CRF’s are generally appended on top of CNN features to finely label the loss of invariance due to CNN. A local-connected CRF would cause over-smoothening as it is constrained only on the local neighbourhood and would force all the pixels in the neighbourhood to be same. However fully connected helps overcome this.
I just want to confirm the reason behind this.
Is it because in a fully connected CRF, a single pixel is not constrained just by the neighbourhood(which might belong to a different class) but also by many other pixels(which might belong to the same class). While a CNN might neglect such a case due to translation invariance, a CRF would detect it by the constraint imposed by all the other pixels.
Is this correct ??
Also, energy in a MRF is generally exponential is it because of its relation with physics(physical energy) and also to consider the log-likelihood. I am asking this because the exponential relation between similar but distant pixels would be less, compared to a non-exponential one. (Referring to DeepLab https://arxiv.org/pdf/1606.00915.pdf equation (3))