This function implements the reverse blend described by Mark Ransom, for an additional small but visible improvement:
reverseBlend[img_Image, alpha_Image, bgcolor_] :=
With[
{c = ImageData[img],
a = ImageData[alpha] + 0.0001, (* this is to minimize ComplexInfinitys and considerably improve performance *)
bc = bgcolor},
ImageClip@
Image[Quiet[(c - bc (1 - a))/a, {Power::infy,
Infinity::indet}] /. {ComplexInfinity -> 0, Indeterminate -> 0}]
]
This is the background removal function. The threshold
parameter is used for the initial binarization of the image, the minSizeCorrection
is for tweaking the size limit of small junk components to be removed after binarization.
removeWhiteBackground[img_, threshold_: 0.05, minSizeCorrection_: 1] :=
Module[
{dim, bigmask, mask, edgemask, alpha},
dim = ImageDimensions[img];
bigmask =
DeleteSmallComponents[
ColorNegate@
MorphologicalBinarize[ColorNegate@ImageResize[img, 4 dim], threshold],
Round[minSizeCorrection Times @@ dim/5]];
mask = ColorNegate@
ImageResize[ColorConvert[bigmask, "GrayScale"], dim];
edgemask =
ImageResize[
ImageAdjust@DistanceTransform@Dilation[EdgeDetect[bigmask, 2], 6],
dim];
alpha =
ImageAdd[
ImageSubtract[
ImageMultiply[ColorNegate@ColorConvert[img, "GrayScale"],
edgemask], ImageMultiply[mask, edgemask]], mask];
SetAlphaChannel[reverseBlend[img, alpha, 1], alpha]
]
Testing the function:
img = Import["http://i.stack.imgur.com/k7E1F.png"];
background =
ImageCrop[
Import["http://cdn.zmescience.com/wp-content/uploads/2011/06/
forest2.jpg"], ImageDimensions[img]];
result = removeWhiteBackground[img]
ImageCompose[background, result]
Rasterize[result, Background -> Red]
Rasterize[result, Background -> Black]
Brief explanation of how it works:
Choose your favourite binariaztion method that produces relatively precise sharp edges
Apply it to an up-scaled image, then downscale the obtained mask
to the original size. This gives us antialiasing. Most of the work is done.
For a small improvement, blend the image onto the background using the brightness of its negative as alpha, then blend the obtained image over the original in a thin region around the edges (edgemask
) to reduce the visibility of white pixels on the edges. The alpha channel corresponding to these operations is calculated (the somewhat cryptic ImageMultiply/Add
expression).
Now we have an estimate of the alpha channel so we can do a reverse blend.
Steps 3 & 4 don't improve that much, but the difference is visible.