Chapter 1, Introduction Video Solutions, Digital Image Processing

Problem 1

Find the memory required, in bytes, to store the following images.
(i) $64 \times 64$ binary image.
(ii) $128 \times 1288$-bit gray-level image.
(iii) $64 \times 6424$-bit full-color image.
(iv) $512 \times 512$ binary image.
(v) $1024 \times 10248$-bit gray-level image.
(vi) $4096 \times 409624$-bit full-color image.

Stanley Enemuo

Numerade Educator

01:17

Problem 2

Find the memory required, in bytes, to store the images given in Exercise (1.1) after
(i) doubling the number of rows and columns and
(ii) reducing the number of rows and columns by a factor of 2 .

Aaron Goree

Numerade Educator

Problem 3

Find the pixel values of the $8 \times 88$-bit gray-level image
$$
\{x(m, n), m=0,1,2, \ldots, 7 \text { and } n=0,1,2, \ldots, 7\}
$$
corresponding to the given 2-D function. (Round the real values of the image to the nearest integer after necessary scaling.)
*(i)
$$
x(m, n)=1+\cos \left(\frac{2 \pi}{8} m+\frac{2 \pi}{8} n-\frac{\pi}{4}\right)
$$
(ii)
$$
x(m, n)=1+\cos \left(\frac{2 \pi}{8} m+\frac{2 \pi}{8} 2 n-\frac{\pi}{6}\right)
$$
(iii)
$$
x(m, n)=1+\cos \left(\frac{2 \pi}{8} 0 m+\frac{2 \pi}{8} 0 n\right)
$$
(iv)
$$
x(m, n)=1+\cos \left(\frac{2 \pi}{8} 4 m+\frac{2 \pi}{8} 4 n\right)
$$
(v)
$$
x(m, n)=1+\cos \left(\frac{2 \pi}{8} 0 m+\frac{2 \pi}{8} n\right)
$$
(vi)
$$
x(m, n)=1+\cos \left(\frac{2 \pi}{8} 2 m+\frac{2 \pi}{8} 0 n\right)
$$

Check back soon!

04:55

Problem 4

Find the pixel values of the $8 \times 8$ binary image by setting the gray-level values between $0-127$ to 0 and 128-255 to 1 for each of the 8-bit gray-level images
$$
\{x(m, n), m=0,1,2, \ldots, 7 \text { and } n=0,1,2, \ldots, 7\}
$$
obtained in Exercise (1.3).

Stanley Enemuo

Numerade Educator

03:45

Problem 5

Find the bit-plane components of the image and verify that the image can be reconstructed from them.
(i)
$$
\left[\begin{array}{rrrr}
8 & 3 & 7 & 3 \\
4 & 11 & 15 & 12 \\
0 & 10 & 11 & 1 \\
2 & 10 & 3 & 6
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{rrrr}
2 & 1 & 7 & 3 \\
1 & 1 & 15 & 12 \\
0 & 13 & 5 & 13 \\
2 & 10 & 4 & 6
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{rrrr}
8 & 1 & 7 & 8 \\
5 & 11 & 15 & 12 \\
0 & 6 & 7 & 13 \\
2 & 10 & 7 & 6
\end{array}\right]
$$
(iv)
$$
\left[\begin{array}{rrrr}
7 & 1 & 7 & 3 \\
1 & 6 & 15 & 12 \\
0 & 11 & 1 & 13 \\
2 & 10 & 9 & 9
\end{array}\right]
$$
(v)
$$
\left[\begin{array}{rrrr}
8 & 1 & 7 & 7 \\
1 & 11 & 6 & 12 \\
0 & 8 & 7 & 13 \\
9 & 10 & 9 & 6
\end{array}\right]
$$

Gideon Idumah

Numerade Educator

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Problem 6

(i) Find the spatial resolution of an image if the scene of size $4 \mathrm{~m}$ by $4 \mathrm{~m}$ is represented by a $256 \times 256$ image.
(ii) Find the spatial resolution of an image if the scene of size $10 \mathrm{~km}$ by $10 \mathrm{~km}$ is represented by a $4096 \times 4096$ image.
(iii) Find the spatial resolution of an image if the scene of size $7 \mathrm{~mm}$ by $7 \mathrm{~mm}$ is represented by a $1024 \times 1024$ image.

James Kiss

Numerade Educator

Problem 7

Let the sampling frequencies along both the directions be 32 cycles per sample. Is there aliasing or not in the image $x(m, n)$ ? If so, what are the impersonated frequencies?
*(i)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 28 m+\frac{2 \pi}{32} 30 n-\frac{\pi}{6}\right)
$$
(ii)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 15 m+\frac{2 \pi}{32} 14 n+\frac{\pi}{2}\right)
$$
(iii)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 27 m+\frac{2 \pi}{32} 22 n-\frac{\pi}{3}\right)
$$
(iv)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 3 m+\frac{2 \pi}{32} 3 n+\frac{\pi}{2}\right)
$$
(v)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 32 m+\frac{2 \pi}{32} 32 n+\frac{\pi}{4}\right)
$$
(vi)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 17 m+\frac{2 \pi}{32} 11 n-\frac{\pi}{3}\right)
$$

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