Wednesday, 21 March 2007

Image Tracking

The last few weeks I've been playing with Image tracking algorythms. After searching around a bit I decided to start with Edard Rosten's FAST Corner Detector (PDF).

It seems to produce good results and has been used by Andrew Davison to do real time monocular SLAM (i.e. one web cam). Although Bob Motram has already done a great c# port of Davison's code (MonoSLAM), it relies on seeing a dark rectangle of known size before starting, which didn't seem appropriate for my usage on a robot and I wanted to get to know the algorythms at first hand.

Finding corners is pretty easy, the hard part is tracking them. The first phase is to find corners in the next frame that look similar, but this also generates a good deal of randomly placed matches.

The first method I attempted created a mean move from all the moving corners, then fine tunned by iteratively re-calculating a mean move by weighing moves based on the probability of being within a gaussian distribution of the last mean move. This has the effect of ignoring outliers a often converging on the true move. In retrospect, the initial mean should have been calculated according to weights based on how similar the corners looked, but it didn't seem to matter too much.

Although this worked OK-ish, unless the camera is on a perfect horizontal and all the objects in the scene are far away, the result of panning a camera really wants to be part of a sphere. My actual robot is likely to have a fixed camera, so I should have been content with only optimising the x displacement (rotation) and leaving it at that, but alas curiosity got the better of me, so I decided to try to look to higher dimensions. Bad move.

Really, there is no escaping it - full 3D is the only proper representation that can account for the movement in the pictures. Alas this isn't just an average or weighted average of pixel movement. It requires simultaneous gradient descent in all the dimensions of the model, and projection of corners into the real world. This involves some hard maths that I wasn't quite prepared for and am far from mastering...

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