# Digital Image Processing Questions and Answers – Histogram Equalization and Processing

This set of Digital Image Processing Multiple Choice Questions & Answers (MCQs) focuses on “Histogram Equalization and Processing”.

1. If h(rk) = nk, rk the kth gray level and nk total pixels with gray level rk, is a histogram in gray level range [0, L – 1]. Then how can we normalize a histogram?
a) If each value of histogram is added by total number of pixels in image, say n, p(rk)=nk+n
b) If each value of histogram is subtracted by total number of pixels in image, say n, p(rk)=nk-n
c) If each value of histogram is multiplied by total number of pixels in image, say n, p(rk)=nk * n
d) If each value of histogram is divided by total number of pixels in image, say n, p(rk)=nk / n
View Answer

Answer: d
Explanation: To normalize a histogram each of its value is divided by total number of pixels in image, say n. p(rk) = nk / n.

2. What is the sum of all components of a normalized histogram?
a) 1
b) -1
c) 0
d) None of the mentioned
View Answer

Answer: a
Explanation: A normalized histogram. p(rk) = nk / n
Where, n is total number of pixels in image, rk the kth gray level and nk total pixels with gray level rk.
Here, p(rk) gives the probability of occurrence of rk.

3. A low contrast image will have what kind of histogram when, the histogram, h(rk) = nk, rk the kth gray level and nk total pixels with gray level rk, is plotted nk versus rk?
a) The histogram that are concentrated on the dark side of gray scale
b) The histogram whose component are biased toward high side of gray scale
c) The histogram that is narrow and centered toward the middle of gray scale
d) The histogram that covers wide range of gray scale and the distribution of pixel is approximately uniform
View Answer

Answer: c
Explanation: The histogram plot is nk versus rk. So, the histogram of a low contrast image will be narrow and centered toward the middle of gray scale.
A dark image will have the histogram that are concentrated on the dark side of gray scale.
A bright image will have the histogram whose component are biased toward high side of gray scale.
A high contrast image will have the histogram that covers wide range of gray scale and the distribution of pixel is approximately uniform.
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4. A bright image will have what kind of histogram, when the histogram, h(rk) = nk, rk the kth gray level and nk total pixels with gray level rk, is plotted nk versus rk?
a) The histogram that are concentrated on the dark side of gray scale
b) The histogram whose component are biased toward high side of gray scale
c) The histogram that is narrow and centered toward the middle of gray scale
d) The histogram that covers wide range of gray scale and the distribution of pixel is approximately uniform
View Answer

Answer: b
Explanation: The histogram plot is nk versus rk. So, the histogram of a low contrast image will be narrow and centered toward the middle of gray scale.
A dark image will have the histogram that are concentrated on the dark side of gray scale.
A bright image will have the histogram whose component are biased toward high side of gray scale.
A high contrast image will have the histogram that covers wide range of gray scale and the distribution of pixel is approximately uniform.

5. 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.
a) I) And II) respectively
b) III) And II) respectively
c) II) And IV) respectively
d) IV) And I) respectively
View Answer

Answer: d
Explanation: The histogram plot is nk versus rk. So, the histogram of a low contrast image will be narrow and centered toward the middle of gray scale.
A dark image will have the histogram that are concentrated on the dark side of gray scale.
A bright image will have the histogram whose component are biased toward high side of gray scale.
A high contrast image will have the histogram that covers wide range of gray scale and the distribution of pixel is approximately uniform.
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6. The transformation s = T(r) producing a gray level s for each pixel value r of input image. Then, if the T(r) is single valued in interval 0 ≤ r ≤ 1, what does it signifies?
a) It guarantees the existence of inverse transformation
b) It is needed to restrict producing of some inverted gray levels in output
c) It guarantees that the output gray level and the input gray level will be in same range
d) All of the mentioned
View Answer

Answer: a
Explanation: The T(r) is single valued in interval 0 ≤ r ≤ 1, guarantees the existence of inverse transformation.

7. The transformation s = T(r) producing a gray level s for each pixel value r of input image. Then, if the T(r) is monotonically increasing in interval 0 ≤ r ≤ 1, what does it signifies?
a) It guarantees the existence of inverse transformation
b) It is needed to restrict producing of some inverted gray levels in output
c) It guarantees that the output gray level and the input gray level will be in same range
d) All of the mentioned
View Answer

Answer: b
Explanation: A T(r) which is not monotonically increasing, could result in an output containing at least a section of inverted intensity range. The T(r) is monotonically increasing in interval 0 ≤ r ≤ 1, is needed to restrict producing of some inverted gray levels in output.
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8. The transformation s = T(r) producing a gray level s for each pixel value r of input image. Then, if the T(r) is satisfying 0 ≤ T(r) ≤ 1 in interval 0 ≤ r ≤ 1, what does it signifies?
a) It guarantees the existence of inverse transformation
b) It is needed to restrict producing of some inverted gray levels in output
c) It guarantees that the output gray level and the input gray level will be in same range
d) All of the mentioned
View Answer

Answer: c
Explanation: If, 0 ≤ T(r) ≤ 1 in interval 0 ≤ r ≤ 1, then the output gray level and the input gray level will be in same range.

9. What is the full form for PDF, a fundamental descriptor of random variables i.e. gray values in an image?
a) Pixel distribution function
b) Portable document format
c) Pel deriving function
d) Probability density function
View Answer

Answer: d
Explanation: For a random variable, a PDF, probability density function, is one of the most fundamental descriptor.
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10. What is the full form of CDF?
a) Cumulative density function
b) Contour derived function
c) Cumulative distribution function
d) None of the mentioned
View Answer

Answer: c
Explanation: CDF of random variable r, gray value of input image, is cumulative distribution function.

11. For the transformation T(r) = [∫0r pr(w) dw], r is gray value of input image, pr(r) is PDF of random variable r and w is a dummy variable. If, the PDF are always positive and that the function under integral gives the area under the function, the transformation is said to be __________
a) Single valued
b) Monotonically increasing
c) All of the mentioned
d) None of the mentioned
View Answer

Answer: c
Explanation: For the given transformation, the PDF being positive and the integral providing area under the function, the transformation function is single valued as well as monotonically increasing.

12. The transformation T (rk) = ∑k(j=0) nj /n, k = 0, 1, 2, …, L-1, where L is max gray value possible and r-k is the kth gray level, is called _______
a) Histogram linearization
b) Histogram equalization
c) All of the mentioned
d) None of the mentioned
View Answer

Answer: c
Explanation: The given transformation is the equation for the Histogram equalization also called as Histogram linearization.

13. If the histogram of same images, with different contrast, are different, then what is the relation between the histogram equalized images?
a) They look visually very different from one another
b) They look visually very similar to one another
c) They look visually different from one another just like the input images
d) None of the mentioned
View Answer

Answer: b
Explanation: This is because the contents of all images is same. The difference is just the contrast.
The histogram equalization increases the contrast and make the gray-level difference of output image visually indistinguishable.

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