Apply ColorFunction to an Image

is there a faster way to change the colors of an image from grayscale to something like this:

Manipulate[coltest2 = (Blend[{{a, Black}, {b, Lighter[Blue, 0.3]}, {c,Lighter[Cyan,0.3]}, {d, White}}, #] &);
Plot[0.2, {x, 0, 1}, ColorFunction -> coltest2, PlotStyle -> Directive[Thickness[1]], PlotRange -> {{0, 1}, {0, 0.5}}, Frame -> True, FrameTicks -> {True, False, None, None}, AspectRatio -> 1/8],
{{a, 0.35}, 0, b, Appearance -> "Labeled"},
{{b, 0.58}, 0, c, Appearance -> "Labeled"},
{{c, 0.7}, 0, d, Appearance -> "Labeled"},
{{d, 0.95}, 0, 1, Appearance -> "Labeled"}]

than using:

Colorize[image,ColorFunction->coltest2]

I would like to have the image in the manipulate rather than the sample of the ColorFunction, but Colorize is way to slow for that...

Answer

What you can do is, you mimic the behaviour of Blend by creating a function that interpolates linearly between colours. What you change with your parameters are the values where the color transitions take place.

Let me give you a simplified example: I use 3 colours. In the compiled function, I only work with their {r,g,b} values. As result, I want a compiled function which does the following:

• it takes a parameter a between 0 and 1 and a pixel value between 0 and 1


• with 3 colours c1, c2 and c3 it will colorise the pixel: from a pixel value of 0 to a it will be colorised with the transition c1 to c2. If the pixel value is greater than a it will be colorised by blending c2 and c3.


• the compiled function should be able to work in parallel on all pixels of an image

Here is a sample implementation of a function that creates such a colorising compiled function for us:

createColorFunc[colors : {_, _, _}] :=
 Function[{c1, c2, c3},
   Compile[{{a, _Real, 0}, {value, _Real, 0}},
    If[value < a,
     c1 + ((-c1 + c2)*value)/a,
     (c3*(a - value) + c2*(-1 + value))/(-1 + a)
     ], Parallelization -> True, RuntimeAttributes -> {Listable}
    ]

   ] @@ List @@@ (ColorConvert[#, "RGB"] & /@ colors)

To test is, we load the Lena image in grayscale an build a small Manipulate:

With[{lena = ColorConvert[ExampleData[{"TestImage", "Lena"}], "Grayscale"]},
 Manipulate[
  func = createColorFunc[{c1, c2, c3}];
  Image[func[a, ImageData[lena, "Real"]]],
  {{a, .5}, 0, 1},
  {c1, Black},
  {c2, Gray},

  {c3, White}
  ]
 ]

You task is now to extend this for more than 3 colours and one color transition position.