ColorConvert
ColorSeparate
ColorCombine
ImageClip
ImageChannels
ImageAdjust
ImageMultiply
PseudoInverse

Image Processing
Life Sciences

Measurement of Dye Concentration

Use a color deconvolution algorithm to separate a microscopy image of stained tissue samples

Open in Cloud
Download Notebook

Start with an image of the tissue stained using Hematoxylin C19 and DAB (3,3'-Diaminobenzidine):

In[1]:=

img=

;

Literature provides the typical RGB colors of the two stains:

In[2]:=

Hematoxylin=

;Diaminobenzidine=

;

Theoretically, the dye colors are obtained by multiplying their color spectrum with the sensitivity spectrum of the red, green and blue channels of the CCD in the recording camera. Obtain the transformation matrix from staining dye to RGB color channels:

In[3]:=

HDABtoRGB=Transpose@{Normalize[List@@Hematoxylin],Normalize[List@@Diaminobenzidine]};MatrixForm[HDABtoRGB]

Out[3]//MatrixForm=

0.650029	0.268148
0.704031	0.570314
0.286013	0.776427

These multiplications are called color convolutions; the inverse operations are called color deconvolutions, which is effectively a color demixing of stain colors. Compute the linear inverse transformation from color to dye concentration:

In[4]:=

RGBtoHDAB=PseudoInverse[HDABtoRGB];MatrixForm[RGBtoHDAB]

Out[4]//MatrixForm=



1.20008	0.685203	-0.917769
-0.689388	0.0235969	1.50871



The actual demixing is performed in the log-scale of color intensities, since the color absorption is exponentially proportional to the dye concentration. Define a function to implement the color deconvolution:

In[5]:=

SeparateStains[img_Image,mat_?MatrixQ]:=Module[{logRGB=Log@ImageClip@ColorConvert[img,"RGB"]+2.0},Map[ImageAdjust,-mat.ColorSeparate[logRGB]]]/;Last@Dimensions[RGBtoHDAB]===ImageChannels[img]

Perform color deconvolution into Hematoxylin and DAB dye concentration:

In[6]:=

HDAB=SeparateStains[img,RGBtoHDAB]

Out[6]=





Multiply each component with the color of its corresponding stain:

In[7]:=

MapThread[ImageMultiply,{HDAB,{Diaminobenzidine,Hematoxylin}}]

Out[7]=

Show the dye concentration with false colors:

In[8]:=

devcol=ColorCombine[{{1,0},{0,1},{0,1}}.HDAB]

Out[8]=

Related Symbols

ColorConvert
ColorSeparate
ColorCombine
ImageClip
ImageChannels
ImageAdjust
ImageMultiply
PseudoInverse

Publisher Information

Contributed by: Wolfram Staff

Wolfram Language Example Repository

Measurement of Dye Concentration

See Also

Publisher Information