It's a very naive and ignorant question, but let's say if we have a 2D matrix (with high dimensionality), are there any methods using which we could create a continuous surface (i.e. described by a function) out of that matrix?
What I want to know is if there exist any mathematical methods through which one can convert a digital image (grey scale), which is basically a large 2D matrix, to an analog mathematical representation in terms of a 2-variable function, i.e. given the x, y values, the function should be able to give us the intensity of the image for any real valued x and y. Maybe, in a way, what the method should be doing is to "fill" with continuous values the discrete gaps between the elements of the 2D matrix.