How can I make a graph network from image of granular packing?

I have an image from experimental data of granular packing. I need to characterize the packing as a network. The network consist of node (center of granular particle) and edge. Two node are connected if there is a contact point of two granular particle.

I have tried to make a skeletonize, but it doesn't work because there are two (even more than two) node in one particle.

Can I extract the network from this image? granular packing

asked Jan 13 at 11:08

Iqbal Rahmadhan

1234

1

$begingroup$
Maybe this can be a starting point for you or for someone who will answer: img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"]; dt = ImageAdjust@DistanceTransform@MedianFilter[Binarize[img], 3]. It's easy to get the disk centres from dt with MaxDetect. I do not have the time to play with this and will not post an answer.
$endgroup$
– Szabolcs
Jan 13 at 12:15

add a comment |

I have tried to make a skeletonize, but it doesn't work because there are two (even more than two) node in one particle.

Can I extract the network from this image? granular packing

asked Jan 13 at 11:08

Iqbal Rahmadhan

1234

1

$begingroup$
Maybe this can be a starting point for you or for someone who will answer: img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"]; dt = ImageAdjust@DistanceTransform@MedianFilter[Binarize[img], 3]. It's easy to get the disk centres from dt with MaxDetect. I do not have the time to play with this and will not post an answer.
$endgroup$
– Szabolcs
Jan 13 at 12:15

add a comment |

I have tried to make a skeletonize, but it doesn't work because there are two (even more than two) node in one particle.

Can I extract the network from this image? granular packing

asked Jan 13 at 11:08

Iqbal Rahmadhan

1234

I have tried to make a skeletonize, but it doesn't work because there are two (even more than two) node in one particle.

Can I extract the network from this image? granular packing

graphs-and-networks image-processing image

asked Jan 13 at 11:08

Iqbal Rahmadhan

1234

asked Jan 13 at 11:08

Iqbal Rahmadhan

1234

asked Jan 13 at 11:08

Iqbal Rahmadhan

1234

asked Jan 13 at 11:08

Iqbal Rahmadhan

1234

asked Jan 13 at 11:08

Iqbal Rahmadhan

1234

1

$begingroup$
Maybe this can be a starting point for you or for someone who will answer: img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"]; dt = ImageAdjust@DistanceTransform@MedianFilter[Binarize[img], 3]. It's easy to get the disk centres from dt with MaxDetect. I do not have the time to play with this and will not post an answer.
$endgroup$
– Szabolcs
Jan 13 at 12:15

add a comment |

1

$begingroup$
Maybe this can be a starting point for you or for someone who will answer: img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"]; dt = ImageAdjust@DistanceTransform@MedianFilter[Binarize[img], 3]. It's easy to get the disk centres from dt with MaxDetect. I do not have the time to play with this and will not post an answer.
$endgroup$
– Szabolcs
Jan 13 at 12:15

Maybe this can be a starting point for you or for someone who will answer:

img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"],     "Grayscale"];  dt = ImageAdjust@DistanceTransform@MedianFilter[Binarize[img], 3]

. It's easy to get the disk centres from dt with MaxDetect. I do not have the time to play with this and will not post an answer.

– Szabolcs
Jan 13 at 12:15

Maybe this can be a starting point for you or for someone who will answer:

img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"],     "Grayscale"];  dt = ImageAdjust@DistanceTransform@MedianFilter[Binarize[img], 3]

. It's easy to get the disk centres from dt with MaxDetect. I do not have the time to play with this and will not post an answer.

– Szabolcs
Jan 13 at 12:15

add a comment |

3 Answers
3

active

oldest

votes

Another starting point, where the objects being more or less fixed size disks is used ad hoc to measure their centroids as components after some mangling, and those which are close enough to each other are connected in the graph if out of sample of four hundred points along the edge at most four are not "white."

Image is in the variable img and plenty of magic constants are employed. (If it's not otherwise obvious, I have to make it explicit: having such hand-picked constants as 0.9, 40, 55, 300, 0.0025 or even 0.25 or 5 is definitely a weakness, not a strong point of a solution.)

