Explain to me like I'm 5: what do Zernike features mean?

Hi all,

I’m a simple biologist and I’m trying to analyse some images for a colleague. She’s interested in cell polarity and I’ve seen that CellProfiler has a function that can help (“MeasureObjectIntensityDistribution”). So far, so good. I get a lot of numbers but I’m unable to explain what they mean.

Whilst I kind of understand that a Zernike is a shape descriptor in general, I’m stuck with what they mean in particular. For example, what does “RadialDistribution_ZernikePhase_Phalloidin_9_5” mean?

Hi @MatthieuV,

Take a look at this : http://cellprofiler-manual.s3.amazonaws.com/CellProfiler-3.0.0/modules/measurement.html#measureobjectintensitydistribution

For each module, if you highlight the module and click on the “?” button (right above the Start Test Mode button), you can see the module help and the measurements it make.

Hope this is helpful!

Hi Nasim,
Thanks! Yes, I’ve seen this and it’s overall helpful but if you don’t know what a Zernike feature is, you get a number that does not mean much. So, how different are Zernike_8-8 to 9-5? What do they mean in particular?

Hi Matthieu,

They are mathematical descriptors of shape- you can see what each of the first 21 represent in this diagram from wikipedia.

In general, the feature you asked about is the 9th row of a chart like this, the position with 5 as the superscript.

It’s hard to interpret Zernike features in an ELI5 kind of way- it’s basically just saying “some subtle aspect of the shape has changed”, but not an easy thing to say “it’s more wavy”, “more skinny”, etc.

The best resource I’ve found for making this intuitive is this paper from Bob Murphy- they add up a bunch of the zernike polynomials describing the top shapes, and get the shapes on the bottom. It shows you that while Zernike polynomials don’t fully tell you everything about the shape, they’re clearly doing some shape description that gives you a rough idea of what the object looks like.


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Hi Beth,

Thanks! I’ve found this https://www.researchgate.net/publication/261439588:

Would you say that “Zernike Phase” is describing the amount of signal in the light grey area in the upper panels (Order) or in the red part of the disk in your Wikipedia panel? If I understand the CellProfiler Wiki correctly, the closer the Phase is to 1, the more polarised the cell.

Would you say that “Zernike Phase” is describing the amount of signal in the light grey area in the upper panels (Order) or in the red part of the disk in your Wikipedia panel?

You definitely want to use the wikipedia-type model, as you’ll notice the zernikes are given with 2 metrics (ie not 1, 2, 3, but 1_1, 5_3, etc).

My understanding there is that the higher the value for any given zernike, the closer that the object matches the red/gray areas- IE a ring-like object will have a low 2_0 value (where value concentrates in the center) but a high 4_0 value (which is low in the center but high in a ring).

If I understand the CellProfiler Wiki correctly, the closer the Phase is to 1, the more polarised the cell.

For some of the Zernikes, that will be true, for others not. I really think for the most part you want to avoid assigning any “human-intuitable-values” to your Zernikes, other than “they represent subtle descriptors of shape”- they’re really most useful for either a) reconstructing shapes (like in the paper I linked) or b) just feeding into an overall unbiased feature model for doing morphological profiling.