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I was reading the paper Fully Convolutional Networks for Semantic Segmentation and on section 3 they introduce the notation for what they call a Fully Convolutional Neural Network (FCN). Are they just describing normal ConvNets? I find their notation confusing specially the following one:

$$ f_{ks} \circ g_{k's'} = (f \circ g)_{k' + (k-1)s', s s'}$$

I find that notation confusing since they don't define what $g$ is or any of its input arguments (k' & s'). The accompanying text is also confusing:

While a general deep net computes a general nonlinear function, a net with only layers of this form computes a nonlinear filter, which we call a deep filter or fully convolutional network. An FCN naturally operates on an input of any size, and produces an output of corresponding (possibly resampled) spatial dimensions.

Are they just trying to use their own notation to say "here is what convnets are"?

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    $\begingroup$ an fcn is a convolutional network with no fully connected layers at the end $\endgroup$ – shimao Jul 30 '19 at 0:52

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