What Does 'Zero Order Hold' and 'First Order Hold' Mean? While studying the Image Magnification in spatial domain, I have come across this definition of Image Magnification by Replication:


  Replication is a zero order hold where each pixel along a scan line is repeated once and then each scan line is repeated.


And the definition for Image Magnification by Interpolation is given as:


  Linear interpolation is a first order hold where a straight line is first fitted in between pixels along a row. Then the pixels along each column are interpolated along a straight line.


Can you please explain the terms 'zero order hold' and 'first order hold' in layman's terms, so that I could understand these two definitions? Thanks.
We need to assume the reader knows some basic stuff to answer that.
Let's give it a try.

Lets understand the sentence - Zero / First Order Hold.
We have the Zero / First Order and the Hold.

Zero / First Order hold means the order of the Taylor Series of the function we use to interpolate. In other words, the degree of the Polynomial we can write the function with.
Zero Order means the function is constant, we interpolate the same value in the missing parts.
First order means we can use linear function to interpolate (Line with a slope).  

Hold means we hold the parameters to be the same until the next sample.