(* Perform image manipulation steps, feeding from one to another. *)

(* You can replace a "//" with "// Echo //" to see an intermediate value. *)

MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

    Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

  (* Measure component centroids on the manipulated image. *)

  ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

 Function[v, 

  (* Select valid edges from all pairs of components:

     - those whose edge length is less than 300, and

     - at most 4 values of 400 sampled along the edge have a value < 0.25 *)

  Select[Subsets[v, {2}],

     EuclideanDistance @@ # < 300 &&

      Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

       _?(# < 0.25 &)] < 5 &] // 

   (* Overlay the graph on top of the original image. *)

   Show[img,

     (* Construct a graph object with vertices on component centroids,

        and edges as filtered by the Select expression. *) 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v, 

      VertexStyle -> Red, VertexSize -> 1/2], ImageSize -> Medium] &]

Following variant just generates the graph g:

g = (MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

      Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

    ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

   Function[v, 

    Select[Subsets[v, {2}],

       EuclideanDistance @@ # < 300 &&

        Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

         _?(# < 0.25 &)] < 5 &] // 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v] &])

... on which you can perform graph operations:

CommunityGraphPlot[g]

edited Jan 14 at 16:16

answered Jan 13 at 12:17

kirma

10.1k13058

3

$begingroup$
Wow, very impressive.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:33

$begingroup$
It is very good and get what I want to do this research. Thank you @kirma But as I am not expert in this notation syntax, I hope someone can transalet this syntax into step by step (line by line) notation. Thank you very much.
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:54

$begingroup$
And also I need to extract the graph for more exploration in network science, like community detection etc. So can I get that?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 23:12

1

$begingroup$
@kirma Oh great! Thank you very much. That's all what I need. And again, thanks for your time, it's very helpful.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:12

1

$begingroup$
I'll try to generalize this code for other data experimantation condition. Thanks.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:13

|
show 5 more comments

This is far from perfect but may serve you as a starter. The main problem is the noise in the lower left corner and the upper right corner of the input image. I was able to get rid of some of it by apllying a MinFilter. Also the resulting graph may be postprocessed to remove some artifacts.

img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"];

G = MorphologicalGraph[MinFilter[img, 5]]; // AbsoluteTiming

Show[img, G, ImageSize -> Medium]

enter image description here

answered Jan 13 at 11:58

Henrik Schumacher

53.2k471148

2

$begingroup$
This will work better if you ImageResize smaller and then MorphologicalBinarize. I get nice results with MorphologicalGraph[MorphologicalBinarize[ImageResize[i, 250]]]. (Try varying the amount to resize by also)
$endgroup$
– Carl Lange
Jan 13 at 12:09

$begingroup$
@Carl Lange Good idea. This take nicely care of the mess in the lower left corner. Several disks around the image boundaries get lost, though. Anyways, feell free to post your own solution. This question is definitely about some filtering and parameter tweaking for which I don't find time at the moment.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:32

add a comment |

First, I find the centroids of the disks (this is similar to what Szabolcs does in a comment):

img = Import["https://i.stack.imgur.com/78BBP.png"];

binarized = Binarize@MeanFilter[img, 10];

distance = ImageAdjust@DistanceTransform[binarized];



centroids = ComponentMeasurements[Binarize[distance, 0.7], "Centroid"][[All, 2]];

HighlightImage[distance, centroids, ImageSize -> 500]

Centroids

Then I guess a disk radius and check how reasonable it is using HighlightImage:

disks = Disk[#, 115] & /@ centroids;

HighlightImage[

 img,

 Graphics[{White, disks}, Background -> Black]

 ]

Disk fit

It's not perfect, but let's compute the graph anyway:

adjacencyMatrix = 

  Outer[EuclideanDistance[#, #2] <= 2 115 &, centroids, centroids, 1];



graph2 = AdjacencyGraph[Boole@adjacencyMatrix, VertexCoordinates -> centroids];

Show[img, graph2, ImageSize -> 500]

