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[Neighbors from Delaunay] Find Average Neighbor Distance From Delaunay Triangulation Demo #ImageJ #Fiji #Macro
* Demo of using Delaunay triangulation to find average inter-neighbor distances
* In reply to ImageJ forum post:
* Olivier Burri, EPFL BIOP (BioImaging And Optics Platform)
* May 1st 2018
* Provided as-is under Creative Commons Attribution 4.0 International License
// Use The Blobs Image to detect a few points
run("Blobs (25K)");
run("Find Maxima...", "noise=100 output=[Point Selection] light");
// Pick up image name
name = getTitle();
// Cleanup
run("Clear Results");
// From a point selection, get the Delaunay data
run("Delaunay Voronoi", "mode=Delaunay make export");
nR = nResults;
Roi.setName("Delaunay Graph");
run("Add Selection...");
// Here begins some of the magic. It would be simpler to implement this in groovy but here you can see all the logic
// Variables to store
totalNeighbors = newArray(0); // Number of neighbors per point
sumDistances = newArray(0); // The total distance of all the neighbors to each point
pointIDs = newArray(0); // The point Identifiers, made into a simple "Hash" based on their XY coordinates
pointIndexes = newArray(0); // The point indexes to help access arrays more easily.
// Go through each result
for(i=0; i<nR; i++) {
cX1 = getResult("x1", i);
cY1 = getResult("y1", i);
cX2 = getResult("x2", i);
cY2 = getResult("y2", i);
twopoints = newArray(""+cX1+""+cY1, ""+cX2+""+cY2); // create a point identification based on the coordinates
for(k=0; k<2; k++) {
pointID = twopoints[k];
// New point, add it to pointIDs, pointIndexes, add a new totalNeighbors entry and a new sumDistances entry
if(isNew(pointIDs, pointID)) {
pointIDs = Array.concat(pointIDs, pointID);
idx = pointIDs.length-1;
pointIndexes = Array.concat(pointIndexes, idx);
totalNeighbors = Array.concat(totalNeighbors, 0);
sumDistances = Array.concat(sumDistances, 0);
// Make it pretty, give this point an index and a name
Roi.setName("Object #"+IJ.pad(idx+1, 2));
} else {
// Point already exists
idx = getPointIdx(pointIDs, pointID);
// this point has a new neighbor
// Get distance from this point to the other point
dist = distance(cX1, cY1, cX2, cY2);
sumDistances[idx] += dist;
// Results
IJ.renameResults("Raw From Delaunay");
for(i=0; i<pointIDs.length; i++) {
setResult("Label", i, name);
setResult("Object", i, pointIndexes[i]+1);
setResult("N Neighbors", i, totalNeighbors[i]);
setResult("Average Distance", i, sumDistances[i]/totalNeighbors[i]);
// Compute XY distance
function distance(x1,y1,x2,y2) {
return sqrt((x1-x2) * (x1-x2) + (y1-y2) * (y1-y2));
// Returns true if we have already seen this point
function getPointIdx(pointIDs, pointID) {
for(i=0; i<pointIDs.length; i++) {
if(pointIDs[i] == pointID) {return i}
return -1;
// Returns the index of the already existing point
function isNew(pointIDs, pointID) {
for(i=0; i<pointIDs.length; i++) {
if(pointIDs[i] == pointID) {return false}
return true;
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