# Digital Image Processing Questions And Answers – Histogram Processing – 2

This set of Digital Image Processing Interview Questions and Answers for freshers focuses on “Histogram Processing – 2”.

1. The histogram of a digital image with gray levels in the range [0, L-1] is represented by a discrete function:
a) h(r_k)=n_k
b) h(r_k )=n/n_k
c) p(r_k )=n_k
d) h(r_k )=n_k/n

Explanation: The histogram of a digital image with gray levels in the range [0, L-1] is a discrete function h(rk )=nk, where rk is the kth gray level and nkis the number of pixels in the image having gray level rk.

2. How is the expression represented for the normalized histogram?
a) p(r_k )=n_k
b) p(r_k )=n_k/n
c) p(r_k)=nn_k
d) p(r_k )=n/n_k

Explanation: It is common practice to normalize a histogram by dividing each of its values by the total number of pixels in the image, denoted by n. Thus, a normalized histogram is given by p(rk )=nk/n, for k=0,1,2…..L-1. Loosely speaking, p(rk ) gives an estimate of the probability of occurrence of gray-level rk. Note that the sum of all components of a normalized histogram is equal to 1.

3. Which of the following conditions does the T(r) must satisfy?
a) T(r) is double-valued and monotonically decreasing in the interval 0≤r≤1; and
0≤T(r)≤1 for 0≤r≤1
b) T(r) is double-valued and monotonically increasing in the interval 0≤r≤1; and
0≤T(r)≤1 for 0≤r≤1
c) T(r) is single-valued and monotonically decreasing in the interval 0≤r≤1; and
0≤T(r)≤1 for 0≤r≤1
d) T(r) is single-valued and monotonically increasing in the interval 0≤r≤1; and
0≤T(r)≤1 for 0≤r≤1

Explanation: For any r satisfying the aforementioned conditions, we focus attention on transformations of the form
s=T(r) For 0≤r≤1
That produces a level s for every pixel value r in the original image.
For reasons that will become obvious shortly, we assume that the transformation function T(r) satisfies the following conditions:
T(r) is single-valued and monotonically increasing in the interval 0≤r≤1; and
0≤T(r)≤1 for 0≤r≤1.

4. The inverse transformation from s back to r is denoted as:
a) s=T-1(r) for 0≤s≤1
b) r=T-1(s) for 0≤r≤1
c) r=T-1(s) for 0≤s≤1
d) r=T-1(s) for 0≥s≥1

Explanation: The inverse transformation from s back to r is denoted by:
r=T-1(s) for 0≤s≤1.

5. The probability density function p_s (s) of the transformed variable s can be obtained by using which of the following formula?
a) p_s (s)=p_r (r)|dr/ds|
b) p_s (s)=p_r (r)|ds/dr|
c) p_r (r)=p_s (s)|dr/ds|
d) p_s (s)=p_r (r)|dr/dr|

Explanation: The probability density function p_s (s) of the transformed variable s can be obtained using a basic formula: p_s (s)=p_r (r)|dr/ds|
Thus, the probability density function of the transformed variable, s, is determined by the gray-level PDF of the input image and by the chosen transformation function.
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6. A transformation function of particular importance in image processing is represented in which of the following form?
a) s=T(r)=∫0 (2r)pr (ω)dω
b) s=T(r)=∫0 (r-1)pr (ω)dω
c) s=T(r)=∫0 (r/2)pr (ω)dω
d) s=T(r)=∫0 pr (ω)dω

Explanation: A transformation function of particular importance in image processing has the form: s=T(r)=∫0 r pr(ω)dw, where ω is a dummy variable of integration. The right side of is recognized as the cumulative distribution function (CDF) of random variable r.

7. Histogram equalization or Histogram linearization is represented by of the following equation:
a) sk =∑k j =1 nj/n k=0,1,2,……,L-1
b) sk =∑k j =0 nj/n k=0,1,2,……,L-1
c) sk =∑k j =0 n/nj k=0,1,2,……,L-1
d) sk =∑k j =n nj/n k=0,1,2,……,L-1

Explanation: A plot of pk_ (rk) versus r_k is called a histogram .The transformation (mapping) given in sk =∑k j =0)k nj/n k=0,1,2,……,L-1 is called histogram equalization or histogram linearization.

8. What is the method that is used to generate a processed image that have a specified histogram?
a) Histogram linearization
b) Histogram equalization
c) Histogram matching
d) Histogram processing

Explanation: In particular, it is useful sometimes to be able to specify the shape of the histogram that we wish the processed image to have. The method used to generate a processed image that has a specified histogram is called histogram matching or histogram specification.

9. Histograms are the basis for numerous spatial domain processing techniques.
a) True
b) False

Explanation: Histograms are the basis for numerous spatial domain processing techniques. Histogram manipulation can be used effectively for image enhancement.

10. In a dark image, the components of histogram are concentrated on which side of the grey scale?
a) High
b) Medium
c) Low
d) Evenly distributed

Explanation: We know that in the dark image, the components of histogram are concentrated mostly on the low i.e., dark side of the grey scale. Similarly, the components of histogram of the bright image are biased towards the high side of the grey scale.

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