# Digital Image Processing Questions and Answers – Representing Digital Images

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This set of Digital Image Processing Multiple Choice Questions & Answers (MCQs) focuses on “Representing Digital Images”.

1. Assume that an image f(x, y) is sampled so that the result has M rows and N columns. If the values of the coordinates at the origin are (x, y) = (0, 0), then the notation (0, 1) is used to signify :
a) Second sample along first row
b) First sample along second row
c) First sample along first row
d) Second sample along second row

Explanation: The values of the coordinates at the origin are (x, y) = (0, 0). Then, the next coordinate values (second sample) along the first row of the image are represented as (x, y) = (0, 1).

2. The resulting image of sampling and quantization is considered a matrix of real numbers. By what name(s) the element of this matrix array is called __________
a) Image element or Picture element
b) Pixel or Pel
c) All of the mentioned
d) None of the mentioned

Explanation: Sampling and Quantization of an image f(x, y) forms a matrix of real numbers and each element of this matrix array is commonly known as Image element or Picture element or Pixel or Pel.

3. 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).
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4. 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

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.

5. 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 gray levels allowed for each pixel. The value M and N have to be:
a) M and N have to be positive integer
b) M and N have to be negative integer
c) M have to be negative and N have to be positive integer
d) M have to be positive and N have to be negative integer

Explanation: 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 level. There are no requirements on M and N, other than that M and N have to be positive integer.

6. 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
a) An integer power of 2 i.e. L = 2k
b) A Real power of 2 i.e. L = 2k
c) Two times the integer value i.e. L = 2k
d) None of the mentioned

Explanation: Due to processing, storage, and considering the sampling hardware, the number of gray levels typically is an integer power of 2 i.e. L = 2k.

7. 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 is an integer power of 2 i.e. L = 2k, allowed for each pixel. If we assume that the discrete levels are equally spaced and that they are integers then they are in the interval __________ and Sometimes the range of values spanned by the gray scale is called the ________ of an image.
a) [0, L – 1] and static range respectively
b) [0, L / 2] and dynamic range respectively
c) [0, L / 2] and static range respectively
d) [0, L – 1] and dynamic range respectively

Explanation: In digitization process M rows and N columns have to be positive and for the number, L, of discrete gray levels typically an integer power of 2 for each pixel. If we assume that the discrete levels are equally spaced and that they are integers then they lie in the interval [0, L-1] and Sometimes the range of values spanned by the gray scale is called the dynamic range of an image.

8. After digitization process a digital image with M rows and N columns have to be positive and for the number, L, max gray levels i.e. an integer power of 2 for each pixel. Then, the number b, of bits required to store a digitized image is:
a) b=M*N*k
b) b=M*N*L
c) b=M*L*k
d) b=L*N*k

Explanation: In digital image of M rows and N columns and L max gray levels an integer power of 2 for each pixel. The number, b, of bits required to store a digitized image is: b=M*N*k.

9. An image whose gray-levels span a significant portion of gray scale have __________ dynamic range while an image with dull, washed out gray look have __________ dynamic range.
a) Low and High respectively
b) High and Low respectively
c) Both have High dynamic range, irrespective of gray levels span significance on gray scale
d) Both have Low dynamic range, irrespective of gray levels span significance on gray scale

Explanation: An image whose gray-levels signifies a large portion of gray scale have High dynamic range, while that with dull, washed out gray look have Low dynamic range.

10. Validate the statement “When in an Image an appreciable number of pixels exhibit high dynamic range, the image will have high contrast.”
a) True
b) False

Explanation: In an Image if an appreciable number of pixels exhibit high dynamic range property, the image will have high contrast.

11. In digital image of M rows and N columns and L discrete gray levels, calculate the bits required to store a digitized image for M=N=32 and L=16.
a) 16384
b) 4096
c) 8192
d) 512

Explanation: In digital image of M rows and N columns and L max gray levels i.e. an integer power of 2 for each pixel. The number, b, of bits required to store a digitized image is: b=M*N*k.
For L=16, k=4.
i.e. b=4096.

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