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)
Answer:D
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)
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).