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Digital Image Processing

D. Sundararajan

Chapter 11

Object Description - all with Video Answers

Educators

Chapter Questions

03:56

Problem 1

Find the chain code for the image.
*(i)
$$
\left[\begin{array}{llllllll}
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{llllllll}
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llllllll}
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
\end{array}\right]
$$

Bryan Lynn
Bryan Lynn
Numerade Educator

Problem 2

Find the signature of the image.
(i)
$$
\left[\begin{array}{llll}
1 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 \\
1 & 0 & 1 & 0 \\
1 & 1 & 1 & 1
\end{array}\right]
$$
*(ii)
$$
\left[\begin{array}{llll}
1 & 1 & 1 & 1 \\
1 & 0 & 0 & 1 \\
1 & 0 & 0 & 1 \\
1 & 1 & 1 & 1
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llll}
0 & 1 & 1 & 0 \\
1 & 0 & 0 & 1 \\
1 & 0 & 0 & 1 \\
0 & 1 & 1 & 0
\end{array}\right]
$$

Check back soon!
02:48

Problem 3

Find the Fourier descriptor of the image. Reconstruct the image from the descriptor and verify that it is the same as the input image.
(i)
$$
\left[\begin{array}{llll}
0 & 1 & 1 & 1 \\
0 & 1 & 0 & 1 \\
0 & 1 & 0 & 1 \\
0 & 1 & 1 & 1
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{llll}
1 & 1 & 1 & 1 \\
0 & 1 & 0 & 1 \\
0 & 0 & 1 & 1 \\
0 & 0 & 0 & 1
\end{array}\right]
$$
* (iii)
$$
\left[\begin{array}{llll}
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 1 \\
1 & 0 & 0 & 1 \\
1 & 1 & 1 & 1
\end{array}\right]
$$

Arun Bana
Arun Bana
Numerade Educator
03:29

Problem 4

Find the area, perimeter, and compactness of the nonzero region in the $3 \times 3$ image.
(i)
$$
\left[\begin{array}{lll}
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{lll}
0 & 0 & 0 \\
0 & 1 & 1 \\
1 & 1 & 1
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{lll}
1 & 0 & 0 \\
1 & 1 & 0 \\
1 & 1 & 1
\end{array}\right]
$$

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator

Problem 5

Find the Euler number of the 8 -connected $4 \times 4$ image.
(i)
$$
\left[\begin{array}{llll}
1 & 1 & 1 & 1 \\
1 & 0 & 1 & 1 \\
1 & 1 & 0 & 1 \\
1 & 1 & 1 & 1
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{llll}
0 & 0 & 0 & 1 \\
0 & 1 & 1 & 0 \\
1 & 1 & 1 & 1 \\
0 & 1 & 1 & 0
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llll}
1 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 \\
1 & 0 & 1 & 0 \\
1 & 1 & 1 & 1
\end{array}\right]
$$

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Problem 6

Find the first two normalized central moments $\phi_1$ and $\phi_2$ of the $4 \times 4$ image.
$$
x(k, l)=\left[\begin{array}{llll}
0 & 1 & 1 & 0 \\
0 & 1 & 1 & 0 \\
0 & 1 & 1 & 1 \\
0 & 0 & 0 & 0
\end{array}\right]
$$

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Problem 7

Find the first two normalized central moments $\phi_1$ and $\phi_2$ of the $4 \times 4$ image.
$$
x(k, l)=\left[\begin{array}{llll}
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 1 & 1 & 1 \\
0 & 1 & 1 & 0
\end{array}\right]
$$

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Problem 8

Find the first two normalized central moments $\phi_1$ and $\phi_2$ of the $4 \times 4$ image.
$$
x(k, l)=\left[\begin{array}{llll}
0 & 1 & 1 & 0 \\
0 & 1 & 1 & 1 \\
0 & 1 & 1 & 0 \\
0 & 0 & 0 & 0
\end{array}\right]
$$

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02:30

Problem 9

Find the histogram of the $4 \times 48$-bit image and derive its histogram-based features.
$$
\left[\begin{array}{rrrr}
108 & 81 & 69 & 92 \\
114 & 105 & 72 & 101 \\
117 & 73 & 67 & 92 \\
105 & 0 & 65 & 101
\end{array}\right]
$$

Luca Alexander
Luca Alexander
Numerade Educator
02:49

Problem 10

Find the histogram of the $4 \times 4$ 8-bit image and derive its histogram-based features.
$$
\left[\begin{array}{rrrr}
120 & 103 & 83 & 78 \\
97 & 99 & 81 & 72 \\
102 & 96 & 78 & 73 \\
121 & 107 & 37 & 0
\end{array}\right]
$$