Graph

As Szabolcs points out in a comment, NearestNeighborGraph can be used as well:

Show[

 img,

 NearestNeighborGraph[centroids, {All, 2 115}],

 ImageSize -> 500

 ]

Graph using nearest neighbors

It has problems but there is some promise in this approach. If anyone is able to improve upon this (or if you were already working in this direction), feel free to post it as your own answer.

edited Jan 13 at 19:20

answered Jan 13 at 13:09

C. E.

50.4k397203

2

$begingroup$
An option is NearestNeighborGraph[points, {All, radius}].
$endgroup$
– Szabolcs
Jan 13 at 14:14

$begingroup$
@Szabolcs Thanks, that's exactly what I needed.
$endgroup$
– C. E.
Jan 13 at 15:43

$begingroup$
It is very good. Is there a way that we can use MorphologicalGraph after get variabel distance?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:57

$begingroup$
@IqbalRahmadhan yeah, but I didn't get great results with it.
$endgroup$
– C. E.
Jan 14 at 4:11

add a comment |

Your Answer

StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\$","\$"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "387"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});

}
});

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f189398%2fhow-can-i-make-a-graph-network-from-image-of-granular-packing%23new-answer', 'question_page');
}
);

Post as a guest

Name

Required, but never shown

3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

(* Perform image manipulation steps, feeding from one to another. *)

(* You can replace a "//" with "// Echo //" to see an intermediate value. *)

MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

    Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

  (* Measure component centroids on the manipulated image. *)

  ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

 Function[v, 

  (* Select valid edges from all pairs of components:

     - those whose edge length is less than 300, and

     - at most 4 values of 400 sampled along the edge have a value < 0.25 *)

  Select[Subsets[v, {2}],

     EuclideanDistance @@ # < 300 &&

      Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

       _?(# < 0.25 &)] < 5 &] // 

   (* Overlay the graph on top of the original image. *)

   Show[img,

     (* Construct a graph object with vertices on component centroids,

        and edges as filtered by the Select expression. *) 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v, 

      VertexStyle -> Red, VertexSize -> 1/2], ImageSize -> Medium] &]

Following variant just generates the graph g:

g = (MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

      Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

    ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

   Function[v, 

    Select[Subsets[v, {2}],

       EuclideanDistance @@ # < 300 &&

        Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

         _?(# < 0.25 &)] < 5 &] // 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v] &])

... on which you can perform graph operations:

CommunityGraphPlot[g]

edited Jan 14 at 16:16

answered Jan 13 at 12:17

kirma

10.1k13058

3

$begingroup$
Wow, very impressive.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:33

$begingroup$
It is very good and get what I want to do this research. Thank you @kirma But as I am not expert in this notation syntax, I hope someone can transalet this syntax into step by step (line by line) notation. Thank you very much.
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:54

$begingroup$
And also I need to extract the graph for more exploration in network science, like community detection etc. So can I get that?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 23:12

1

$begingroup$
@kirma Oh great! Thank you very much. That's all what I need. And again, thanks for your time, it's very helpful.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:12

1

$begingroup$
I'll try to generalize this code for other data experimantation condition. Thanks.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:13

|
show 5 more comments

(* Perform image manipulation steps, feeding from one to another. *)

(* You can replace a "//" with "// Echo //" to see an intermediate value. *)

MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

    Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

  (* Measure component centroids on the manipulated image. *)

  ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

 Function[v, 

  (* Select valid edges from all pairs of components:

     - those whose edge length is less than 300, and

     - at most 4 values of 400 sampled along the edge have a value < 0.25 *)

  Select[Subsets[v, {2}],

     EuclideanDistance @@ # < 300 &&

      Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

       _?(# < 0.25 &)] < 5 &] // 

   (* Overlay the graph on top of the original image. *)

   Show[img,

     (* Construct a graph object with vertices on component centroids,

        and edges as filtered by the Select expression. *) 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v, 

      VertexStyle -> Red, VertexSize -> 1/2], ImageSize -> Medium] &]

