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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?

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? Correct Answer The Digital image then becomes a 2-D function whose coordinates and amplitude values are integers

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.

Related Questions

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 high contrast image and a dark image will have what kind of histogram respectively, when the histogram, h(rk) = nk, rk the kth gray level and nk total pixels with gray level rk, is plotted nk versus rk? The histogram that are concentrated on the dark side of gray scale. The histogram whose component are biased toward high side of gray scale. The histogram that is narrow and centered toward the middle of gray scale. The histogram that covers wide range of gray scale and the distribution of pixel is approximately uniform.
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Validate the statement: “For a given image in one-dimension given by function f(x, y), to sample the function we take equally spaced samples, superimposed on the function, along a horizontal line. However, the sample values still span (vertically) a continuous range of gray-level values. So, to convert the given function into a digital function, the gray-level values must be divided into various discrete levels.”
Match the items in List - I (Techniques of sampling) with that of List - II (characteristics of procedure). Choose appropriate code for your answer : Set - I (Techniques of sampling) Set – II           (Characteristics of procedure) (a) Purposive sampling (i) Dividing the population into subgroups and taking one or more groups at random (b) Multistage sampling (ii) Researcher relies on his or her own judgment when choosing members from the population (c) Systematic sampling   (iii) Obtaining K ‘interval’ through N/n and using it for constituting the sample (d) Stratified sampling   (iv) Researcher divides the entire population into homogeneous subgroups and randomly selects the final sample
A contrast stretching result been obtained by setting (r1, s1) = (rmin, 0) and (r2, s2) = (rmax, L – 1), where, r and s are gray-values of image before and after processing respectively, L is the max gray value allowed and rmax and rmin are maximum and minimum gray-values in image respectively. What should we term the transformation function if r1 = r2 = m, some mean gray-value.
Which of the two statements from the following statements are correct? (A) Sampling - related error is subsumed under the category non-sampling error. (B) Sampling error doesn't occur in multi-stage cluster sampling. (C) Inaccurate sampling frame and non-response are examples of sampling related error. (D) There is an inverse relation between heterogeneity of population and sampling error. Choose the correct option:
From the list given below, identify those which are called ‘Non-Probability Sampling’ procedures: (i) Simple random sampling (ii) Dimensional sampling (iii) Snowball sampling (iv) Cluster sampling (v) Quota sampling (vi) Stratified sampling Choose the correct option:
Two unequal pairs of numbers satisfy the following conditions: (i) The product of the two numbers in each pair is 2160 (ii) The HCF of the two numbers in each pair is 12. If x is the mean of the numbers in the first pair and y is the mean of the numbers in the second pair, then what is the mean of x and y?
The digitization process i.e. the digital image has M rows and N columns, requires decisions about values for M, N, and for the number, L, of max gray levels. There are no requirements on M and N, other than that M and N have to be positive integer. However, the number of gray levels typically is