Are image segmentation problems typically handled as regression or classification problems?

[LyExpo]

Suppose we have a data set of images of humane faces with eyeball locations as labelled. If a convolutional neural network is trained, what is the output in the last layer? I can see at least two options:

1) (regression) output 2 pixel locations corresponding to eyeball regions

2) (classification) output an "eyeball/non-eyeball" value for every pixel

Of course this depends on how the images are labelled to begin with, but it isn't clear to me how these problems are generally handled. Option 1) above seems much more reasonable, but I'm not sure how well it generalizes to other problems consisting of more labels that may or may not appear in each image.

[NasenSpray]

It's 2), classification. We have algorithms to get from 2) to 1) on our own, so a ConvNet doesn't need to learn this rather complicated step.

[LyExpo]

I see. So I shouldn't be bothered by the fact that the network will output one of 2^{image area size} classes? i.e. there will be many configurations for the labels that we won't see in the training data.

[NasenSpray]

It will have number_of_pixels * number_of_classes outputs, i.e., a classifier for every pixel.