Following variant just generates the graph g:

g = (MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

      Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

    ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

   Function[v, 

    Select[Subsets[v, {2}],

       EuclideanDistance @@ # < 300 &&

        Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

         _?(# < 0.25 &)] < 5 &] // 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v] &])

... on which you can perform graph operations:

CommunityGraphPlot[g]

edited Jan 14 at 16:16

answered Jan 13 at 12:17

kirma

10.1k13058

3

$begingroup$
Wow, very impressive.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:33

$begingroup$
It is very good and get what I want to do this research. Thank you @kirma But as I am not expert in this notation syntax, I hope someone can transalet this syntax into step by step (line by line) notation. Thank you very much.
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:54

$begingroup$
And also I need to extract the graph for more exploration in network science, like community detection etc. So can I get that?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 23:12

1

$begingroup$
@kirma Oh great! Thank you very much. That's all what I need. And again, thanks for your time, it's very helpful.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:12

1

$begingroup$
I'll try to generalize this code for other data experimantation condition. Thanks.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:13

|
show 5 more comments

(* Perform image manipulation steps, feeding from one to another. *)

(* You can replace a "//" with "// Echo //" to see an intermediate value. *)

MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

    Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

  (* Measure component centroids on the manipulated image. *)

  ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

 Function[v, 

  (* Select valid edges from all pairs of components:

     - those whose edge length is less than 300, and

     - at most 4 values of 400 sampled along the edge have a value < 0.25 *)

  Select[Subsets[v, {2}],

     EuclideanDistance @@ # < 300 &&

      Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

       _?(# < 0.25 &)] < 5 &] // 

   (* Overlay the graph on top of the original image. *)

   Show[img,

     (* Construct a graph object with vertices on component centroids,

        and edges as filtered by the Select expression. *) 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v, 

      VertexStyle -> Red, VertexSize -> 1/2], ImageSize -> Medium] &]

Following variant just generates the graph g:

g = (MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

      Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

    ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

   Function[v, 

    Select[Subsets[v, {2}],

       EuclideanDistance @@ # < 300 &&

        Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

         _?(# < 0.25 &)] < 5 &] // 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v] &])

... on which you can perform graph operations:

CommunityGraphPlot[g]

edited Jan 14 at 16:16

answered Jan 13 at 12:17

kirma

10.1k13058

(* Perform image manipulation steps, feeding from one to another. *)

(* You can replace a "//" with "// Echo //" to see an intermediate value. *)

MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

    Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

  (* Measure component centroids on the manipulated image. *)

  ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

 Function[v, 

  (* Select valid edges from all pairs of components:

     - those whose edge length is less than 300, and

     - at most 4 values of 400 sampled along the edge have a value < 0.25 *)

  Select[Subsets[v, {2}],

     EuclideanDistance @@ # < 300 &&

      Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

       _?(# < 0.25 &)] < 5 &] // 

   (* Overlay the graph on top of the original image. *)

   Show[img,

     (* Construct a graph object with vertices on component centroids,

        and edges as filtered by the Select expression. *) 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v, 

      VertexStyle -> Red, VertexSize -> 1/2], ImageSize -> Medium] &]

Following variant just generates the graph g:

g = (MorphologicalBinarize[img, 0.9] // Blur[#, 40] & // 

      Binarize[#, 0.9] & // HitMissTransform[#, DiskMatrix[55]] & // 

    ComponentMeasurements[#, "Centroid"][[All, 2]] & // 

   Function[v, 

    Select[Subsets[v, {2}],

       EuclideanDistance @@ # < 300 &&

        Count[Table[Min@PixelValue[img, {t, 1 - t}.#], {t, 0, 1, 0.0025}],

         _?(# < 0.25 &)] < 5 &] // 

     Graph[v, UndirectedEdge @@@ #, VertexCoordinates -> v] &])

... on which you can perform graph operations:

