locmeasures2d {SpatialVx}

Binary Image Measures

Description

Calculate some binary image measures between two fields.

Usage

locmeasures2d(object, which.stats = c("bdelta", "haus", "qdmapdiff", 
    "med", "msd", "ph", "fom"), distfun = "distmapfun", distfun.params = NULL, 
    k = NULL, alpha = 0.1, bdconst = NULL, p = 2, ...)

## Default S3 method:
locmeasures2d(object, which.stats = c("bdelta", "haus", "qdmapdiff", 
    "med", "msd", "ph", "fom"), distfun = "distmapfun", distfun.params = NULL, 
    k = NULL, alpha = 0.1, bdconst = NULL, p = 2, ..., Y, thresholds=NULL)

## S3 method for class 'SpatialVx'
locmeasures2d(object, which.stats = c("bdelta", "haus", "qdmapdiff", 
    "med", "msd", "ph", "fom"), distfun = "distmapfun", distfun.params = NULL, 
    k = NULL, alpha = 0.1, bdconst = NULL, p = 2, ..., time.point = 1, 
    obs = 1, model = 1)

## S3 method for class 'locmeasures2d'
print(x, ...)

## S3 method for class 'locmeasures2d'
summary(object, ...)

Arguments

object

For locmeasures2d, an object of class “SpatialVx” or a valid matrix in which case Y must be explicitly provided. For summary method function, a list object output from locmeasures2d.

x

returned object from locmeasures2d.

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 are to be calculated. Must return a matrix of the same dimension as x.

distfun.params

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

k

numeric vector for use with the partial Hausdorff distance. For k that are whole numerics or integers >= 1, then the k-th highest value is returned by locmeasures2d. If 0 <= k < 1, then the corresponding quantile is returned.

alpha

numeric giving the alpha parameter for Pratt's Figure of Merit (FOM). See the help file for locperf for more details.

bdconst

numeric giving the cut-off value for Baddeley's delta metric.

p

numeric vector giving one or more values for the parameter p in Baddeley's delta metric. Usually this is just 2.

Y

m X n matrix giving the forecast field.

thresholds

numeric or two-column matrix giving the threshold to be applied to the verification (column one) and forecast (column two) fields. If a vector, same thresholds are applied to both fields.

time.point

numeric or character indicating which time point from the “SpatialVx” verification set to select for analysis.

obs, model

numeric indicating which observation/forecast model to select for the analysis.

...

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

Details

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

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:

“bdelta” Baddeley delta metric (Baddeley, 1992a,b; Gilleland, 2011; Schwedler and Baldwin, 2011)

“haus” Hausdorff distance (Baddeley, 1992b; Schwedler and Baldwin, 2011)

“qdmapdiff” Quantile (or rank) of the differences in distance maps. 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.

“ph” Partial Hausdorff distance. 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.

Value

A list with at least one of the following components depending on the argument which.stats

bdelta

p by q matrix giving the Baddeley delta metric for each desired value of p (rows) and each threshold (columns)

haus

numeric vector giving the Hausdorff distance for each threshold

qdmapdiff

k by q matrix giving the difference in distance maps for each of the k-th largest value(s) or quantile(s) (rows) for each threshold (columns).

medMiss, medFalseAlarm, msdMiss, msdFalseAlarm

two-row matrix giving the mean error (or square error) distance as (Forecast, Observation) or misses and (Observation, Forecast) or false alarms.

ph

k by q matrix giving the k-th largest value(s) or quantile(s) (rows) for each threshold (columns) of the maximum between the distances from one field to the other.

fom

numeric vector giving Pratt's figure of merit.

Note

Binary fields are determined by having values >= the thresholds.

Author(s)

Eric Gilleland

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, make.SpatialVx

Examples

x <- y <- matrix(0, 10, 12)
x[2,3] <- 1
y[4,7] <- 1

hold <- make.SpatialVx(x, y, thresholds = 0.1,
    field.type = "random", units = "grid squares")
locmeasures2d(hold, k = 1)

# Alternatively ...
locmeasures2d(x, thresholds = 0.1, k = 1, Y = y)

## Not run: 
data( "geom000" )
data( "geom001" )
data( "ICPg240Locs" )

hold <- make.SpatialVx( geom000, geom001, thresholds = c(0.1, 50.1), 
    projection = TRUE, map=TRUE, loc = ICPg240Locs, loc.byrow = TRUE,
    field.type = "Precipitation", units = "in/100",
    data.name= "ICP Geometric Cases", obs.name = "geom000",
    model.name = "geom001" )

hold2 <- locmeasures2d(hold, k=c(4, 0.975), alpha=c(0.1,0.9))
summary(hold2)

## End(Not run)