Laplacian in Frequency Domain MCQ [Free PDF] - Objective Question Answer for Laplacian in Frequency Domain Quiz

1. The expression [∂² f(x,y)/∂x² +∂² f(x,y)/∂y²] is considered as _________ where f(x, y) is an input image.

A. Laplacian of f(x, y)
B. Gradient of f(x, y)
C. All of the mentioned
D. None of the mentioned

Answer: A

The Laplacian for an image f(x, y) is defined as ∇² f=∂² f/∂x² + ∂² f/∂y².

2. If the Laplacian in the frequency domain is:

where is the Fourier transform operator and F(u, v) is the Fourier transformed function of f(x, y), then what is -(u²+ v²) is considered as?

A. Laplacian operation
B. Filtering operation
C. Shift operation
D. None of the mentioned

Answer: B

The Laplacian in the frequency domain is simply implemented by using a filter:
H(u, v)= -(u²+ v²).

3. The Laplacian in frequency domain is simply implemented by using filter __________

A. H(u, v)= -(u²– v²)
B. H(u, v)= -(1)
C. H(u, v)= -(u²+ v²)
D. none of the mentioned

Answer: C

Laplacian in frequency domain is: I[(∂² f(x,y))/∂x² +(∂² f(x,y))/∂y² ]= -(u²+v²)F(u,v), where ℑ is the Fourier transform operator and F(u, v) is Fourier transformed function of f(x, y) and -(u²+ v²) is the filter.

4. Assuming that the origin of F(u, v), Fourier transformed the function of f(x, y) an input image, has been correlated by performing the operation f(x, y)(-1)x+y before taking the transform of the image. If F and f are of the same size, then what does the given operation is/are supposed to do?

A. Resize the transform
B. Rotate the transform
C. Shifts the center transform
D. All of the mentioned

Answer: C

The given operation f(x, y)(-1)x+y shifts the center transform so that (u, v)=(0,0) is at point (M/2, N/2) for F and f of the same size M*N.

5. Assuming that the origin of F(u, v), Fourier transformed the function of f(x, y) an input image, has been correlated by performing the operation f(x, y)(-1)x+y before taking the transform of the image. If F and f are of the same size M*N, where do the point (u, v) =(0,0) shift?

A. (M -1, N -1)
B. (M/2, N/2)
C. (M+1, N+1)
D. (0, 0)

Answer: B

The given operation f(x, y)(-1)x+y shifts the center transform so that (u, v)=(0, 0) is at point (M/2, N/2) for F and f of the same size M*N.

6. Assuming that the origin of F(u, v), Fourier transformed the function of f(x, y) an input image, has been correlated by performing the operation f(x, y)(-1)x+y before taking the transform of the image. If F and f are of the same size M*N, then which of the following is an expression for H(u, v), the filter used for implementing Laplacian in the frequency domain?

A. H(u, v)= -(u²+ v²)
B. H(u, v)= -(u²– v²)
C. H(u, v)= -[(u – M/2)²+ (v – N/2)²].
D. H(u, v)= -[(u – M/2)²– (v – N/2)²].

Answer: C

The given operation f(x, y)(-1)x+y shifts the center transform so that (u, v)=(0, 0) is at point (M/2, N/2) and hence the filter is: H(u, v)= -[(u – M/2)²+ (v – N/2)²].

7. Computing the Fourier transform of the Laplacian result in the spatial domain is equivalent to multiplying the F(u, v), Fourier transformed the function of f(x, y) an input image, and H(u, v), the filter used for implementing Laplacian in the frequency domain. This dual relationship is expressed as _________

A. Fourier transform pair notation
B. Laplacian
C. Gradient
D. None of the mentioned

Answer: A

The Fourier transform of the Laplacian result in the spatial domain is equivalent to multiplying the F(u, v) and H(u, v). This dual relationship is expressed as Fourier transform pair notation given by: ∇² f(x,y)-[(u – M/2)²+ (v – N/2)²]F(u,v), for an image of size M *N.

8. Computing the Fourier transform of the Laplacian result in the spatial domain is equivalent to multiplying the F(u, v), Fourier transformed the function of f(x, y) an input image of size M*N, and H(u, v), the filter used for implementing Laplacian in the frequency domain. This dual relationship is expressed as Fourier transform pair notation given by_____________

A. ∇² f(x,y)↔[(u –M/2)²+ (v –N/2)²]F(u,v)
B. ∇² f(x,y)↔-[(u+M/2)²– (v+N/2)²]F(u,v)
C. ∇² f(x,y)↔-[(u –M/2)²+ (v –N/2)²]F(u,v)
D. ∇² f(x,y)↔[(u+M/2)²– (v+N/2)²]F(u,v)

Answer: C

The Fourier transform of the Laplacian result in the spatial domain is equivalent to multiplying the F(u, v) and H(u, v). This dual relationship is expressed as Fourier transform pair notation given by:∇² f(x,y)↔-[(u – M/2)²+ (v – N/2)²]F(u,v), for an image of size M*N.

9. An enhanced image can be obtained as g(x,y)=f(x,y)-∇² f(x,y), where Laplacian is being subtracted from f(x, y) the input image. What does this conclude?

A. That the center spike would be negative
B. That the immediate neighbors of the center spike would be positive.
C. All of the mentioned
D. None of the mentioned

Answer: C

For the above given enhanced image, the Laplacian subtraction suggests that the center coefficient of the Laplacian mask is negative and so the center spike is negative with its immediate neighbors being positive.

10. An enhanced image can be obtained as g(x,y)=f(x,y)-∇² f(x,y), where Laplacian is being subtracted from f(x, y) the input image of size M*Non which an operation f(x, y)(-1)x+yis applied. Unlike enhancing in spatial domain with one single mask, it is possible to perform the same in the frequency domain using one filter. Which of the following is/are the required filter(s)?

A. H(u, v)= -[1 + u²+ v²].
B. H(u, v)= -[(u – M/2)2+ (v– N/2)2].
C. H(u, v)= [1 + (u – M/2)2+ (v – N/2)2].
D. All of the mentioned

Answer: C

The filter H(u, v)= [1 + (u – M/2)²+ (v – N/2)²] is used to perform the same enhancement in the frequency domain as in the spatial domain.

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