CommunityGraphPlot[g]

edited Jan 14 at 16:16

answered Jan 13 at 12:17

kirma

10.1k13058

edited Jan 14 at 16:16

answered Jan 13 at 12:17

kirma

10.1k13058

answered Jan 13 at 12:17

kirma

10.1k13058

answered Jan 13 at 12:17

kirma

10.1k13058

3

$begingroup$
Wow, very impressive.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:33

$begingroup$
It is very good and get what I want to do this research. Thank you @kirma But as I am not expert in this notation syntax, I hope someone can transalet this syntax into step by step (line by line) notation. Thank you very much.
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:54

$begingroup$
And also I need to extract the graph for more exploration in network science, like community detection etc. So can I get that?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 23:12

1

$begingroup$
@kirma Oh great! Thank you very much. That's all what I need. And again, thanks for your time, it's very helpful.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:12

1

$begingroup$
I'll try to generalize this code for other data experimantation condition. Thanks.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:13

|
show 5 more comments

3

$begingroup$
Wow, very impressive.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:33

$begingroup$
It is very good and get what I want to do this research. Thank you @kirma But as I am not expert in this notation syntax, I hope someone can transalet this syntax into step by step (line by line) notation. Thank you very much.
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:54

$begingroup$
And also I need to extract the graph for more exploration in network science, like community detection etc. So can I get that?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 23:12

1

$begingroup$
@kirma Oh great! Thank you very much. That's all what I need. And again, thanks for your time, it's very helpful.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:12

1

$begingroup$
I'll try to generalize this code for other data experimantation condition. Thanks.
$endgroup$
– Iqbal Rahmadhan
Jan 14 at 19:13

Wow, very impressive.

– Henrik Schumacher
Jan 13 at 12:33

It is very good and get what I want to do this research. Thank you @kirma But as I am not expert in this notation syntax, I hope someone can transalet this syntax into step by step (line by line) notation. Thank you very much.

– Iqbal Rahmadhan
Jan 13 at 22:54

And also I need to extract the graph for more exploration in network science, like community detection etc. So can I get that?

– Iqbal Rahmadhan
Jan 13 at 23:12

@kirma Oh great! Thank you very much. That's all what I need. And again, thanks for your time, it's very helpful.

– Iqbal Rahmadhan
Jan 14 at 19:12

I'll try to generalize this code for other data experimantation condition. Thanks.

– Iqbal Rahmadhan
Jan 14 at 19:13

|
show 5 more comments

img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"];

G = MorphologicalGraph[MinFilter[img, 5]]; // AbsoluteTiming

Show[img, G, ImageSize -> Medium]

enter image description here

answered Jan 13 at 11:58

Henrik Schumacher

53.2k471148

2

$begingroup$
This will work better if you ImageResize smaller and then MorphologicalBinarize. I get nice results with MorphologicalGraph[MorphologicalBinarize[ImageResize[i, 250]]]. (Try varying the amount to resize by also)
$endgroup$
– Carl Lange
Jan 13 at 12:09

$begingroup$
@Carl Lange Good idea. This take nicely care of the mess in the lower left corner. Several disks around the image boundaries get lost, though. Anyways, feell free to post your own solution. This question is definitely about some filtering and parameter tweaking for which I don't find time at the moment.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:32

add a comment |

img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"];

G = MorphologicalGraph[MinFilter[img, 5]]; // AbsoluteTiming

Show[img, G, ImageSize -> Medium]

enter image description here

answered Jan 13 at 11:58

Henrik Schumacher

53.2k471148

2

$begingroup$
This will work better if you ImageResize smaller and then MorphologicalBinarize. I get nice results with MorphologicalGraph[MorphologicalBinarize[ImageResize[i, 250]]]. (Try varying the amount to resize by also)
$endgroup$
– Carl Lange
Jan 13 at 12:09

$begingroup$
@Carl Lange Good idea. This take nicely care of the mess in the lower left corner. Several disks around the image boundaries get lost, though. Anyways, feell free to post your own solution. This question is definitely about some filtering and parameter tweaking for which I don't find time at the moment.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:32

add a comment |

img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"];

