image processing - ImageHistogram with logarithmic y scale

ImageHistogram is much faster than Histogram with ImageData.

The only problem: I cannot find out how to make the y axis logarithmic. Is this possible?

I am using Mathematica 10.3.1.

Answer

Here is an answer from the Wolfram Technical Support:

Mathematica does not currently allow for an option for a logarithmic scale in ImageHistogram. However, taking apart the underlying structure, it is possible to rescale the data. The underlying structure is a GraphicsComplex, such that the following code should get you started on a workaround for your interests:

LogImageHistogram[input_Image, base_?NumericQ /; base >= 2] :=
 Module[
  {
   imh = ImageHistogram[input], logdata
   },
  logdata = MapAt[
     Log[#]/Log[base] &, 
     First@Cases[imh, GraphicsComplex[x_, y_] :> x, Infinity], {All, 2}
     ] /. Indeterminate -> -1;


  (
    imh /. GraphicsComplex[x_, y_] :> GraphicsComplex[logdata, y]
    ) /.
   {
    Rule[FrameTicks, x_] :> Rule
      [
      FrameTicks, {
       {
        {#, base^#} & /@ Range[1, 10] // N, None

        }, {Automatic, Automatic}
       }
      ],
    Rule[PlotRange, x_] :> Rule[PlotRange, {0, Max[logdata]}]
    }
  ]

This function takes two arguments,

1) the input image and

2) the logarithmic base with which to scale the y-axis.

This function isn't perfect because I only generate 10 tick marks, but these things can be adjusted by hand.

Also, because the GraphicsComplex contains some zeroes for the y-coordinates, I've artificially set these to -1 because the Log[0] is Indeterminate. You won't see these because the PlotRange starts at 0.

Show
 [
  LogImageHistogram[image, #], 
  BaseStyle -> {FontFamily -> "Calibri", FontSize -> 20}, 
  ImageSize -> 800
 ] & /@ {10, 2}

gives: