Background: I'm trying to make a system that tracks a number of bubbles in a video

I'm implementing the bubble detection in the single image case using the Circular Hough Transform. Due to occlusion, blur and other factors, this detection will never be 100% accurate. I am tuning the detection procedure for high recall, possibly at the expense of precision.

Once this is done and applied to a sequence of frames from a video, I will have a number of detections that can be characterised as points in 4D space - x-position, y-position, radius and frame index.

Is there a procedure that can recover curves from this 4D point cloud?

  • 1
    $\begingroup$ Cross-posted $\endgroup$
    – Emre
    Apr 18, 2012 at 21:10
  • $\begingroup$ apply a 4d median filter and then manifold learning techniques (such as diffusion map etc..) $\endgroup$
    – bla
    Oct 30, 2012 at 6:22
  • 2
    $\begingroup$ Have you considered prediction the motion of the bubbles ? That would allow smoothing over time, which could improve your results. $\endgroup$
    – Mr. White
    Dec 24, 2012 at 8:59
  • 1
    $\begingroup$ Some images might be helpful $\endgroup$ Aug 9, 2013 at 18:42

1 Answer 1


Your problem is very similar to the cell-tracking problem. This has been solved quite well using tracklet based approaches, where each object (bubble, cell etc) is modeled as a Maximum-a-Posteriori (MAP) estimation. The solution to which is through linear programming. You can get a good idea of the approaches and a web-based implementation here


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