Question

I have a 2D area with ‘dots’ distributed on this area. I now am trying to detect ‘clusters’ of dots, that is, areas with a certain high density of dots.

Any thoughts on (or links to articles with thoughts on) how to elegantly detect these areas?

Answer 1

How about defining an arbitrary resolution for your space, and calculate for each point in that matrix, a measure of the distance from that point to all dots, then you could make a ‘heat graph’ and use a threshold to define the clusters.

It’s a nice exercise for processing, maybe later I will post a solution.

EDIT:

Here it is:

//load the image PImage sample; sample = loadImage('test.png'); size(sample.width, sample.height); image(sample, 0, 0); int[][] heat = new int[width][height];  //parameters int resolution = 5; //distance between points in the gridq int distance = 8; //distance at wich two points are considered near float threshold = 0.5; int level = 240; //leven to detect the dots int sensitivity = 1; //how much does each dot matters  //calculate the 'heat' on each point of the grid color black = color(0,0,0); loadPixels(); for(int a=0; a<width; a+=resolution){   for(int b=0; b<height; b+=resolution){     for(int x=0; x<width; x++){       for(int y=0; y<height; y++){         color c = sample.pixels[y*sample.width+x];                 /**          * the heat should be a function of the brightness and the distance,           * but this works (tm)          */         if(brightness(c)<level && dist(x,y,a,b)<distance){           heat[a][b] += sensitivity;         }       }     }   } }  //render the output for(int a=0; a<width; ++a){   for(int b=0; b<height; ++b){     pixels[b*sample.width+a] = color(heat[a][b],0,0);   } } updatePixels(); filter(THRESHOLD,threshold); 

EDIT 2 (slighly less inefficient code but same output):

//load the image PImage sample; sample = loadImage('test.png'); size(sample.width, sample.height); image(sample, 0, 0); int[][] heat = new int[width][height]; int dotQ = 0; int[][] dots = new int[width*height][2]; int X = 0; int Y = 1;   //parameters int resolution = 1; //distance between points in the grid int distance = 20; //distance at wich two points are considered near float threshold = 0.6; int level = 240; //minimum brightness to detect the dots int sensitivity = 1; //how much does each dot matters  //detect all dots in the sample loadPixels(); for(int x=0; x<width; x++){  for(int y=0; y<height; y++){    color c = pixels[y*sample.width+x];    if(brightness(c)<level) {        dots[dotQ][X] += x;        dots[dotQ++][Y] += y;    }  } }  //calculate heat for(int x=0; x<width; x+=resolution){  for(int y=0; y<height; y+=resolution){    for(int d=0; d<dotQ; d++){      if(dist(x,y,dots[d][X],dots[d][Y]) < distance)        heat[x][y]+=sensitivity;    }  } }  //render the output for(int a=0; a<width; ++a){  for(int b=0; b<height; ++b){    pixels[b*sample.width+a] = color(heat[a][b],0,0);  } } updatePixels(); filter(THRESHOLD,threshold);  /** This smooths the ouput with low resolutions * for(int i=0; i<10; ++i) filter(DILATE); * for(int i=0; i<3; ++i) filter(BLUR); * filter(THRESHOLD); */ 

And the output with (a reduced) Kent sample: