measuring distances between colours?

Hi Michael,

Thanks for the Wikipedia tip -- I'd looked there but didn't find this
article. The article explains that the Lab colour space was formulated to
provide uniform perceptual differences between colours, with a JND of
approximately of 2.3. Ken Knoblauch made a similar point. The article goes
on to describe relatively complicated adjustments meant to improve the LAV
distance metric, which are probably overkill for my application.

I've programmed Lab colour matching as follows, using Euclidean distances
and adapting Kevin Wright's modification of my original code. I used
convertColor(), which Martin Maechler pointed out to me.

----------- snip --------------

r2c <- function(){
     all.names <- colors()
     all.lab <- t(convertColor(t(col2rgb(all.names)), from="sRGB", to="Lab",
scale.in=255))
     find.near <- function(x.lab) {
         sq.dist <- colSums((all.lab - x.lab)^2)
         rbind(all.names[which.min(sq.dist)], min(sq.dist))
     }
     function(cols.hex, near=2.3){
         cols.lab <- t(convertColor(t(col2rgb(cols.hex)), from="sRGB",
to="Lab", scale.in=255))
         cols.near <- apply(cols.lab, 2, find.near)
         ifelse(cols.near[2, ] < near^2, cols.near[1, ], cols.hex)
     }
}

rgb2col <- r2c()

----------- snip --------------

A bit of experimentation suggests that this works better than using (as I
did previously) direct RGB distances, matching more colours to names and
providing (to my eye, with my monitor) perceptually closer matches, though
sometimes with (again to my eye) perceptible differences. Here's an
illustration, adapting one of Kevin's examples:

----------- snip --------------

cols <- c("#010101", "#EEEEEE", "#AA0000", "#00AA00", "#0000AA", "#AAAA00",
"#AA00AA", "#00AAAA")
(nms <- rgb2col(cols))
pie(rep(1, 2*length(cols)), labels=c(cols, nms), col=c(cols, nms))

----------- snip --------------

Thanks again to everyone who responded to my original, na?ve, question.

Best,
  John

-----Original Message-----
From: Michael Friendly [mailto:friendly at yorku.ca]
Sent: Friday, May 31, 2013 10:24 AM
To: John Fox
Cc: r-help at r-project.org; 'Martin Maechler'
Subject: Re: measuring distances between colours?

Hi John
This has been an interesting discussion.
Though you have a solution for your needs, you might be interested in
this javascript implementation that allows you to visually compare
color
distances in various color spaces

http://stevehanov.ca/blog/index.php?id=116

And, all the theory of color distance is described in
http://en.wikipedia.org/wiki/Color_difference

PS: This is a very handy function.  When I last tried
aplpack::bagplot(), it was annoying that the colors could *only*
be specified in hex.

-Michael



On 5/30/2013 5:14 PM, John Fox wrote:

Dear all,

My thanks to everyone who addressed my question. I've incorporated

Eik

Vettorazzi's suggestion for improved conversion of hexadecimal RGB

colours

to decimal numbers, and Martin Maechler's hint to look at

demo(colors). I've

loosened the default definition of "close enough" from the latter,

since the

following seems to work well for my purposes.

r2c <- function(){
      hex2dec <- function(hexnums) {
          # suggestion of Eik Vettorazzi
          sapply(strtoi(hexnums, 16L), function(x) x %/% 256^(2:0) %%

256)

      }
      findMatch <- function(dec.col) {
          sq.dist <- colSums((hsv - dec.col)^2)
          rbind(which.min(sq.dist), min(sq.dist))
      }
      colors <- colors()
      hsv <- rgb2hsv(col2rgb(colors))
      function(cols, near=0.25){
          cols <- sub("^#", "", toupper(cols))
          dec.cols <- rgb2hsv(hex2dec(cols))
          which.col <- apply(dec.cols, 2, findMatch)
          matches <- colors[which.col[1, ]]
          unmatched <- which.col[2, ] > near^2
          matches[unmatched] <- paste("#", cols[unmatched], sep="")
          matches
      }
}

rgb2col <- r2c()

For example,

rgb2col(c("010101", "EEEEEE", "AA0000", "00AA00", "0000AA",

"AAAA00",

"AA00AA", "00AAAA"))
[1] "black"         "gray93"        "darkred"       "green4"
[5] "blue4"         "darkgoldenrod" "darkmagenta"   "cyan4"

rgb2col(c("010101", "090909", "090000", "000900", "000009",

"090900",

"090009", "000909"))
[1] "black"   "gray3"   "#090000" "#000900" "#000009" "#090900"
[7] "#090009" "#000909"

Thanks again,
   John

--
Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept. & Chair, Quantitative Methods
York University      Voice: 416 736-2100 x66249 Fax: 416 736-5814
4700 Keele Street    Web:   http://www.datavis.ca
Toronto, ONT  M3J 1P3 CANADA