G = MorphologicalGraph[MinFilter[img, 5]]; // AbsoluteTiming

Show[img, G, ImageSize -> Medium]

enter image description here

answered Jan 13 at 11:58

Henrik Schumacher

53.2k471148

img = ColorConvert[Import["https://i.stack.imgur.com/78BBP.png"], "Grayscale"];

G = MorphologicalGraph[MinFilter[img, 5]]; // AbsoluteTiming

Show[img, G, ImageSize -> Medium]

enter image description here

answered Jan 13 at 11:58

Henrik Schumacher

53.2k471148

answered Jan 13 at 11:58

Henrik Schumacher

53.2k471148

answered Jan 13 at 11:58

Henrik Schumacher

53.2k471148

answered Jan 13 at 11:58

Henrik Schumacher

53.2k471148

2

$begingroup$
This will work better if you ImageResize smaller and then MorphologicalBinarize. I get nice results with MorphologicalGraph[MorphologicalBinarize[ImageResize[i, 250]]]. (Try varying the amount to resize by also)
$endgroup$
– Carl Lange
Jan 13 at 12:09

$begingroup$
@Carl Lange Good idea. This take nicely care of the mess in the lower left corner. Several disks around the image boundaries get lost, though. Anyways, feell free to post your own solution. This question is definitely about some filtering and parameter tweaking for which I don't find time at the moment.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:32

add a comment |

2

$begingroup$
This will work better if you ImageResize smaller and then MorphologicalBinarize. I get nice results with MorphologicalGraph[MorphologicalBinarize[ImageResize[i, 250]]]. (Try varying the amount to resize by also)
$endgroup$
– Carl Lange
Jan 13 at 12:09

$begingroup$
@Carl Lange Good idea. This take nicely care of the mess in the lower left corner. Several disks around the image boundaries get lost, though. Anyways, feell free to post your own solution. This question is definitely about some filtering and parameter tweaking for which I don't find time at the moment.
$endgroup$
– Henrik Schumacher
Jan 13 at 12:32

This will work better if you ImageResize smaller and then MorphologicalBinarize. I get nice results with MorphologicalGraph[MorphologicalBinarize[ImageResize[i, 250]]]. (Try varying the amount to resize by also)

– Carl Lange
Jan 13 at 12:09

@Carl Lange Good idea. This take nicely care of the mess in the lower left corner. Several disks around the image boundaries get lost, though. Anyways, feell free to post your own solution. This question is definitely about some filtering and parameter tweaking for which I don't find time at the moment.

– Henrik Schumacher
Jan 13 at 12:32

add a comment |

First, I find the centroids of the disks (this is similar to what Szabolcs does in a comment):

img = Import["https://i.stack.imgur.com/78BBP.png"];

binarized = Binarize@MeanFilter[img, 10];

distance = ImageAdjust@DistanceTransform[binarized];



centroids = ComponentMeasurements[Binarize[distance, 0.7], "Centroid"][[All, 2]];

HighlightImage[distance, centroids, ImageSize -> 500]

Centroids

Then I guess a disk radius and check how reasonable it is using HighlightImage:

disks = Disk[#, 115] & /@ centroids;

HighlightImage[

 img,

 Graphics[{White, disks}, Background -> Black]

 ]

Disk fit

It's not perfect, but let's compute the graph anyway:

adjacencyMatrix = 

  Outer[EuclideanDistance[#, #2] <= 2 115 &, centroids, centroids, 1];



graph2 = AdjacencyGraph[Boole@adjacencyMatrix, VertexCoordinates -> centroids];

Show[img, graph2, ImageSize -> 500]

Graph

As Szabolcs points out in a comment, NearestNeighborGraph can be used as well:

Show[

 img,

 NearestNeighborGraph[centroids, {All, 2 115}],

 ImageSize -> 500

 ]

Graph using nearest neighbors

It has problems but there is some promise in this approach. If anyone is able to improve upon this (or if you were already working in this direction), feel free to post it as your own answer.

