smooth3D {aws}  R Documentation 
smooth3D
and medianFilter3D
are auxiliary functions for nonadaptive
smoothing of 3D image data using kernel or median smoothing. Both function restrict
to subareas determined by a mask. The functions are used in packages dti
and
qMRI
.
Functions aws3Dmask
and aws3Dmaskfull
perform adaptive weights smoothing on
statistical parametric maps in fMRI. Variability of results is determined from smoothed
(using the same weighting schemes) residuals in order to correctly account for spatial
correlation. These functions are intended to be used internally in package fmri
.
They have been moved here because they share significant parts of the
openMP parallelized Fortran code underlying function aws
.
smooth3D(y, h, mask, lkern = "Gaussian", weighted = FALSE, sigma2 = NULL, wghts = NULL) medianFilter3D(y, h = 10, mask = NULL) aws3Dmask(y, mask, lambda, hmax, res = NULL, sigma2 = NULL, lkern = "Gaussian", skern = "Plateau", weighted = TRUE, u = NULL, wghts = NULL, h0 = c(0, 0, 0), testprop = FALSE) aws3Dmaskfull(y, mask, lambda, hmax, res = NULL, sigma2 = NULL, lkern = "Gaussian", skern = "Plateau", weighted = TRUE, u = NULL, wghts = NULL, testprop = FALSE)
y 
3D array of data in case of functions 
lkern 
character: location kernel, either "Triangle", "Plateau", "Quadratic", "Cubic" or "Gaussian". The default "Triangle" is equivalent to using an Epanechnikov kernel, "Quadratic" and "Cubic" refer to a Biweight and Triweight kernel, see Fan and Gijbels (1996). "Gaussian" is a truncated (compact support) Gaussian kernel. This is included for comparisons only and should be avoided due to its large computational costs. 
weighted 
logical: use inverse variances as weights. 
sigma2 

mask 
optional logical mask, same dimensionality as 
h 
bandwidth to use. In case of 
wghts 
voxel dimensions. Defaults to 
lambda 
kritical scale parameter in hypothesis testing (adaptive weights smoothing) 
hmax 
maximum bandwidth for adaptive weights smoothing 
res 
array of residuals with dimension 
skern 

u 
For test purposes in simulations: noisless 3D data. 
h0 
Vector of 3 bandwidths corresponding to a Gaussian kernel that would produce a comparable spatial correlation by convoluting iid data. 
testprop 
logical: test the validity of a propagation condition for the specified value of 
Functions smooth3D
and medianFilter3D
return a 3D array.
Functions awsmask*
return a list with smoothed values of y
in
component theta
and smoothed residuals in component res
.
Functions awsmask*
are used intenally in package fmri
. They refer to the
situation, typical for fMRI, where the data are spatially correlated and this correlation
can be accessed using residuals with respect to a model.
Joerg Polzehl polzehl@wiasberlin.de, Karsten Tabelow tabelow@wiasberlin.de