areaest function

Performs area estimation of the numerically described object in plane.

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.

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.

Returns

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")