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Distance of lines in image: works but slow

Maximilian Ulbrich

Maximilian Ulbrich, University of Freiburg

Posted 2 years ago

Hi all, my typical (raster) image consists of many lines that are changing their distance to the other lines. The data are extracted from a biological sample that shows a pattern. I want to calculate for each point of the lines the distance to the closest other line. My idea is to take a small portion of the image around the target point, delete all (bright) pixels that are directly connected, and calculate the minimum of all the distances to the left-over (bright) pixels. s0 = 20; (* half size of the sub-image ) d0 = ImageData[img0]; a0 = ReplacePart[ ConstantArray[0, {2 s0 + 1, 2 s0 + 1}], {s0 + 1, s0 + 1} -> 1]; ( make an image with a white pixel in the center ) pos1 = DeleteCases[ Position[d0, 1], _?(#[[1]] <= s0 \|\| #[[2]] <= s0 \|\| #[[1]] >= Dimensions[d0][[1]] - s0 \|\| #[[2]] >= Dimensions[d0][[2]] - s0 &), 1]; ( extract bright pixels from original image ) repl = (imgsm1 = Take[d0, Sequence @@ Outer[Plus, #, {-s0, s0}]]; ( Take sub-image from original image ) imgsm2 = Subtract[imgsm1, GeodesicDilation[a0, imgsm1]]; ( delete pixels connected to center pixel ) (# -> Min[Sqrt[ N@(Plus @@@ ((# - {s0 + 1, s0 + 1} & /@ Position[imgsm2, 1])^2))], 100]) ( calculate min distance of all left-over pixles *) ) & /@ pos1; d1 = ReplacePart[d0, repl]; img1 = Colorize[Image[d1/25], ColorFunction -> (Hue[1 - #] &), ColorRules -> {0 -> Black}] The original image and the result are here: The code works but is very slow. Does someone have an idea how to accelerate this? Thanks! Max

Hi all,

my typical (raster) image consists of many lines that are changing their distance to the other lines. The data are extracted from a biological sample that shows a pattern.

I want to calculate for each point of the lines the distance to the closest other line. My idea is to take a small portion of the image around the target point, delete all (bright) pixels that are directly connected, and calculate the minimum of all the distances to the left-over (bright) pixels.

s0 = 20; (* half size of the sub-image *)
d0 = ImageData[img0];
a0 = ReplacePart[
   ConstantArray[0, {2 s0 + 1, 2 s0 + 1}], {s0 + 1, s0 + 1} -> 
    1]; (* make an image with a white pixel in the center *)
pos1 = DeleteCases[
  Position[d0, 
   1], _?(#[[1]] <= s0 || #[[2]] <= s0 || #[[1]] >= 
       Dimensions[d0][[1]] - s0 || #[[2]] >= 
       Dimensions[d0][[2]] - s0 &), 
  1]; (* extract bright pixels from original image *)

repl =
  (imgsm1 = Take[d0, Sequence @@ Outer[Plus, #, {-s0, s0}]]; (* 
     Take sub-image from original image *)
     imgsm2 = Subtract[imgsm1, GeodesicDilation[a0, imgsm1]]; (* 
     delete pixels connected to center pixel *)
     (# -> 
       Min[Sqrt[
         N@(Plus @@@ ((# - {s0 + 1, s0 + 1} & /@ 
                Position[imgsm2, 1])^2))], 100]) (* 
     calculate min distance of all left-over pixles *)
     ) & /@ pos1;

d1 = ReplacePart[d0, repl]; 

img1 = Colorize[Image[d1/25], ColorFunction -> (Hue[1 - #] &), 
  ColorRules -> {0 -> Black}]

The original image and the result are here:

The code works but is very slow. Does someone have an idea how to accelerate this?

Thanks!

