disp2D (version 1.0)

disp2D-package: Hausdorff and Simplex Dispersion orderings

Description

Given a 2D point set, different three point sets are selected. The Hausdorff distances between the convex hulls are calculated exactly.

Details

Package:

disp2D

Type:

Package

Version:

1.0

Date:

2012-05-24

License:

GPL-2

LazyLoad:

yes

References

Ayala G. and Lopez M. The simplex dispersion ordering and its application to the evaluation of human corneal endothelia. Journal of Multivariate Analysis, 100:1447-1464, 2009. G. Ayala, M.C. Lopez-Diaz, M. Lopez-Diaz, and L. Martinez-Costa. Studying hypertension in ocular fundus images using Hausdorff dispersion ordering. Mathematical Medicine and Biology: A journal of the IMA, 2011. Miguel Lopez-Diaz. An indexed multivariate dispersion ordering based on the Hausdorff distance. Journal of Multivariate Analysis, 97(7):1623 - 1637, 2006. G. Ayala, M.C. Lopez-Diaz, M. Lopez-Diaz and L. Martinez-Costa. Methods and algorithms to test the simplex and Hausdorff dispersion orders with a simulation study and an Ophthalmological application. Technical Report. 2012

Examples

library(disp2D)
library(geometry)
library(mvtnorm)
sigma1 = matrix(c(0.912897,1.092679,1.092679,1.336440),byrow=TRUE,ncol=2)
sigma2 = sigma1 + diag(1,ncol=2,nrow=2)
A = rmvnorm(200,mean=rep(0,2),sigma=sigma1)
B = rmvnorm(200,mean=rep(0,2),sigma=sigma2)
r=.1
prob = probA = probB =  rep(1/200,200)
HA = exactHausdorff(A,probA,r)
HB = exactHausdorff(B,probB,r)
plot(HA$distance, cumsum(HA$probability), type = "l", xlab = "",
     ylab = "DF", xlim = range(c(HA,HB)))
 lines(HB$distance, cumsum(HB$probability), lty = 2)
d1 = simplex(A,bootstrap=TRUE,nresamples=100)