Question

Let Z be the set of real integers and R the set of real numbers. The sampling process may be viewed as partitioning the x-y plane into a grid, with the central coordinates of each grid being from the Cartesian product Z2, that is a set of all ordered pairs (zi, zj), with zi and zj being integers from Z. Then, f(x, y) is said a digital image if:

(a) (x, y) are integers from Z2 and f is a function that assigns a gray-level value (from Z) to each distinct pair of coordinates (x, y)

(b) (x, y) are integers from R2 and f is a function that assigns a gray-level value (from R) to each distinct pair of coordinates (x, y)

(c) (x, y) are integers from R2 and f is a function that assigns a gray-level value (from Z) to each distinct pair of coordinates (x, y)

(d) (x, y) are integers from Z2 and f is a function that assigns a gray-level value (from R) to each distinct pair of coordinates (x, y)

I had been asked this question in a job interview.

The question is from Representing Digital Images topic in section Digital Image Fundamentals of Digital Image Processing

Answer 1

Right answer is (d) (x, y) are integers from Z2 and f is a function that assigns a gray-level value (from R) to each distinct pair of coordinates (x, y)

Easy explanation: In the given condition, f(x, y) is a digital image if (x, y) are integers from Z2 and f a function that assigns a gray-level value (that is, a real number from the set R) to each distinct coordinate pair (x, y).