JPLLK_surface {DRIP}

Jump-Preserving Local Linear Kernel Smoothing

Description

Estimate surface using piecewise local linear kernel smoothing. The bandwidth is chosen by leave-one-out cross validation.

Usage

JPLLK_surface(image, bandwidth, plot = FALSE)

Arguments

image

A square matrix, no missing value allowed.

bandwidth

A numeric vector of positive integers, which specifies the number of pixels used in the local smoothing. The final fitted surface uses the optimal bandwidth chosen from those provided by users.

plot

If plot = TRUE, the image of the fitted surface is plotted.

Details

At each pixel, the gradient is estimated by a local linear kernel smoothing procedure. Next, the local neighborhood is divided into two halves along the direction perpendicular to (\widehat{f}'_{x}, \widehat{f}'_{y}). Then the one- sided local linear kernel (LLK) estimates are obtained in the two half neighborhoods respectively. Among these two one-sided estimates, the one with smaller weighted mean square error is chosen to be the final estimate of the regression surface at the pixel.

Value

A list of fitted values, residuals, chosen bandwidth and estimated sigma.

References

Qiu, P. (2009) "Jump-Preserving Surface Reconstruction from Noisy Data", Annals of the Institute of Statistical Mathematics, 61(3), 715 – 751, doi:10.1007/s10463-007-0166-9.

See Also

threeStage, surfaceCluster

Examples

data(sar) # SAR image is bundled with the package and it is a 
          # standard test image in statistics literature.
fit <- JPLLK_surface(image=sar, bandwidth=c(3, 4))