Y)
# 0.2861322 Procrustes distance between reference and slided shape
# (minimizing bending energy)
rot2refOrig <- rotonto(shortnose.lm,longnose.lm)
angle.calc(rot2refOrig$X,rot2refOrig$Y)
# 0.3014957 Procrustes distance between reference and original shape
##result: while minimizing Procrustes distance, displacement is not
##guaranteed to be smooth
# add surface
wire3d(shortnose.mesh, col="white")
## finally relax two meshes with corresponding vertices:
mediumnose.mesh <- tps3d(shortnose.mesh,shortnose.lm, (shortnose.lm+longnose.lm)/2,threads=1)
## we use Procrustes distance as criterion as bending energy is pretty slow because
## of too many coordinates (more than 3000 is very unreasonable).
relaxMesh <- relaxLM(shortnose.mesh,mediumnose.mesh,iterations=2,bending=FALSE,stepsize=0.05)
## End(Not run)
``` |

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