I noticed the same thing. I was able to really boost my score by just drawing over the 'same' circle a bunch of times. Doing that got my score up into the 7-8 million range.
Using a Hough transform to find a circle with an unknown radius is expensive. You have a 3D parameter space, and each point has to "vote" for a 2D subsurface of that space. Discretizing the entire volume at a high resolution is going to require a lot of memory.
I agree it is going to expensive but it's not because of memory. You could probably just try every (x,y) center and have all points vote for the radius, and just keep max before moving on to next point.
A sensible, easy thing to do here seems to be to just find the centroid of the cluster points. Then convert all the points into polar coordinates around that centre, and average the R's. The R's could be weighted rather than taken at face value.
I believe this website is using what the paper calls the geometric fit, which is considered one of the better methods, but the paper develops an even better method.
(I had to use this, strangely, in a physics lab course. I was measuring the Zeeman effect by looking at the diameter of rings of light projected by an interferometer; I took webcam images of the ring and used the algorithm to fit circles to the ring and hence measure its diameter.)
This make me remember the Giotto big O history [1]. The pope was looking for a painter and requested samples to artists and Giotto sent for him just a circle.
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[ 5.0 ms ] story [ 68.9 ms ] threadA smattering of poits scribbled close together nets me 220000, while a single big ring earns only 700.
If there were a contest out of this, it could be disqualified: i.e. you start and finish on approximately the same point.
Edit: Just got 902017 for 232 points, 62 radius.
Why not use a Hough transform with each drawn point voting for a center, then average the radius?
It's not a critic - just me wondering why.
https://projecteuclid.org/euclid.ejs/1251119958
I believe this website is using what the paper calls the geometric fit, which is considered one of the better methods, but the paper develops an even better method.
(I had to use this, strangely, in a physics lab course. I was measuring the Zeeman effect by looking at the diameter of rings of light projected by an interferometer; I took webcam images of the ring and used the algorithm to fit circles to the ring and hence measure its diameter.)
http://tube.geogebra.org/student/m1113573
http://i.imgur.com/m8MOtUU.jpg
... fitting! :)
<brag>Tried four times; hit 3.5M on third try, then 4.8M, and got bored.</brag>
https://www.desmos.com/calculator/7dpcup8iwk
Here you move the points by dragging instead of creating them by drawing, which I find more fun in some ways, and less fun in others.
Edit: constraining the radius makes the system behave like a hoop attached to springs https://www.desmos.com/calculator/a2pfwqrtmb
[1] https://100swallows.wordpress.com/2007/09/14/giottos-o/