This set of Digital Image Processing Questions and Answers for Freshers focuses on “Sharpening Spatial Filters-2”.

1. The objective of sharpening spatial filters is/are to ___________

a) Highlight fine detail in an image

b) Enhance detail that has been blurred because of some error

c) Enhance detail that has been blurred because of some natural effect of some method of image acquisition

d) All of the mentioned

View Answer

Explanation: Highlighting the fine detail in an image or Enhancing detail that has been blurred because of some error or some natural effect of some method of image acquisition, is the principal objective of sharpening spatial filters.

2. Sharpening is analogous to which of the following operations?

a) To spatial integration

b) To spatial differentiation

c) All of the mentioned

d) None of the mentioned

View Answer

Explanation: Smoothing is analogous to integration and so, sharpening to spatial differentiation.

3. Which of the following fact(s) is/are true about sharpening spatial filters using digital differentiation?

a) Sharpening spatial filter response is proportional to the discontinuity of the image at the point where the derivative operation is applied

b) Sharpening spatial filters enhances edges and discontinuities like noise

c) Sharpening spatial filters deemphasizes areas that have slowly varying gray-level values

d) All of the mentioned

View Answer

Explanation: Derivative operator’s response is proportional to the discontinuity of the image at the point where the derivative operation is applied.

Image differentiation enhances edges and discontinuities like noise and deemphasizes areas that have slowly varying gray-level values.

Since a sharpening spatial filters are analogous to differentiation, so, all the above mentioned facts are true for sharpening spatial filters.

4. Which of the facts(s) is/are true for the first order derivative of a digital function?

a) Must be nonzero in the areas of constant grey values

b) Must be zero at the onset of a gray-level step or ramp discontinuities

c) Must be nonzero along the gray-level ramps

d) None of the mentioned

View Answer

Explanation: The first order derivative of a digital function is defined as:

Must be zero in the areas of constant grey values.

Must be nonzero at the onset of a gray-level step or ramp discontinuities.

Must be nonzero along the gray-level ramps.

5. Which of the facts(s) is/are true for the second order derivative of a digital function?

a) Must be zero in the flat areas

b) Must be nonzero at the onset and end of a gray-level step or ramp discontinuities

c) Must be zero along the ramps of constant slope

d) All of the mentioned

View Answer

Explanation: The second order derivative of a digital function is defined as:

Must be zero in the flat areas i.e. areas of constant grey values.

Must be nonzero at the onset of a gray-level step or ramp discontinuities.

Must be zero along the gray-level ramps of constant slope.

6. The derivative of digital function is defined in terms of difference. Then, which of the following defines the first order derivative ∂f/∂x= ___________ of a one-dimensional function f(x)?

a) f(x+1)-f(x)

b) f(x+1)+ f(x-1)-2f(x)

c) All of the mentioned depending upon the time when partial derivative will be dealt along two spatial axes

d) None of the mentioned

View Answer

Explanation: The definition of a first order derivative of a one dimensional image f(x) is:

∂f/∂x= f(x+1)-f(x), where the partial derivative is used to keep notation same even for f(x, y) when partial derivative will be dealt along two spatial axes.

7. The derivative of digital function is defined in terms of difference. Then, which of the following defines the second order derivative ∂^{2} f/∂x^{2} = ___________ of a one-dimensional function f(x)?

a) f(x+1)-f(x)

b) f(x+1)+ f(x-1)-2f(x)

c) All of the mentioned depending upon the time when partial derivative will be dealt along two spatial axes

d) None of the mentioned

View Answer

Explanation: The definition of a second order derivative of a one dimensional image f(x) is:

(∂

^{2}f)/∂x

^{2}=f(x+1)+ f(x-1)-2f(x), where the partial derivative is used to keep notation same even for f(x, y) when partial derivative will be dealt along two spatial axes.

8. What kind of relation can be obtained between first order derivative and second order derivative of an image having a on the basis of edge productions that shows a transition like a ramp of constant slope?

a) First order derivative produces thick edge while second order produces a very fine edge

b) Second order derivative produces thick edge while first order produces a very fine edge

c) Both first and second order produces thick edge

d) Both first and second order produces a very fine edge

View Answer

Explanation: the first order derivative remains nonzero along the entire ramp of constant slope, while the second order derivative remain nonzero only at onset and end of such ramps.

If an edge in an image shows transition like the ramp of constant slope, the first order and second order derivative values shows the production of thick and finer edge respectively.

9. What kind of relation can be obtained between first order derivative and second order derivative of an image on the response obtained by encountering an isolated noise point in the image?

a) First order derivative has a stronger response than a second order

b) Second order derivative has a stronger response than a first order

c) Both enhances the same and so the response is same for both first and second order derivative

d) None of the mentioned

View Answer

Explanation: This is because a second order derivative is more aggressive toward enhancing sharp changes than a first order.

10. What kind of relation can be obtained between the response of first order derivative and second order derivative of an image having a transition into gray-level step from zero?

a) First order derivative has a stronger response than a second order

b) Second order derivative has a stronger response than a first order

c) Both first and second order derivative has the same response

d) None of the mentioned

View Answer

Explanation: This is because a first order derivative has stronger response to a gray-level step than a second order, but, the response becomes same if transition into gray-level step is from zero.

11. If in an image there exist similar change in gray-level values in the image, which of the following shows a stronger response using second order derivative operator for sharpening?

a) A line

b) A step

c) A point

d) None of the mentioned

View Answer

Explanation: second order derivative shows a stronger response to a line than a step and to a point than a line, if there is similar changes in gray-level values in an image.

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