EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Tutorial Set G Solutions
Question 1
1
Question 2
2
Question 3
S = A B = (A B) B
(1)
x | (B)
x Ac
S c = (A B)c = cfw_(B)
(2)
3
Question 4
Part (a)
4
Part (b)
5
Question 5
Part (a)
I(E) = logr P

Sem. 1, 2014/15
EE3206 ICVIP
Tutorial Set B Solutions
Question 1
Part (a)
The FT of (x, y) is
F cfw_(x, y) =
+
(x, y) exp[j2(ux + vy)] dx dy
(by definition)
= exp[j2(ux + vy)]|x,y=0
= 1
Part (b)
The inverse FT of (u, v) is
F
1
cfw_(u, v) =
+
(u, v) exp[j2

7 SEGMENTATION
Segmentation is the process that partitions a scene into its constituent
parts or objects. These components are then subsequently analyzed.
There are two main approaches:
Based on discontinuity:
Contour tracking
Local analysis edge linkin

EE3206
Intro to Computer Vision and Image Processing
I - INTRODUCTION
1
What is an image?
f ( x, y )
An image is a two-dimensional function f(x,y),
where
- x and y are spatial coordinates
- the amplitude of f at a point (x,y) gives the
intensity or gray l

9 MORPHOLOGICAL PROCESSING
Morphology is a branch of biology that deals with the form and structure of animals and plants. In the image processing context, mathematical morphology is a tool
for extracting image components that are useful in representatio

4 NOISE REDUCTION
Image noise may be present as a result of sampling, quantization,
transmission, or disturbances in the environment during image acquisition. In this chapter, we look at some techniques for reducing noise.
1
Noise is classied based on the

3 IMAGE TRANSFORMS (B)
THE DISCRETE FOURIER TRANSFORM
Suppose that a continuous function f (x) is discretized into a sequence
cfw_f (x0 ), f (x0 + x), f (x0 + 2x), . . . , f (x0 + [N 1]x)
by taking N samples x units apart.
Note that x may be used as eithe

6 EDGE DETECTION
Changes or discontinuities in an image attribute such as luminance
or texture are important primitive features of an image since they
often provide an indication of the physical extent of objects within
the image. Edge detection contribut

10 IMAGE COMPRESSION (B)
ERROR-FREE COMPRESSION
In many applications, error-free compression is required, e.g., in archival
and transmission of medical images. Furthermore, many lossy coding
schemes make use of lossless coding components to minimize the r

8
REPRESENTATION AND DESCRIPTION (B)
IMAGE MOMENTS
When a region is given in terms of its interior points, we can describe it
by a set of moments. These moment values can be used to characterise
the shape of a region and also the spatial distribution of t

5 IMAGE ENHANCEMENT (B)
IMAGE SHARPENING
Sharpening techniques are used primarily as enhancement tools to
enhance blurred images or to highlight ne details.
1
A sharpening operation is similar to highpass ltering in that edges,
i.e., high-frequency compon

Sem. 1, 2014
EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Tutorial Set D Solutions
Question 1
0 < < 1: The image tends to get brighter as the gray levels get
transformed to higher levels.
= 1: No change.
> 1: The image tends to get darke

EE3206 Intro to Computer Vision and
Image Processing
A/Prof. ONG Sim Heng
Dept of ECE
Office: E4-05-14
Tel: 65162245
Email: eleongsh@nus.edu.sg
What this module is about
The use of computers to process and analyze digital images
has many applications in s

Sem. 1, 2014
EE3206/EE3206E ICVIP
Tutorial Set A Solutions
Question 1
M1 smooths (blurs) in a horizontal direction.
M2 smooths (blurs) in a vertical direction.
1
M3 gives a strong (positive or negative) response at the pixels where
there is a relativel

5 IMAGE ENHANCEMENT (A)
Image enhancement refers to accentuation or sharpening of image features such as edges, boundaries, or contrast to improve the image
for display and analysis. The enhancement process does not increase
the information content in the

Sem. 1, 2014/15
EE3206 ICVIP
Tutorial Set C Solutions
Question 1
Part (a)
Compare the rst number in the initial list with the second number. If
the rst number is smaller, interchange the positions; otherwise compare
the second number with the third, and s

10 IMAGE COMPRESSION (A)
Image compression is the science of eectively coding digital images
to reduce the number of bits required in representing an image. The
purpose of doing so is to reduce the storage and transmission costs
while maintaining good qua

3 IMAGE TRANSFORMS (A)
A transform maps image data into a dierent mathematical space via a
transformation equation. Many transforms are used in image processing, e.g., Fourier transform, cosine transform, Walsh-Hadamard transform, Haar transform, principa

EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Semester 1, 2014/2015
Tutorial Set A
1. Consider the three masks M1 , M2 and M3 and the image I. (The rest of the image
that is not shown is assumed to consist of 0s.)
(a) Show the results
I1 = I

EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Semester 1, 2014/2015
Tutorial Set E
1. You are given these edge points in an image:
P 1 : (4, 0)
P 2 : (2, 1)
P 3 : (0, 1)
P 4 : (2, 1.5)
P 5 : (4, 2)
P 6 : (6, 2)
(a) Obtain their ab representa

2 IMAGE ACQUISITION
1
Image acquisition is the conversion of an optical picture, typically
representing a 2D or 3D scene, into a digitized form suitable for use with
computers.
Many acquisition systems comprise an input device:
a scanner, or
a digital c

8
REPRESENTATION AND DESCRIPTION (A)
After an image has been segmented into regions, the resulting collection of segmented pixels are usually represented and described in a
form suitable for further processing.
The representation of an object may be based

Sem. 1, 2014/15
EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Tutorial Set F Solution
Question 1
Part (a)
The compactness of the rectangle is
=
=
=
=
P2
4A
(2ka + 2a)2
4 ka2
4(k + 1)2
4k
(k + 1)2
k
(1)
d/dk = 0 k = 1, i.e. the minimum value

EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Semester 1, 2014/2015
Tutorial Set B
1. Verify the (continuous) Fourier transform pairs
(a) (x, y) 1
(b) 1 (u, v)
2. A continuous image f(x, y) consists of a light rectangle on a dark background.

EE3206INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Semester 1, 2014/2015
Tutorial Set F
1. Compactness is dened as
=
2
(perimeter)
.
4 area
(a) For the rectangle shown in Figure 1(a), express as a function of k. Sketch
vs k, and show that is mmin

EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Semester 1, 2014/2015
Tutorial Set D
1. Consider a continuous image function f(x, y) with PDF p(r), 0 r 1. The
exponential function
T (r) = r , > 0
may be used as a transformation function for im

EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Semester 1, 2014/2015
Tutorial Set C
1. (a) Describe a simple procedure, based on the bubble sort algorithm, for computing the median of an k k neighbourhood. Obtain an expression for C1 , the
nu

EE3206 INTRODUCTION TO
COMPUTER VISION AND IMAGE PROCESSING
Semester 1, 2014/2015
Tutorial Set G
1. Given A and B in the gure, obtain
(a)
(b)
(c)
(d)
(e)
(f)
AB
AB
AB
AB
(A B) B
(A B) B
2. Binary image I in the gure consists of a square, a rectangle and a