areaest {LeArEst}

Performs area estimation of the numerically described object in plane.

Description

Use this function if you have a data set of uniformly distributed points on an elliptical domain in the plane but captured with additive errors. The estimation algorithm takes many horizontal and vertical, or star-shaped slices of the object. Length estimation procedure is conducted on each slice and in that way the set of edge points is obtained. An ellipse or a circle is fitted to these edge points by function EllipseDirectFit or CircleFitByPratt from the package conicfit and its semi-axes and area are returned as a result. Function optionally plots input points, calculated edge points and the resulting ellipse or circle.

Usage

areaest(data, nrSlices = 10, error = c("laplace", "gauss", "student"),
  var.est = c("MM", "ML"), var = NULL, plot = FALSE,
  parallel = FALSE, slicing = c("hv", "star"),
  representation = c("ellipse", "circle"))

Arguments

data

Two-column data matrix containing the points that describe observed object. First column represents x coordinate of the point, while second column represents y coordinate.

nrSlices

Number of slices applied for plain data cutting. Defaults to 10.

error

A character string specifying the error distribution. Must be one of "laplace", "gauss" or "student". Can be abbreviated.

var.est

A character string specifying the method of error variance estimation. Must be given if var is not given. Can be "MM" (Method of Moments) or "ML" (Maximum Likelihood).

var

Explicit error variance. Needs to be given if var.est is not given.

plot

Logical parameter (TRUE or FALSE) that determines whether to plot given object, calculated edge points and the resulting ellipse. Defaults to FALSE.

parallel

Logical parameter (TRUE or FALSE) that determines whether to perform estimation procedure in a parallel manner. Can shorten estimation time if many border points need to be calculated. Defaults to FALSE.

slicing

A character string specifying the method of slicing. Can be "hv" (horizontal and vertical slicing) or "star" (star-shaped slicing). Can be abbreviated.

representation

A character string specifying the shape of an observed object. Can be "ellipse" or "circle". Can be abbreviated.

Value

List containing:

• area: Estimated area of the object,

• points: Set of calculated object's edge points,

• semiaxes: Resulting ellipse's semi-axes or circle radius.

Examples

# load a data set representing the ellipse with additive Gaussian error,
# run area estimation on it, and plot the results
inputfile <- system.file("extdata", "ellipse_3_4_0.1_gauss.txt", package = "LeArEst")
inputdata <- read.table(inputfile)
area <- areaest(inputdata, error = "gauss", var.est = "ML", plot = TRUE,
                slicing = "hv", representation = "ellipse")

# load a data set representing the ellipse with additive Laplacian error,
# run area estimation on it, and plot the results
inputfile <- system.file("extdata", "ellipse_3_4_0.1_laplace.txt", package = "LeArEst")
inputdata <- read.table(inputfile)
area <- areaest(inputdata, error = "laplace", var = 0.1, nrSlices = 5, plot = TRUE,
                slicing = "star", representation = "ellipse")