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 a digital image if (x, y) are integers from Z2 and f is a function that assigns a gray-level value (that is, a real number from the set R) to each distinct coordinate pair (x, y). What happens to the digital image if the gray levels also are integers?

(a) The Digital image then becomes a 2-D function whose coordinates and amplitude values are integers

(b) The Digital image then becomes a 1-D function whose coordinates and amplitude values are integers

(c) The gray level can never be integer

(d) None of the mentioned

I got this question in my homework.

This interesting question is from Representing Digital Images in portion Digital Image Fundamentals of Digital Image Processing

Answer 1

Right option is (a) The Digital image then becomes a 2-D function whose coordinates and amplitude values are integers

Explanation: In Quantization Process if the gray levels also are integers the Digital image then becomes a 2-D function whose coordinates and amplitude values are integers.