edited Jan 13 at 19:20

answered Jan 13 at 13:09

C. E.

50.4k397203

2

$begingroup$
An option is NearestNeighborGraph[points, {All, radius}].
$endgroup$
– Szabolcs
Jan 13 at 14:14

$begingroup$
@Szabolcs Thanks, that's exactly what I needed.
$endgroup$
– C. E.
Jan 13 at 15:43

$begingroup$
It is very good. Is there a way that we can use MorphologicalGraph after get variabel distance?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:57

$begingroup$
@IqbalRahmadhan yeah, but I didn't get great results with it.
$endgroup$
– C. E.
Jan 14 at 4:11

add a comment |

First, I find the centroids of the disks (this is similar to what Szabolcs does in a comment):

img = Import["https://i.stack.imgur.com/78BBP.png"];

binarized = Binarize@MeanFilter[img, 10];

distance = ImageAdjust@DistanceTransform[binarized];



centroids = ComponentMeasurements[Binarize[distance, 0.7], "Centroid"][[All, 2]];

HighlightImage[distance, centroids, ImageSize -> 500]

Centroids

Then I guess a disk radius and check how reasonable it is using HighlightImage:

disks = Disk[#, 115] & /@ centroids;

HighlightImage[

 img,

 Graphics[{White, disks}, Background -> Black]

 ]

Disk fit

It's not perfect, but let's compute the graph anyway:

adjacencyMatrix = 

  Outer[EuclideanDistance[#, #2] <= 2 115 &, centroids, centroids, 1];



graph2 = AdjacencyGraph[Boole@adjacencyMatrix, VertexCoordinates -> centroids];

Show[img, graph2, ImageSize -> 500]

Graph

As Szabolcs points out in a comment, NearestNeighborGraph can be used as well:

Show[

 img,

 NearestNeighborGraph[centroids, {All, 2 115}],

 ImageSize -> 500

 ]

Graph using nearest neighbors

It has problems but there is some promise in this approach. If anyone is able to improve upon this (or if you were already working in this direction), feel free to post it as your own answer.

edited Jan 13 at 19:20

answered Jan 13 at 13:09

C. E.

50.4k397203

2

$begingroup$
An option is NearestNeighborGraph[points, {All, radius}].
$endgroup$
– Szabolcs
Jan 13 at 14:14

$begingroup$
@Szabolcs Thanks, that's exactly what I needed.
$endgroup$
– C. E.
Jan 13 at 15:43

$begingroup$
It is very good. Is there a way that we can use MorphologicalGraph after get variabel distance?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:57

$begingroup$
@IqbalRahmadhan yeah, but I didn't get great results with it.
$endgroup$
– C. E.
Jan 14 at 4:11

add a comment |

First, I find the centroids of the disks (this is similar to what Szabolcs does in a comment):

img = Import["https://i.stack.imgur.com/78BBP.png"];

binarized = Binarize@MeanFilter[img, 10];

distance = ImageAdjust@DistanceTransform[binarized];



centroids = ComponentMeasurements[Binarize[distance, 0.7], "Centroid"][[All, 2]];

HighlightImage[distance, centroids, ImageSize -> 500]

Centroids

Then I guess a disk radius and check how reasonable it is using HighlightImage:

disks = Disk[#, 115] & /@ centroids;

HighlightImage[

 img,

 Graphics[{White, disks}, Background -> Black]

 ]

Disk fit

It's not perfect, but let's compute the graph anyway:

adjacencyMatrix = 

  Outer[EuclideanDistance[#, #2] <= 2 115 &, centroids, centroids, 1];



graph2 = AdjacencyGraph[Boole@adjacencyMatrix, VertexCoordinates -> centroids];

Show[img, graph2, ImageSize -> 500]

Graph

As Szabolcs points out in a comment, NearestNeighborGraph can be used as well:

Show[

 img,

 NearestNeighborGraph[centroids, {All, 2 115}],

 ImageSize -> 500

 ]

Graph using nearest neighbors

It has problems but there is some promise in this approach. If anyone is able to improve upon this (or if you were already working in this direction), feel free to post it as your own answer.

