Digital Image Processing Questions and Answers – Use of Second Order Derivative for Enhancement

This set of Digital Image Processing Multiple Choice Questions & Answers (MCQs) focuses on “Use of Second Order Derivative for Enhancement”.

1. A filter is applied to an image whose response is independent of the direction of discontinuities in the image. The filter is/are ________
a) Isotropic filters
b) Box filters
c) Median filter
d) All of the mentioned
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2. In isotropic filtering, which of the following is/are the simplest isotropic derivative operator?
a) Laplacian
b) Gradient
c) All of the mentioned
d) None of the mentioned
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3. The Laplacian is which of the following operator?
a) Nonlinear operator
b) Order-Statistic operator
c) Linear operator
d) None of the mentioned
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4. A Laplacian for an image f(x, y) is defined as: is given by ________
a) [f(x + 1, y) + f(x – 1, y) – 2f(x, y)] and [f(x, y + 1) + f(x, y – 1) – 2f(x, y)] respectively
b) [f(x + 1, y + 1) + f(x, y – 1) – 2f(x, y)] and [f(x , y + 1) + f(x – 1, y) – 2f(x, y)] respectively
c) [f(x, y + 1) + f(x, y – 1) – 2f(x, y)] and [f(x + 1, y) + f(x – 1, y) – 2f(x, y)] respectively
d) None of the mentioned
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Answer: a
Explanation: For a Laplacian given by:∇² f=
Applying second order derivative in x direction (∂² f)/∂x² = [f(x + 1, y) + f(x – 1, y) – 2f(x, y)], and
Applying second order derivative in y direction (∂² f)/∂y² = [f(x, y + 1) + f(x, y – 1) – 2f(x, y)].

5. The Laplacian ∇² f=[f(x + 1, y) + f(x – 1, y) + f(x, y + 1) + f(x, y – 1) – 4f(x, y)], gives an isotropic result for rotations in increment by what degree?
a) 90^o
b) 0^o
c) 45^o
d) None of the mentioned
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6. The Laplacian incorporated with diagonal directions, i.e. ∇² f=[f(x + 1, y) + f(x – 1, y) + f(x, y + 1) + f(x, y – 1) – 8f(x, y)], gives an isotropic result for rotations in increment by what degree?
a) 90^o
b) 0^o
c) 45^o
d) None of the mentioned
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7. Applying Laplacian has which of the following result(s)?
a) Produces image having greyish edge lines
b) Produces image having featureless background
c) All of the mentioned
d) None of the mentioned
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8. Applying Laplacian produces image having featureless background which is recovered maintaining the sharpness of Laplacian operation by either adding or subtracting it from the original image depending upon the Laplacian definition used. Which of the following is true based on above statement?
a) If definition used has a negative center coefficient, then subtraction is done
b) If definition used has a positive center coefficient, then subtraction is done
c) If definition used has a negative center coefficient, then addition is done
d) None of the mentioned
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9. A mask of size 3*3 is formed using Laplacian including diagonal neighbors that has central coefficient as 9. Then, what would be the central coefficient of same mask if it is made without diagonal neighbors?
a) 5
b) -5
c) 8
d) -8
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10. Which of the following mask(s) is/are used to sharpen images by subtracting a blurred version of original image from the original image itself?
a) Unsharp mask
b) High-boost filter
c) All of the mentioned
d) None of the mentioned
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11. Which of the following gives an expression for high boost filtered image f_hb, if f represents an image, f blurred version of f, fs unsharp mask filtered image and A ≥ 1?
a) f_hb = (A – 1) f(x, y) + f(x, y) – f x, y)
b) f_hb = A f(x, y) – f(x,y)
c) f_hb = (A – 1) f(x, y) + f_s(x, y)
d) All of the mentioned
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12. If we use a Laplacian to obtain sharp image for unsharp mask filtered image fs(x, y) of f(x, y) as input image, and if the center coefficient of the Laplacian mask is negative then, which of the following expression gives the high boost filtered image f_hb, if ∇² f represent Laplacian?
a) f_hb = A f(x, y) – ∇² f(x,y)
b) f_hb = A f(x, y) + ∇² f(x,y)
c) f_hb = ∇² f(x,y)
d) None of the mentioned
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Answer: a
Explanation: If Laplacian is used to obtain sharp image for unsharp mask filtered image, then
.

13. If for an input image f(x, y) and the ∇² f represents Laplacian, then if, high boost filtered image is given by
.

For what value of A this high boost filtering becomes the standard Laplacian sharpening filter?
a) 0
b) 1
c) -1
d) ∞
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Answer: b
Explanation: for A=1 the high boost filtering is given by:
.

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