Select the bandwidth parameter for the function
surfaceCluster using cross validation. In the
cases when there is no blur involved (i.e., denoising only),
leave-one-out cross validation is used. In the cases when there
is blur involved, a modified cross validation is used.
surfaceCluster_bandwidth(image, bandwidths, sig.level, sigma,
phi0, mean_std_abs, relwt = 0.5, cw = 3, blur = FALSE)A list: 'cv_dataframe', a data frame containing the cross validation scores corresponding to each candidate bandwidth, 'bandwidth_hat', the selected bandwidth, 'sigma', the estimated standard deviation of the random error, 'phi0', the estimated density of the error distribution at 0, and 'mean_std_abs', the estimated absolute mean of the error distribution.
A square matrix, no missing value allowed.
An array of positive integers that specifies the candidate bandwidth parameters. All the array elements must be positive integers because the bandwidth is specified in terms of number of pixels.
The significance level for the hypothesis test deciding whether to cluster pixels or not.
The noise level (i.e., standard deviation of the error distribution). It is used for computing the asymptotic threshold for residuals, which are defined to be the difference between the local linear kernel smoothing output and the center weighted median filter output. If not specified by the user, a jump-preserving local linear kernel smoothing surface estimation (Qiu 2009) is used to obtain an estimated sigma.
The density of the standardized error distribution at 0. It is used for computing the asymptotic threshold for residuals, whose definition is given above. If not specified by the user, a jump-preserving local linear kernel smoothing surface estimation (Qiu 2009) is used to obtain an estimated value.
The mean of absolute value of the standardized error. It is used for computing the asymptotic threshold for residuals, whose definition is given above. If not specified by the user, a jump-preserving local linear kernel smoothing surface estimation (Qiu 2009) is used to obtain an estimated value.
The relative weight assigned to the cross validation score in the continuity region. That is, 1 - relwt is assigned to the cross validation score around the step edges. It is used only when there is blur involved.
The center weight for the center weighted median filter. It must be a positive integer.
If blur = TRUE, besides a conventional 2-D kernel function, a univariate increasing kernel function is used in the local kernel smoothing to address the issue with blur.
Yicheng Kang
Kang, Y., Mukherjee, P.S. and Qiu, P. (2018) "Efficient Blind Image Deblurring Using Nonparametric Regression and Local Pixel Clustering", Technometrics, 60(4), 522 -- 531, tools:::Rd_expr_doi("10.1080/00401706.2017.1415975").
Qiu, P. (2009) "Jump-Preserving Surface Reconstruction from Noisy Data", Annals of the Institute of Statistical Mathematics, 61, 715 -- 751, tools:::Rd_expr_doi("10.1007/s10463-007-0166-9").
JPLLK_surface, threeStage
data(brain)
bandwidth_select <- surfaceCluster_bandwidth(image = brain,
bandwidths = c(3:4), sig.level = .9995, blur = FALSE)
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