T490: Digital Image Processing
Mock Examination----MODEL SOLUTION
Total Time: 120 Minutes
Instructions:
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This exam consists of 3 parts worth 100 marks.
Part 1 is worth 10% of the marks.
Part 2 is worth 30% of the marks.
Part 3 is worth 60% of the marks.
You are advised to spend proportional amount of time in solving
each part of the exam.
 You are only allowed to bring a pen and a calculator to the exam
center. The calculator must not contain inside it anything related to
the course.
 You must use a separate answer book, to be provided to you
separately, to solve the exam.
 You must not solve any part of the exam on this exam paper and
you must provide all answers on the separate answer book including
answers to Part 1, Part 2 and Part 3.
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Part 1: This part carries 10% of the total examination marks. You should
attempt all parts. Each part carries 1 mark.
Question 1: (10 marks) Answer the following by selecting the most
appropriate choice.
i.
ii.
iii.
iv.
v.
____________ is the process of using known data to estimate
values at unknown locations .
a) Decimation
b) Interpolation
c) Formulation
d) All of the above
e) None of the above
An image element is usually called a _____________
a) Pixel
b) Fixel
c) Drexel
d) All of the above
e) None of the above
The process of moving a filter mask over the image and
computing the sum of
products at each location is defined by_____________
a) Convolution
b) Rotation
c) Linearity
d) Correlation
e) None of the above
The sum of all components of a normalised histogram is equal
to_________
a) Size of the image
b) Size of rows of the image
c) Size of columns of the image
d) One
e) MxN
Image restoration usually uses a model that is based on ____
a) Additive noise
b) Multiplicative noise
c) Division noise
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d) Subtractive noise
e) None of the above
vi. Convolution is usually used in the ________ domain.
a) Frequency
b) Spatial
c) Feature
d) Featureless
e) None of the above
vii. Fourier transform is a ________________ transform
a) Linear
b) Nonlinear
c) Bilinear
d) Bicubic
e) None of the above
viii. Ideal filters can be ____________
a) LPF
b) HPF
c) BPF
d) All of the above
e) None of the above
ix. The Rayleigh density can be used to approximate ______
a) Ideal histograms
b) Non-Ideal histograms
c) Butterworth histograms
d) Gaussian histograms
e) Skewed histograms
x. Which of the following filters is effective in the presence of saltand-pepper
noise?
a) Average filter
b) Median filter
c) Sobel filter
d) Robert filter
e) All of the above
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Part 2: This part carries 30% of the total examination marks. Each question
carries 10 marks. For full marks, your work must be clearly presented.
Question 2: (10 marks)
What is the general expression for intensity transformation? Explain the 3
basic types of intensity transformation functions used for image
enhancement.
Intensity transformation function:
 Let the neighbourhood be of size 1x1 (that is, a single pixel).
 In this case, g depends only on the value of f at (x, y), and T becomes an intensity (also
called a gray-level or mapping) transformation function of the form
s=T(r)
 where, for simplicity in notation, r and s are variables denoting, respectively, the gray
level of f(x, y) and g(x, y) at any point (x, y).
Some Basic Intensity Transformation Functions
Three basic types of functions used frequently for image enhancement:
1. Linear (negative and identity transformations),
2. logarithmic (log and inverse-log transformations),
3. power-law (nth power and nth root transformations).
Question 3: (10 marks)
Briefly explain in your own words the relationship between filtering in the
Spatial Domain to its effect in the Frequency Domain. Write the
mathematical expression relating the convolution operation in the two
domains.
Model answer would be (students need to explain more):
Filtering in the spatial domain is usually represented by the convolution
sum. In the frequency domain, the convolution sum becomes a
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multiplication operation. Hence filtering in the Spatial Domain is equivalent
to multiplication in the Frequency Domain.
f(x,y)*g(x,y)==F(u,v).G(u,v)
Question 4: (10 marks)
Briefly explain the operation of the Alpha-trimmed mean filter. What are its
uses for image processing?
Ans:
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Part 3: This part carries 60% of the total examination marks. Each question
carries 30 marks. For full marks, your work must be clearly presented.
Question 5: (30 marks)
a. Consider the noisy image given below. What does the
histogram associated with this image indicate about the type of
noise present in the noisy image?
Ans:
Exponential noise PDF.
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b. What is the significance of the small strip in the figure below?
What are the two most important quantities that can be derived
from this strip and for what purpose?
Ans:
The strip is used to estimate histogram values.
The two quantities are the Mean and Variance and the purpose is to
estimate histogram/PDF values.
c. Provide a model of the image degradation and restoration
process in block diagram form. Write its mathematical
expressions in both spatial and frequency domains.
Ans:
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Question 6: (30 marks)
a.
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Ans:
b. Consider the 3 images given below. The first image is the
original image and the next two are processed images. Explain
what type of filters have produced the effects in these two
images.
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Ans:
Fig1: Original
Fig2: LPF effect
Fig3: HPF effect
c. Plot or draw the approximate histograms of the images given
below.
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Ans:
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