Ryan Mcalister
Ryan Mcalister
Numerade Educator
02:49

Problem 11

Find the histogram of the $4 \times 4$ 8-bit image and derive its histogram-based features.
$$
\left[\begin{array}{rrrrr}
10 & 133 & 175 & 170 \\
0 & 61 & 171 & 170 \\
3 & 15 & 131 & 172 \\
1 & 3 & 70 & 167
\end{array}\right]
$$

Ryan Mcalister
Ryan Mcalister
Numerade Educator
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Problem 12

Find the co-occurrence matrix of the $8 \times 8$ 3-bit image.
$$
\left[\begin{array}{llllllll}
5 & 2 & 2 & 2 & 2 & 1 & 1 & 2 \\
5 & 4 & 1 & 2 & 2 & 2 & 1 & 1 \\
5 & 5 & 2 & 2 & 2 & 2 & 1 & 1 \\
5 & 5 & 4 & 1 & 2 & 2 & 1 & 1 \\
6 & 5 & 6 & 2 & 2 & 2 & 2 & 1 \\
6 & 4 & 5 & 4 & 1 & 2 & 2 & 1 \\
5 & 5 & 5 & 5 & 2 & 2 & 2 & 1 \\
5 & 4 & 5 & 5 & 3 & 2 & 2 & 2
\end{array}\right]
$$
Let the spatial relationship of a pair of pixels be $x(m, n)$ and $x(m, n+1)$. That is, a pixel and its immediate right neighbor form the pair. Find the contrast, correlation, energy, and homogeneity.

Victor Salazar
Victor Salazar
Numerade Educator
View

Problem 13

Find the co-occurrence matrix of the $8 \times 8$ 3-bit image.
$$
\left[\begin{array}{llllllll}
1 & 0 & 0 & 0 & 1 & 2 & 2 & 5 \\
1 & 0 & 0 & 0 & 1 & 2 & 2 & 5 \\
1 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\
1 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\
2 & 1 & 0 & 0 & 1 & 2 & 2 & 3 \\
2 & 1 & 0 & 0 & 1 & 1 & 1 & 3 \\
2 & 1 & 0 & 0 & 1 & 1 & 1 & 3 \\
2 & 1 & 0 & 0 & 1 & 1 & 1 & 3
\end{array}\right]
$$
Let the spatial relationship of a pair of pixels be $x(m, n)$ and $x(m, n+1)$. That is, a pixel and its immediate right neighbor form the pair. Find the contrast, correlation, energy, and homogeneity.

Victor Salazar
Victor Salazar
Numerade Educator
View

Problem 14

Find the co-occurrence matrix of the $8 \times 83$-bit image.
$$
\left[\begin{array}{llllllll}
5 & 4 & 4 & 5 & 5 & 2 & 2 & 2 \\
5 & 2 & 4 & 5 & 5 & 2 & 2 & 2 \\
3 & 2 & 5 & 5 & 6 & 3 & 2 & 2 \\
2 & 4 & 4 & 5 & 5 & 4 & 2 & 2 \\
4 & 5 & 5 & 5 & 6 & 4 & 2 & 2 \\
5 & 5 & 5 & 5 & 4 & 4 & 2 & 2 \\
5 & 5 & 5 & 3 & 3 & 4 & 2 & 2 \\
5 & 5 & 4 & 3 & 4 & 5 & 2 & 2
\end{array}\right]
$$
Let the spatial relationship of a pair of pixels be $x(m, n)$ and $x(m, n+1)$. That is, a pixel and its immediate right neighbor form the pair. Find the contrast, correlation, energy, and homogeneity.

Victor Salazar
Victor Salazar
Numerade Educator
02:53

Problem 15

Given two $2 \times 2$ images, find the corresponding PCA components and their covariance. Then, reconstruct the original images from the PCA components.
$$
a(m, n)=\left[\begin{array}{ll}
2 & 1 \\
3 & 4
\end{array}\right] \quad b(m, n)=\left[\begin{array}{ll}
3 & 1 \\
2 & 4
\end{array}\right]
$$

Jack Chen
Jack Chen
Numerade Educator
02:53

Problem 16

Given two $2 \times 2$ images, find the corresponding PCA components and their covariance. Then, reconstruct the original images from the PCA components.
$$
a(m, n)=\left[\begin{array}{ll}
1 & 1 \\
2 & 3
\end{array}\right] \quad b(m, n)=\left[\begin{array}{ll}
3 & 1 \\
2 & 4
\end{array}\right]
$$

Jack Chen
Jack Chen
Numerade Educator
02:53

Problem 17

Given two $2 \times 2$ images, find the corresponding PCA components and their covariance. Then, reconstruct the original images from the PCA components.
$$
a(m, n)=\left[\begin{array}{ll}
2 & 1 \\
3 & 4
\end{array}\right] \quad b(m, n)=\left[\begin{array}{ll}
2 & 2 \\
1 & 3
\end{array}\right]
$$

Jack Chen
Jack Chen
Numerade Educator