awsimage {adimpro}  R Documentation 
This functions implement the PropagationSeparation approach
(local constant and local polynomial model) for smoothing images.
Function awsaniso
uses anisotropic location weights. This is done by evaluating local gradient estimates obtained from the actual estimated color values.
awsimage(object, hmax=4, aws=TRUE, varmodel=NULL, ladjust=1.25, mask=NULL, xind = NULL, yind = NULL, wghts=c(1,1,1,1), scorr=TRUE, lkern="Plateau", plateau=NULL, homogen=TRUE, earlystop=TRUE, demo=FALSE, graph=FALSE, max.pixel=4.e2, clip = FALSE, compress=TRUE) awspimage(object, hmax=12, aws=TRUE, degree=1, varmodel = NULL, ladjust=1.0, xind = NULL, yind = NULL, wghts=c(1,1,1,1), scorr= TRUE, lkern="Plateau", plateau=NULL, homogen=TRUE, earlystop=TRUE, demo=FALSE, graph=FALSE, max.pixel= 4.e2, clip = FALSE, compress=TRUE) awsaniso(object, hmax = 4, g = 3, rho = 0, aws = TRUE, varmodel = NULL, ladjust = 1, xind = NULL, yind = NULL, wghts = c(1, 1, 1, 1), scorr = TRUE, lkern = "Triangle", demo = FALSE, graph = FALSE, satexp = 0.25, max.pixel = 400, clip = FALSE, compress = TRUE)
object 
Image object, class "adimpro", as from

hmax 
Maximum bandwidth to use in the iteration procedure. 
g 
Bandwidth for anisotropic smoothing gradient estimates,
preferably g >= 3 for images with line type texture and small
g approx 1 for improving edges between homogeneous regions (function 
rho 
Regularization parameter for anisotropic smoothing gradient estimates,
preferably rho = 0 for images with line type texture and large
rho approx 3 for improving edges between homogeneous regions. (function 
aws 
(logical). If 
degree 
Degree of the local polynomial model for

varmodel 

ladjust 
adjustment factor for lambda (>=1). Default values for
lambda are selected for Gaussian distributions and default settings of
parameters 
mask 
logical array of the same size as the image or

xind, yind 
Restrict smoothing to rectangular area defined by pixel
indices 
wghts 
allows to weight the information from
different (up to 4) color channels. The weights are used in the
statistical penalty of the PSprocedure. Note that lambdavalues are selected for 
scorr 
(logical). Specifies whether spatial correlation is to be
estimated. Defaults to 
lkern 
Specifies the location kernel. Defaults to "Triangle", other choices are "Quadratic", "Cubic" and "Uniform". The use of "Triangle" corresponds to the Epanechnicov kernel nonparametric kernel regression. 
plateau 
Extension of the plateau in the statistical kernel. Can take
values from (0,1), defaults to 
homogen 
If TRUE the algorithm determines, in each design point i, a circle of maximum radius,
such that the statistical penalty 
earlystop 
If TRUE the algorithm determines, in each design point i, a circle of minimal radius,
such that the circle includes all point j with positive weights 
demo 
(logical). If 
graph 
(logical). If 
max.pixel 
Maximum dimension of images for display
if 
satexp 
exponent used for scaling saturation in anisotropy visualization (function 
clip 
(logical). If 
compress 
logical, determines if image data are stored in rawformat. 
The function implements the PropagationSeparation (PS) approach to nonparametric smoothing (formerly introduced as Adaptive Weights Smoothing) for varying coefficient likelihood (awsimage) and local polynomial (awspimage) models for greyscale and color images.
The distribution of grey (color) values is considered to be Gaussian. Noise can be colored.
The numerical complexity of the procedure is mainly determined by
hmax
. The number of iterations is 2*log(hmax)/log(1.25)
.
Comlexity in each iteration step is Const*hakt*n
with hakt
being the actual bandwith in the iteration step and n
the number of pixels.
hmax
determines the maximal possible variance reduction.
All other parameters of the approach only depend on the specified
values for skern/lkern
and are therefore set internally to
meaningful default values.
For a detailed description of the procedure see references below.
The script used to control the values of parameter lambda
is stored in
directory inst/adjust.
Object of class "adimpro"
img 
Contains the reconstructed image. 
ni 
Contains the sum of weights, i.e. 
ni0 
Contains the maximum sum of weights for an nonadaptive kernel estimate with the same bandwidth. 
hmax 
Bandwidth used in the last iteration. 
call 
The arguments of the function call. 
varcoef 
Estimated coefficients in the variance model for the
color channels, if 
wghts 
The weights used for the color channels. 
scorr 
Estimated spatial correlations for each channel, if 
chcorr 
Estimated correlations between
color channels, if 
Karsten Tabelow tabelow@wiasberlin.de and Joerg Polzehl polzehl@wiasberlin.de
Polzehl and Spokoiny (2006). PropagationSeparation Approach for Local Likelihood Estimation. Probability Theory and Related Fields. 3 (135) 335  362.
Polzehl and Spokoiny (2005). Structural adaptive smoothing adaptive smoothing by PropagationSeparationmethods. WIASPreprint No. 1068.
Polzehl, J. and Tabelow, K. (2007). Adaptive smoothing of digital images, Journal of Statistical Software 19 (1).
read.image
, read.raw
, make.image
, show.image
, clip.image
## Not run: demo(awsimage)