We are discussing the mathematical model of the system that has been found to be the most proper to deal with the practical problems that arise about image proc

We are discussing the mathematical model of the system that has been found to be the most proper to deal with the practical problems that arise about image processing. When he says "the device integrates over..." what he means is that we can model the display device as a reconstruction filter integrating over the point sample lattice. Remember, we are discussing the mathematical model of image processing. In the purely physical model the pixels in the memory are probably a linear array of n-bit numbers, that drive voltages over the illuminants of the display. However, the "linear array of n-bit numbers in a framebuffer" is a really awkward model to start discussing e.g. image processing algorithms. The point sample model, as the author tries to persuade, provides a simple formalism for a lot of practical problems and is also, from the point of view of sampling theory, the correct model.