Recover curves from noisy collection of points 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?
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