where [] is the clipping range of the input, i.e. the boundaries of permissible inputs. [] is the range in quantized output space that it is mapped to. For 8-bit quantization, the output range <img src="https://latex.codecogs.com/gif.latex?\beta_q - \alpha_q <= (2^8 - 1)">.
 acts as a bias to ensure that a 0 in the input space maps perfectly to a 0 in the quantized space. 
Calibration