y contains the observed response data. dim(y) determines the dimensionality and extend of the grid design.
level
center of second class
delta
half width of second class
hmax
hmax specifies the maximal bandwidth. Defaults to hmax=250, 12, 5 for dd=1, 2, 3, respectively.
hpre
Describe hpre Bandwidth used for an initial nonadaptive estimate. The first estimate
of variance parameters is obtained from residuals with respect to this estimate.
varmodel
Implemented are "Constant", "Linear" and "Quadratic" refering to a polynomial model of degree 0 to 2.
lkern
character: location kernel, either "Triangle", "Plateau", "Quadratic", "Cubic" or "Gaussian"
scorr
The vector scorr allows to specify a first order correlations of the noise for each coordinate direction,
defaults to 0 (no correlation).
ladjust
factor to increase the default value of lambda
wghts
wghts specifies the diagonal elements of a weight matrix to adjust for different distances between grid-points
in different coordinate directions, i.e. allows to define a more appropriate metric in the design space.
u
a "true" value of the regression function, may be provided to
report risks at each iteration. This can be used to test the propagation condition with u=0
varprop
Small variance estimates are replaced by varprop times the mean variance.
ext
Intermediate results are fixed if the test statistics exceeds the critical value by ext.
graph
If graph=TRUE intermediate results are illustrated after each iteration step. Defaults to graph=FALSE.
demo
If demo=TRUE the function pauses after each iteration. Defaults to demo=FALSE.
fov
Field of view. Size of region (sample size) to adjust for in multiscale testing.
Details
The image is segmented into three parts by performing multiscale tests
of the hypotheses H1
value >= level - delta and H2 value <= level + delta.
Pixel where the first hypotesis is rejected are classified as -1 (segment 1)
while rejection of H2 results in classification 1 (segment 3).
Pixel where neither H1 or H2 are rejected ar assigned to a value 0 (segment 2). Critical values for the tests are adjusted for smoothness at the different scales inspected in the iteration process using results from multiscale testing,
see e.g. Duembgen and Spokoiny (2001). Critical values also depend on the
size of the region of interest specified in parameter fov.
Within segment 2 structural adaptive smoothing is performed while if a pair of pixel belongs to segment 1 or segment 3 the corresponding weight will be nonadaptive.
Value
returns anobject of class aws with slots
y = "numeric"
y
dy = "numeric"
dim(y)
x = "numeric"
numeric(0)
ni = "integer"
integer(0)
mask = "logical"
logical(0)
segment = "integer"
Segmentation results, class numbers 1-3
theta = "numeric"
Estimates of regression function, length: length(y)
mae = "numeric"
Mean absolute error for each iteration step if u was specified, numeric(0) else
var = "numeric"
approx. variance of the estimates of the regression function. Please note that this does not reflect variability due to randomness of weights.
xmin = "numeric"
numeric(0)
xmax = "numeric"
numeric(0)
wghts = "numeric"
numeric(0)
degree = "integer"
0
hmax = "numeric"
effective hmax
sigma2 = "numeric"
provided or estimated error variance
scorr = "numeric"
scorr
family = "character"
"Gaussian"
shape = "numeric"
NULL
lkern = "integer"
integer code for lkern,
1="Plateau", 2="Triangle", 3="Quadratic", 4="Cubic", 5="Gaussian"
lambda = "numeric"
effective value of lambda
ladjust = "numeric"
effective value of ladjust
aws = "logical"
aws
memory = "logical"
memory
homogen = "logical"
FALSE
earlystop = "logical"
FALSE
varmodel = "character"
varmodel
vcoef = "numeric"
estimated parameters of the variance model
call = "function"
the arguments of the call to aws.gaussian
Note
This function is still experimental and may be changes considerably in future.
Duembgen, L. and Spokoiny, V. (2001). Multiscale testing of qualitative hypoteses. Ann. Stat. 29, 124–152.
Polzehl, J. and Spokoiny, V. (2006). Propagation-Separation Approach for Local
Likelihood Estimation. Probability Theory and Related Fields. 3 (135)
335 - 362.