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:
