When we want to quantize an image, is it necessary to do sampling? When we know that image is a discrete signal, is it necessary to find the best samples with Nyquist rate?
Quantization of a continuous signal is the process of representing an infinite set of input values, $x(t)$, that fall into an interval $I_k=[a_k,b_k]$, with a single level $y_k(t)$, the output, that represents all the inputs to that interval with some optimality criterion.
You can quantize an analog signal without sampling it. (however don't mix this with binarization of its amplitude). To do so, you can pass the analog signal from a set of reference thresholders, whose output will be constant as long as the input signal remains in a given interval. Binarization is not necessary if you do not want to convert this into a digital signal.