Algorithm for detecting “clusters” of dots [closed]

Answer 1

Apply a blur filter to a copy of your 2D area. Something like

1 2 3 2 1
2 4 6 4 2
3 6 9 6 3
2 4 6 4 2
1 2 3 2 1

The "darker" areas now identify clusters of dots.

Answer 2

You could overlay a logical grid over your plane. If a grid has a certain number of contained dots, it is considered "dense" and could then be thinned. This is done a lot in GIS applications when working with cluster tolerances. Using the grid helps compartmentalize your thinning algorithm.

Answer 3

You could try creating a Quadtree representation of the data. The shorter paths in the graph would correspond to high density areas.

Or, to put it more clearly: given a Quadtree and level-order traversal, each lower-level node composed of "dots" would represent a high density area. As the level of the nodes increases, such nodes represent lower density areas of "dots"

Answer 4

This really sounds like an academic question.

The solution that comes to mind involves r* trees. This divides your total area in individually sized and possibly overlapping boxes. After doing this you can then determine if each box represents a 'cluster' or not for you by calculating the mean distance.

R* Trees

If that approach becomes difficult to implement you may be better off splitting your datagrid into equal-sized subdivisions and determining if a cluster occurs in each; you will have to be very mindful of edge conditions with this approach though. I would suggest that after the initial division you go through and recombine areas with datapoints within a certain threshold of the defined edge.

Answer 5

I would suggest using a mean-shift kernel to find the density center of your dots.

Mean-shift illustration http://cvr.yorku.ca/members/gradstudents/kosta/compvis/file_mean_shift_path.gif

This figure shows a mean-shift kernel (centered initially on the edge of the cluster) converge towards the cluster's point of highest density.

In theory (in a nutshell):

Several answers to this questions already hinted at the mean-shift way of doing it:

• P Daddy's blurring the image and finding the darkest spot is actually a kernel density estimation (KDE) method, which is the theoretical basis of the mean-shift.

• Both j0rd4n and Bill the Lizard suggested to discretize your space into blocks and inspect their densities.

What you see in the animated figure is a combination of these two suggestions: it uses a moving "block" (i.e. the kernel) to seek the locally highest density.

The mean-shift is an iterative method that uses a pixel neighborhood called the kernel (similar to this one) and uses it to compute the mean of the underlying image data. The mean in this context is the pixel-weighted average of the kernel coordinates.

In each iteration the kernel's mean defines its center coordinates for the next iteration - this is called the shift. Hence the name mean-shift. The stop condition for the iterations is when the shift distance drops to 0 (i.e. we are at the most dense spot in the neighborhood).

A comprehensive introduction to mean-shift (both in theory and application) can be found in this ppt presentation.

In practice:

An implementation of the mean-shift is available in OpenCV:

int cvMeanShift( const CvArr* prob_image, CvRect window,
                 CvTermCriteria criteria, CvConnectedComp* comp );

O'Reilly's Learning OpenCv (google book excerpts) also has a nice explanation on how it works. Basically just feed it your dots image (prob_image).

In practice, the trick is to choose the adequate kernel size. The smaller the kernel, the closer you need to initiate it to the cluster. The bigger the kernel, the more random your initial position can be. However, if there are several clusters of dots in your image, the kernel might converge right between them.

Answer 6

To add a bit of aide to Trebs statement, I think it important to realistically first define what the definition of a cluster is, sure, "dots closer together", thats rather vauge.

Take this sample set I generated, I know there's a cluster shape there, I created it.

However, programmatically identifying this "cluster" might be hard.

A human might deem that a large toroidal cluster, but your automated program is more likely going to decide it a series of smaller clusters in semi-close proximity.

Also, note that there are regions of super-high-density, which are in the context of the bigger picture, merely distractions

You'll need to consider this behaviour and possibly chain together clusters of similar density separated only by insignificant voids of lower density, depending on the specific application.

Whatever you develop, I would at least be interested in how it identifies the data in this set.

( I think looking into the technologies behind HDRI ToneMapping might be in order, because these work more-or-less on Light density, and there are "local" tonemaps and "global" tone maps, each yielding different results )