# Correlation with zernike features, but what does it mean!

Hello,

I wonder if anyone can help me… I have been looking for correlations between certain biological properties of colonies of a primary human cell line and the size, shape, cell density etc. of these colonies - probing the latter using cell profiler. There is an inverse correlation with my property of interest and the ‘eccentricity’ of the colony shape suggesting circularity is relevant, but there is also a correlation with certain zernike features. Specifically, zernike ‘6 6’ for which there is a good negative correlation over the range 0.002 - 0.011. There is also a negative correlation with the sums of the zernike features (if that means anything) over the range 0.460-0.581. I’ve copied and pasted the list of zernikes with the corresponding R2 value for the correlation with my property of interest at the bottom of this post. I’ve also attacher an image of the 12 colony shapes ranked according to my property of interest .

I know multiple comparisons such as I’ve done are statistically dodgy but it would help me weigh up whether the correlation is interesting or not if I knew what it meant…! I’ve been browsing lots of articles but I have to say that they are all a bit beyond me. Any pointers would be much appreciated (especially if they come without equations!)

thanks

jon

and thanks to the cellprofiler team for an awesome resource!

1 1 …0.017536974
2 0 …0.118418771
2 2 …0.238829273
Sum of 2 …0.340868173
Sum of 1&2 …0.337366893
3 1 …0.275595982
3 3 …0.002391311
Sum of 3 …0.2083681
Sum of 1-3 …0.458606822
4 0 …0.463725234
4 2 …0.279502328
4 4 …0.265158976
Sum of 4 …0.080721624
Sum of 1-4 …0.302732752
5 1 …0.006461294
5 3 …0.03418431
5 5 …0.025478357
Sum of 5 …0.006509283
Sum of 1-5 …0.321657119
6 0 …0.079320561
6 2 …0.003114777
6 4 …0.227566627
6 6 …0.593296892
Sum of 6 …0.341169631
Sum of 1-6 …0.627433229
7 1 …0.001013277
7 3 …0.000131616
7 5 …0.034213096
7 7 …0.146625932
Sum of 7 …0.000474104
Sum of 1-7 …0.510500777
8 0 …0.244045533
8 2 …0.002000277
8 4 …0.196964253
8 6 …0.119374538
8 8 …0.042992997
Sum of 8 …0.004463649
Sum of 1-8 …0.436617994
9 1 …0.080625903
9 3 …0.079641718
9 5 …0.072705498
9 7 …0.011855241
9 9 …0.255323243
Sum of 9 …0.431769649
Sum of 1-9 …0.520728336

apologies … the image didn’t upload. here it is.
jon

Hello,

Sorry for the delay - clearly no one is excited about explaining zernikes without equations! The next best thing is an image:
lambda-factory.co.jp/Free/ze … yE1024.png

Zernike 6_6 is the shape shown at the bottom right. The Zernikes in CellProfiler measure shape only, not texture/intensity. Most likely, this Zernike 6_6 is responding to shapes with wiggly edges, and also shapes that are fairly round (you can see that if a shape is not very round but with wiggly edges, it will nonetheless not line up well with 6_6.

As for the sums of some Zernikes being helpful… certainly it could be statistical chance as you rightly point out. It could also be that the individual zernikes respond a bit and adding them magnifies the response (in the same way that you might get higher correlations by taking the square of any feature that is itself correlated, although doing this is of dubious value.) Anyway, you could take a look at the individual Zernike shapes according to that chart and see whether any of them make sense in light of the colony shape differences you see by eye.

Best wishes,
Anne