[GRASS-stats] How to calculate the Bhattacharyya distance/index?

[Nikos Alexandris]

I need to calculate the Bhattacharyya distance (or better said the
Bhatt. separability index) for unburned and burned area samples
extracted from both prefire and postfire MODIS surface reflectance
products.

I haven't found any foss "tool" that will do this for me. So I am trying
to code it in R.

#==================================================
# Calculate bhattacharayya distance in R

# define new function
dBh <- function(PRE, POST){

        # column-wise mean and cov for PRE
        m.pre <- colMeans(PRE)
        c.pre <- cov(PRE)

        # column-wise mean and cov for POST
        m.post <- colMeans(POST)
        c.post <- cov(POST)

        # mean difference and its transpose matrix
        m.diff <- as.matrix(m.pre - m.post)
                m.diff.t <- t(m.diff)

        # halfsum of covariances
        C <- (c.pre + c.post)/2

# the index
index <- 0.125 * m.diff.t %*% C %*% m.diff + 0.5 *
log10( det(C)/sqrt( det(c.pre)*det(c.post)))

# print result
index
}
#===================================================

I am trying to use the code on two matrices with the following
structure:

# rows are the total number of pixels sampled
# columns correspond to MODIS bands 1, 2, 5, 6 and 7
> str(pre.bs6)

 int [1:371, 1:5] 986 986 1086 1094 1094 1217 1217 1258 1391 1475 ...
 - attr(*, "dimnames")=List of 2
  ..$ : NULL
  ..$ : chr [1:5] "prefire.band1" "prefire.band2" "prefire.band5"
"prefire.band6" ...


> str(post.bs6)

 int [1:371, 1:5] 1007 1175 1007 1039 1146 1077 1078 1280 1249 1218 ...
 - attr(*, "dimnames")=List of 2
  ..$ : NULL
  ..$ : chr [1:5] "postfire.band1" "postfire.band2" "postfire.band5"
"postfire.band6" ...


My problem is that (a) I have coded it falsely  or  (b) I don't
understand "how to use the result given that the above instructions are
correct. The result is *too* big, thus it will probably ground the
Bhattacharayya coefficient to 0.

I expect that prefire samples against postfire samples [ given the very
good (or good) discrimination ability of those two "classes" in MODIS
bands 2, 5, (6 and 7) ] will return some "great" Bhattacharayya
coefficient. Or am I wrong?

Any instructions on how to get it done?
Thanks, Nikos

---
[1] http://en.wikipedia.org/wiki/Bhattacharyya_coefficient
[2] http://en.wikipedia.org/wiki/Bhattacharya_coefficient