edited Jan 13 at 19:20

answered Jan 13 at 13:09

C. E.

50.4k397203

First, I find the centroids of the disks (this is similar to what Szabolcs does in a comment):

img = Import["https://i.stack.imgur.com/78BBP.png"];

binarized = Binarize@MeanFilter[img, 10];

distance = ImageAdjust@DistanceTransform[binarized];



centroids = ComponentMeasurements[Binarize[distance, 0.7], "Centroid"][[All, 2]];

HighlightImage[distance, centroids, ImageSize -> 500]

Centroids

Then I guess a disk radius and check how reasonable it is using HighlightImage:

disks = Disk[#, 115] & /@ centroids;

HighlightImage[

 img,

 Graphics[{White, disks}, Background -> Black]

 ]

Disk fit

It's not perfect, but let's compute the graph anyway:

adjacencyMatrix = 

  Outer[EuclideanDistance[#, #2] <= 2 115 &, centroids, centroids, 1];



graph2 = AdjacencyGraph[Boole@adjacencyMatrix, VertexCoordinates -> centroids];

Show[img, graph2, ImageSize -> 500]

Graph

As Szabolcs points out in a comment, NearestNeighborGraph can be used as well:

Show[

 img,

 NearestNeighborGraph[centroids, {All, 2 115}],

 ImageSize -> 500

 ]

Graph using nearest neighbors

It has problems but there is some promise in this approach. If anyone is able to improve upon this (or if you were already working in this direction), feel free to post it as your own answer.

edited Jan 13 at 19:20

answered Jan 13 at 13:09

C. E.

50.4k397203

edited Jan 13 at 19:20

answered Jan 13 at 13:09

C. E.

50.4k397203

answered Jan 13 at 13:09

C. E.

50.4k397203

answered Jan 13 at 13:09

C. E.

50.4k397203

2

$begingroup$
An option is NearestNeighborGraph[points, {All, radius}].
$endgroup$
– Szabolcs
Jan 13 at 14:14

$begingroup$
@Szabolcs Thanks, that's exactly what I needed.
$endgroup$
– C. E.
Jan 13 at 15:43

$begingroup$
It is very good. Is there a way that we can use MorphologicalGraph after get variabel distance?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:57

$begingroup$
@IqbalRahmadhan yeah, but I didn't get great results with it.
$endgroup$
– C. E.
Jan 14 at 4:11

add a comment |

2

$begingroup$
An option is NearestNeighborGraph[points, {All, radius}].
$endgroup$
– Szabolcs
Jan 13 at 14:14

$begingroup$
@Szabolcs Thanks, that's exactly what I needed.
$endgroup$
– C. E.
Jan 13 at 15:43

$begingroup$
It is very good. Is there a way that we can use MorphologicalGraph after get variabel distance?
$endgroup$
– Iqbal Rahmadhan
Jan 13 at 22:57

$begingroup$
@IqbalRahmadhan yeah, but I didn't get great results with it.
$endgroup$
– C. E.
Jan 14 at 4:11

An option is NearestNeighborGraph[points, {All, radius}].

– Szabolcs
Jan 13 at 14:14

@Szabolcs Thanks, that's exactly what I needed.

– C. E.
Jan 13 at 15:43

It is very good. Is there a way that we can use MorphologicalGraph after get variabel distance?

– Iqbal Rahmadhan
Jan 13 at 22:57

@IqbalRahmadhan yeah, but I didn't get great results with it.

– C. E.
Jan 14 at 4:11

add a comment |

draft saved

draft discarded

Thanks for contributing an answer to Mathematica Stack Exchange!

Please be sure to answer the question. Provide details and share your research!

But avoid …

Asking for help, clarification, or responding to other answers.

Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.

To learn more, see our tips on writing great answers.

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Post as a guest

Name

Required, but never shown

Name

Required, but never shown

Name

Required, but never shown

This page is only for reference, If you need detailed information, please check here

Search This Blog

Ufyukyu