awsimage {adimpro}R Documentation

Propagation-Separation approach for smoothing of 2D images

Description

This functions implement the Propagation-Separation 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.

Usage

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="Triangle", 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="Triangle", 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)

Arguments

object Image object, class "adimpro", as from read.image, read.raw, or make.image.
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 awsaniso only).
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 awsaniso only)
aws (logical). If TRUE the propagation - separation (PS) approach from Polzehl and Spokoiny (2006) is used. aws=FALSE turns off the statistical penalty resulting in a nonadaptive kernel estimate using a kernel with bandwidth hmax.
degree Degree of the local polynomial model for awspimage. 0, 1, or 2 only.
varmodel varmodel specifies how variances are to be estimated. This can be a homogeneous variance estimate (varmodel="None") assuming uncorrelated errors (both spatial and between channels). Alternatives are an adaptive homogeneous or linear (function of the mean) variance estimate that depends on estimated correlations and on residuals from the last iteration step. The default varmodel=NULL corresponds to varmodel == "Linear" if img$gamma==FALSE and varmodel == "Constant" otherwise.
ladjust adjustment factor for lambda (>=1). Default values for lambda are selected for Gaussian distributions. Skewed or heavy tailed distributions may require slightly larger values for lambda to meet the propagation condition. ladjust allows to increase lambda in such situations.
mask logical array of the same size as the image or NULL (default). Smoothing is restricted to the smallest rectangle including all pixel where mask==TRUE and restricts computations to these pixel. This need not be a connected area (Typical usage: smooth all bright regions)! Only used if is.null(xind) && is.null(yind). Inactive if mask==NULL. Can only be used if varmodel="None".
xind, yind Restrict smoothing to rectangular area defined by pixel indices xind,yind in x- and y-direction. Full range if NULL (default).
wghts allows to weight the information from different (up to 4) color channels. The weights are used in the statistical penalty of the PS-procedure.
scorr (logical). Specifies whether spatial correlation is to be estimated. Defaults to TRUE. Is set to FALSE if mask is not NULL.
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 0.25.
homogen If TRUE the algorithm determines, in each design point i, a circle of maximum radius, such that the statistical penalty s_{ij} for all points j within the circle is less than the value specified in plateau. In subsequent iteration steps the statistical penalty for such points is set to zero. This is only used if plateau>0. This results in more stable intermediate estimates and in a smoother reconstruction. homogen=TRUE leads to increased memory requirements.
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 w_{ij}. if this radius is considerably smaller than the actual bandwidth then the estimate in point i is fixed. This should considarably reduce computing time in case of large hmax.earlystop=TRUE slightly increases memory requirements.
demo (logical). If demo=TRUE the function pauses after each iteration. Defaults to FALSE.
graph (logical). If graph=TRUE intermediate results are illustrated after each iteration step. Defaults to FALSE.
max.pixel Maximum dimension of images for display if graph=TRUE. If the true dimension is larger, the images are downscaled for display. See also show.image.
satexp exponent used for scaling saturation in anisotropy visualization (function awsaniso only)
clip (logical). If TRUE a clipping region is selected, see clip.image, using the information contained in xind or yind. If both are NULL a clipping region can be defined by left mouse clicks. The image object is reduced to the clipping region before smoothing.
compress logical, determines if image data are stored in raw-format.

Details

The function implements the Propagation-Separation (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.

Value

Object of class "adimpro"

img Contains the reconstructed image.
ni Contains the sum of weights, i.e. trace(W_i), in all grid points i.
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 varmodel is "Constant" or "Linear".
wghts The weights used for the color channels.
scorr Estimated spatial correlations for each channel, if scorr=TRUE
chcorr Estimated correlations between color channels, if scorr=TRUE

Author(s)

Karsten Tabelow tabelow@wias-berlin.de and Joerg Polzehl polzehl@wias-berlin.de

References

Polzehl and Spokoiny (2006). Propagation-Separation Approach for Local Likelihood Estimation. Probability Theory and Related Fields. 3 (135) 335 - 362.

Polzehl and Spokoiny (2005). Structural adaptive smoothing index{adaptive smoothing} by Propagation-Separation-methods. WIAS-Preprint No. 1068.

Polzehl, J. and Tabelow, K. (2007). Adaptive smoothing of digital images, Journal of Statistical Software 19 (1).

See Also

read.image, read.raw, make.image, show.image, clip.image

Examples

## Not run: demo(awsimage)

[Package adimpro version 0.7.1 Index]