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I am attempting building a neural net to segment pixels in volumetric data: I have microscopy images in 3D (about 500x500x500px each) which contain signal from nuclei.

In the data form it means I have a 3D matrix of dimension 500x500x500, which can be approximated by a noise space filled by many 3D gaussians of sigma $\approxeq$ 6–7. The training set has about 90000 segmented nucleis.

My goal is to build a neural net capable of segmenting the pixels where such nuclei are present against the noise and background.

As a raw idea, I am going for an encoder-decoder style neural net.

My intuition tells me there is information to be gained from feeding into the net a 3D cube—as the object itself is a 3D object. But another approach is to train on 2D slices and feed each slice one at a time.

The second solution is a much easier one, with a lot of documentation on 2D pictures pixel segmentation.

Will I loose a lot by doing a 2D stack VS a 3D cube?

Is it even doable to do a 3D cube?

If you think a 3D architecture would be better, could you recommend some papers / documentation?

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Will I loose a lot by doing a 2D stack VS a 3D cube?

That is hard to say; I recommend trying the easy approach first and if you are unsatisfied with the results, proceed to a 3D network. From your description it sounds that the data are quite easy and the 2D approach could actually work.

Is it even doable to do a 3D cube?

Yes, convolutional networks operating on 3D data are not uncommon, especially in domains like medical imaging. These networks, however, suffer usually from the GPU memory limitations, so you will probably have to make trade-offs in terms of network depth and layer sizes. For reference, see following papers:

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