Hi all! I have a specific problem that I think lends itself to a Kalman filter. Since I’ve never used a Kalman filter before and I’m not sure how exactly I could apply it on my data, I thought I’d reach-out here. My data I have time-lapse images of roots growing. As they grow they emit a bit of li…

[image] yakir12: find some robust way of getting the tip’s trajectories I think the following is a pretty decent way of getting an approximation of the tip’s locations: W = 10 cols = [col for row in -W:W for col in -W:W] rows = [row for row in -W:W for col in -W:W] win = CartesianIndex.(rows…

Your data is not in state space form (that I could easily imagine as applicable for the Kalman filter). Eg your state could be (x, y) coordinates of the root tips, and then perhaps you could use a random walk or an I(1) process (“velocity” changes randomly), but those coordinates would need to be ex…

I’ve successfully followed the tip by just finding the closest and brightest pixel below the previous one. So I could generate an approximation for where the tips might be.

Yes, amazing pictures. To have something more robust, instead of taking the brightest pixel, you can do the following: Given the current position, you can apply a window or kernel and then compute the average of the light location (mean of the light distribution) within the window. ij(x,y) = round…

This video looks amazing! Is there any hope that you could publish the data set somewhere in the open so that others could play around with it?

Thanks! Cool, but could you please explain what the function ij is or does (my only guess was round(Int, x), but that doesn’t seem to work)?

Ah, sorry, You had it almost. ij(x,y) = round(Int, y), round(Int, x) I’ll edit.

Wow! Awesome! So what do you mean by track in: [image] mschauer: You can also use track to obtain a velocity vector. ?

track is just the function name. If you take xnew, ynew = track(imgs[:, :, frame], xpred, ypred, 10, 16) dx = xcur - xnew dy = ycur - ynew you can use that in filtering.

Right, right. So, I played around with it, and it seems like if I increase the noise by one order of magnitude: imgs[i] = 5e2 then it really breaks down. I might need to play with the window size and kernel variance… A similar solution I’ve used before is to calculate the weighted mean of the wi…

As @Tamas_Papp said: Kalman-filtering is mostly orthogonal, if you use a function like track to obtain the noisy position signal, you can use Kalman filtering to update the position x, y taking a linear model for the dynamics of the root location and the current position into account.

Help implement Kalman filter

General Usage

yakir12 February 1, 2018, 6:21pm 16

Cool. Well, now all that remains, unless I misunderstood something, is to refine that with the Kalman filter (see here).

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Help implement Kalman filter

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