1. A variable data image watermarking method comprising: receiving input image data that define an input image in terms of RGB data defining a red (R) color separation, a green (G) color separation, and a blue (B) color separation; performing a color transform on said RGB data to a CMYK image defining a cyan (C), magenta (M), yellow (Y) and black (K) separation, to define a constant K image that corresponds in appearance to said input image and that includes a constant K black color separation K′; receiving variable infrared (IR) mark data defining an IR mark to be embedded in the constant K image; defining a watermarked black separation K″ by embedding a sparse two-dimensional pattern of black pixels into said constant K black separation K′, wherein said sparse two-dimensional pattern of black pixels corresponds to said received variable IR mark data and is defined with a density of black pixels that is less than or equal to a threshold T; correcting local neighborhood values in the watermarked black separation K″, excluding the black pixels corresponding to said received variable IR mark, to maintain local average black levels; said color transformed cyan, magenta, and yellow color separations C, M, Y and said watermarked black separation K″ defining a watermarked image; and, generating a watermarked document by printing said watermarked image on paper using a multicolorant printer.