Creates a penalty matrix for use by gen.ridge for
two-dimensional smoothing.
laplacian(size, compose)
laplacian(size = 16, compose = FALSE)dimension of the image is size x size; default is 16.
default is compose=FALSE, which means the
penalty is returned as an eigen-decomposition. If compose=TRUE, a penalty matrix is returned.
If compose=FALSE, an eigen-decomposition object is
returned. The vectors component is a size^2 x size^2
orthogonal matrix, and the $values component is a size^2
vector of non-negative eigen-values. If compose=TRUE, these are
multiplied together to form a single matrix.
Formulas are used to construct a laplacian for smoothing a square image.
Here we follow very closely the material on page 635 in JASA 1991 of O'Sullivan's article on discretized Laplacian Smoothing