pgrid-object: Class of Pixel Grids

In transport: Computation of Optimal Transport Plans and Wasserstein Distances

Class of Pixel Grids

Description

The class "pgrid" (for pixel grid) represents regular quantizations of measures on (bounded subsets of) R^d. Currently only square quantizations of measures on a rectangles are supported, which in 2-d can be thought of as grey scale images.

Details

Objects of class "pgrid" can be created by the function pgrid, and are most commonly used as input to the function transport. There are methods plot, print and summary for this class.

An object of class "pgrid" contains the following elements:

structure	the structure of the grid. Currently only "square" and "rectangular" are supported.
dimension	the dimension d of the space in which the grid is embedded. Must be \geq 2.
n	the number of pixels along the various coordinates, a vector of length dimension.
N	the total number of pixels.
boundary	the outer boundary of the "picture" (i.e. of the support of the measure). A vector of
	length 2*dimension, where the odd entries contain the left and the even entries
	contain the right endpoints of the various coordinates.
gridtriple	the rule for generating the pixel centres along the various coordinates.
	A dim by 3 matrix where each row is of the form c(start, end, step).
generators	the pixel centres along the various coordinates. A list of length dim where the
	i-th element is a vector of length n[i].
mass	the array of masses in each pixel / at each pixel centre. In 2-d orientation corresponds
	to the standard orientation of images, see e.g. image. This means that
	pixels are arranged on coordinate axes in the order of their indices.

Author(s)

Dominic Schuhmacher [e-mail]

See Also

Constructor function pgrid.

transport documentation built on July 9, 2023, 7:43 p.m.