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# Accurately measuring relative distance between a set of fiducials (Augmented reality game application)

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### #1jkh13  Members   -  Reputation: 125

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Posted 05 December 2011 - 10:00 AM

Let's say I have a set of 5 markers. I am trying to find the relative distances between each marker using an augmented reality framework such as ARToolkit. In my camera feed thee first 20 frames show me the first 2 markers only so I can work out the transformation between the 2 markers. The second 20 frames show me the 2nd and 3rd markers only and so on. The last 20 frames show me the 5th and 1st markers. I want to build up a 3D map of the marker positions of all 5 markers.

My question is, knowing that there will be inaccuracies with the distances due to low quality of the video feed, how do I minimise the inaccuracies given all the information I have gathered?

My naive approach would be to use the first marker as a base point, from the first 20 frames take the mean of the transformations and place the 2nd marker and so forth for the 3rd and 4th. For the 5th marker place it inbetween the 4th and 1st by placing it in the middle of the mean of the transformations between the 5th and 1st and the 4th and 5th. This approach I feel has a bias towards the first marker placement though and doesn't take into account the camera seeing more than 2 markers per frame.

Ultimately I want my system to be able to work out the map of x number of markers. In any given frame up to x markers can appear and there are non-systemic errors due to the image quality.

Any help regarding the correct approach to this problem would be greatly appreciated.

### #2inprazia  Members   -  Reputation: 107

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Posted 07 December 2011 - 07:37 AM

Well, given the fact that you don't know the uncertainty in the input data, the optimal approach would be to apply some kind of least squares fitting. Try to obtain Y equations for your X markers, where Y >= X, describing the transformations you are talking about. Resolve the obtained system of equations by optimizing the least square error iteratively using the Gauss-Newton algorithm. And don't forget to have fun.

### #3GenPFault  Members   -  Reputation: 160

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Posted 08 December 2011 - 02:02 PM

It sounds like you're trying to do SLAM.

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