### The *H* function

The full system *F* is a chain of the CNN *G* to produce probability distribution from the input, and *H* which predicts the final pixel value based on the outputs of *G*. This covers the entire algorithm.

I looked at *G* yesterday, so today I’ll define the *H* function.

There are a number of options to convert the probability distribution to pixel values.

**Mode** You can use the mode of the probability distribution to return Y_hat. This is shown as the right most images in fig 4. It gives vibrant colors but at the expense of spatially inconsistent results. See the red spot on the bus.

**Mean** The mean produces a spatially consistent result, at the expense of color vibrancy.

**Annealed Mean** The authors choose to interpolate between the mean and mode to attempt the best of both worlds. There is a parameter *T* which corresponds to the temperature of the softmax distributions, which can be adjusted. They then take the *mean* of that readjustment.