SpatialVx (version 0.1-5)

locmeasures2d: Binary Image Measures

Description

Calculate some binary image measures between two fields.

Usage

locmeasures2d(object,
    which.stats = c("baddeley", "hausdorff", "ph", "mhd", "med", "msd", "fom"),
    distfun = "distmapfun", distfun.params = NULL, ...)
## S3 method for class 'locmeasures2d':
summary(object, ...)

Arguments

object

list object returned from locmeasures2dPrep for locmeasures2d function, and a list object output from locmeasures2d for the summary method.

which.stats

character vector telling which measures should be calculated.

distfun

character naming a function to calculate the shortest distances between each point x in the grid and the set of events. Default is the Euclidean distance metric. Must take x as an argument, which is the event field for which the distances ar

distfun.params

list with named components giving any additional arguments to the distfun function.

...

optional arguments to deltametric and distmap from package spatstat. Not used by the summary method here.

Value

• A list with at least one of the following components depending on the argument which.stats
• baddeley
  p by q matrix giving the Baddeley delta metric for each desired value of p (rows) and each threshold (columns)
• hausdorff
  numeric vector giving the Hausdorff distance for each threshold
• ph
  k by q matrix giving the partial Hausdorff distance for each k-th largest value (rows) and each threshold (columns)
• mhd
  numeric vector giving the modified Hausdorff distance for each threshold.
• med
  numeric vector giving the mean error distance.
• msd
  numeric vector giving the mean square error distance.
• fom
  numeric vector giving Pratt's figure of merit.

Details

It is useful to introduce some notation. Let d(x,A) be the shortest distance from a point x, from the entire grid, to a set A contained in the grid. Here, Euclidean distance is used for d(x,A), but note that some papers (e.g., Venugopal et al., 2005) use other distances, such as the taxi-cab distance.

The Hausdorff distance between two sets A and B contained in the finite grid is given by max( max( d(x,A), x in B), max( d(x,B), x in A)), and can be re-written as H(A,B) = max( abs( d(x,A) - d(x,B))), where x is taken over all points in the grid. Several of the distances here are modifications of the Hausdorff distance. The Baddeley metric, for example, is the Lp norm of abs( w(d(x,A)) - w(d(x,B))), where again x is taken from over the entire grid, and w is any concave continuous function that is strictly increasing at zero. Here, w(t) = min( t, c), where c is some constant given by the bdconst argument.

Calculates one or more of the following binary image measures:

baddeley Baddeley delta metric (Baddeley, 1992a,b; Gilleland, 2011; Schwedler and Baldwin, 2011)

hausdorff Hausdorff distance (Baddeley, 1992b; Schwedler and Baldwin, 2011)

ph Partial Hausdorff distance (Schwedler and Baldwin, 2011). See the help file for locperf.

mhd Modified Hausdorff Distance (Schwedler and Baldwin, 2011). See the help file for locperf.

med Mean Error Distance (Peli and Malah, 1982; Baddeley, 1992a). See the help file for locperf.

msd Mean Square Error Distance (Peli and Malah, 1982; Baddeley, 1992a). See the help file for locperf.

fom Pratt's Figure of Merit (Peli and Malah, 1982; Baddeley, 1992a, Eq (1)). See the help file for locperf.

These distances are summaries in and of themselves, so the summary method function simply displays the results in an easy to read manner.

References

Baddeley, A. (1992a) An error metric for binary images. In Robust Computer Vision Algorithms, W. Forstner and S. Ruwiedel, Eds., Wichmann, 59--78.

Baddeley, A. (1992b) Errors in binary images and an Lp version of the Hausdorff metric. Nieuw Arch. Wiskunde, 10, 157--183.

Gilleland, E. (2011) Spatial forecast verification: Baddeley's delta metric applied to the ICP test cases. Wea. Forecasting, 26, 409--415, doi:10.1175/WAF-D-10-05061.1.

Peli, T. and Malah, D. (1982) A study on edge detection algorithms. Computer Graphics and Image Processing, 20, 1--21.

Schwedler, B. R. J. and Baldwin, M. E. (2011) Diagnosing the sensitivity of binary image measures to bias, location, and event frequency within a forecast verification framework. Wea. Forecasting, 26, 1032--1044, doi:10.1175/WAF-D-11-00032.1.

Venugopal, V., Basu, S. and Foufoula-Georgiou, E. (2005) A new metric for comparing precipitation patterns with an application to ensemble forecasts. J. Geophys. Res., 110, D08111, doi:10.1029/2004JD005395, 11pp.

See Also

deltametric, distmap, locmeasures2dPrep

Examples

x <- y <- matrix(0, 10, 12)
x[2,3] <- 1
y[4,7] <- 1
hold <- locmeasures2dPrep("x", "y", thresholds=0.1, k=1, units="grid squares")
locmeasures2d( hold)

data( geom000)
data(geom001)
hold <- locmeasures2dPrep("geom000", "geom001", thresholds=c(0.1,50.1), k=c(4,0.975),
	alpha=c(0.1,0.9), units="in/100")
hold2 <- locmeasures2d( hold)
summary( hold2)