Max

POSTED BY: Maximilian Ulbrich

3 Replies

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Maximilian Ulbrich

Maximilian Ulbrich, University of Freiburg

Posted 2 years ago

Dear Henrik, this is exactly what I was looking for! As always, you nailed it! Thanks so much again. Best wishes, Max

POSTED BY: Maximilian Ulbrich

Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 2 years ago

OK, a better attempt: As far as I can see in your code you do not make use of any morphological functions nor of `Nearest` - but this could speed up your code considerably. Already `MorphologicalComponents` can disassemble your structures perfectly: img = DeleteSmallComponents[Binarize[ Import["https://community.wolfram.com//c/portal/getImageAttachment?filename=img0.png&userId=549626"]], 20]; MorphologicalComponents[img] // Colorize In this sense I do the following: (* list of points according to structures: ) structPts = Position[#, 1] &@Normal@Last /@ ComponentMeasurements[img, "Mask"]; ( global: matrix to be filled with neares neighbor pixel distances: ) distMat = ConstantArray[-1, ImageDimensions[img]]; ( calculation of nearest neighbor distances ) lineDistCalc[indx_] := Module[{lpts, environment, nfunc}, {lpts, environment} = TakeDrop[structPts, {indx}]; lpts = First[lpts]; environment = Flatten[environment, 1]; nfunc = Nearest[environment]; With[{r = First[#], c = Last[#]}, distMat[[r, c]] = N@EuclideanDistance[First@nfunc[#], #]] & /@ lpts;] ( filling matrix 'distMat': ) Do[lineDistCalc[indx], {indx, Length[structPts]}] Now `distMat` is filled with distance values in place for each pixel - the essential information! A nice colored image can be calculated from this like so: ( range of distances: ) distRange = MinMax[Select[Flatten[distMat], # > 0 &]]; ( according image data for colored image: *) distImgData = Map[If[# > 0, ColorData["BrightBands"][Rescale[#, distRange]], Black] &, distMat, {2}]; Image[distImgData] I guess this is more what you are expecting - and (due to usage of Wolfram functions) it runs reasonable fast! Best regards to Freiburg! -- Henrik

OK, a better attempt:

As far as I can see in your code you do not make use of any morphological functions nor of Nearest - but this could speed up your code considerably. Already MorphologicalComponents can disassemble your structures perfectly:

img = DeleteSmallComponents[Binarize[
    Import["https://community.wolfram.com//c/portal/getImageAttachment?filename=img0.png&userId=549626"]], 20];
MorphologicalComponents[img] // Colorize

enter image description here

In this sense I do the following:

(* list of points according to structures: *)
structPts = Position[#, 1] &@*Normal@*Last /@ ComponentMeasurements[img, "Mask"];
(* global: matrix to be filled with neares neighbor pixel distances: *)
distMat = ConstantArray[-1, ImageDimensions[img]];

(* calculation of nearest neighbor distances *)
lineDistCalc[indx_] := Module[{lpts, environment, nfunc},
  {lpts, environment} = TakeDrop[structPts, {indx}];
  lpts = First[lpts];
  environment = Flatten[environment, 1];
  nfunc = Nearest[environment];
  With[{r = First[#], c = Last[#]},
     distMat[[r, c]] = N@EuclideanDistance[First@nfunc[#], #]] & /@ 
   lpts;]

(* filling matrix 'distMat': *)
Do[lineDistCalc[indx], {indx, Length[structPts]}]

Now distMat is filled with distance values in place for each pixel - the essential information!

A nice colored image can be calculated from this like so:

(* range of distances: *)
distRange = MinMax[Select[Flatten[distMat], # > 0 &]];
(* according image data for colored image: *)
distImgData = Map[If[# > 0, ColorData["BrightBands"][Rescale[#, distRange]], Black] &, distMat, {2}];
Image[distImgData]

enter image description here

I guess this is more what you are expecting - and (due to usage of Wolfram functions) it runs reasonable fast!

Best regards to Freiburg! -- Henrik

POSTED BY: Henrik Schachner

Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 2 years ago

Hi Maximilian, one simple idea would be to overlap your image with its point density: img = Binarize[ < your original image > ]; dims = ImageDimensions[img]; pos1 = ImageValuePositions[img, 1]; cimg = SmoothDensityHistogram[pos1, 15, Frame -> False, ColorFunction -> "Rainbow", ImageSize -> dims, PlotPoints -> 100, PlotRange -> Full]; ImageMultiply[cimg, img] Does that help? It runs fast, at least ...

Hi Maximilian,

one simple idea would be to overlap your image with its point density:

img = Binarize[ < your original image > ];
dims = ImageDimensions[img];
pos1 = ImageValuePositions[img, 1];
cimg = SmoothDensityHistogram[pos1, 15, Frame -> False, 
   ColorFunction -> "Rainbow", ImageSize -> dims, PlotPoints -> 100, 
   PlotRange -> Full];
ImageMultiply[cimg, img]

enter image description here

Does that help? It runs fast, at least ...

POSTED BY: Henrik Schachner

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