Can we learn 3d features using Autoencoder? Typically, we use Autoencoder to learn 2d features on 2d images (e.g. pen-strokes of digit). 
For example, if I have 10000 3d 31x31x31 images (e.g. car images). I unroll each of the images, i.e. 31x31x31 to 29791. So, I have 29791x10000 as my input vectors. If I run unsupervised learning---autoencoder on it with 100 hidden units, can I obtain 100 distinct 3d features?
Will the 3d optimal activation equation(in term of weights) for each feature be the same as 2d ones? 
 A: Plain auto encoders do not make use of the fact that the data they are fed is 2d, 3d or something that does not even have a spatial meaning. There is no reason why it should not work.
A: Yes you can do this check these papers
http://arxiv-web3.library.cornell.edu/abs/1409.7164v1
http://liris.cnrs.fr/Documents/Liris-5670.pdf
I think you have to do some dimensionality reduction algorithm like PCA, LDA or one of the variations to make it speedier.
For your example of checking car features you can stack multiple autoencoders and use a greedy layer-wise algorithm to train it to detect features instead of having a single autoencoder for 3D features.
A: This paper trains a GAN on point clouds: https://arxiv.org/pdf/1707.02392.pdf
In that process they created an auto-encoder framework. So they were able to get those distinct feature vectors, and they show an example of traversing the latent space.
I figure that new challenges arise in working in 3D. One of them is that it is not clear the best way to order 3d data, in this paper they don't order the data, so evaluation functions need to be symmetric (permutation agnostic). So they used 1-D convolution layers. They use the same activation functions as 2D representation (ReLU), since it is symmetric.
Seems that there is a lot of untraversed territory at the intersection of 3d representations and ML.
Edit- adding citation:
Panos Achlioptas and
Olga Diamanti and
Ioannis Mitliagkas and
Leonidas J. Guibas,
Representation Learning and Adversarial Generation of 3D Point Clouds,
CoRR, Sun, 06 Aug 2017
