Question

Detect the lines in the $4 \times 4$ binary image $x(m, n)$. Choose a suitable threshold. * (i) $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 \end{array}\right] $$ (ii) $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}\right] $$ (iii) $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 \end{array}\right] $$ (iv) $$ x(m, n)=\left[\begin{array}{llll} 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right] $$ (v) $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right] $$

   Detect the lines in the $4 \times 4$ binary image $x(m, n)$. Choose a suitable threshold. * (i)
$$
x(m, n)=\left[\begin{array}{llll}
0 & 0 & 1 & 0 \\
1 & 0 & 1 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 1 & 0
\end{array}\right]
$$
(ii)
$$
x(m, n)=\left[\begin{array}{llll}
0 & 0 & 0 & 0 \\
1 & 1 & 1 & 1 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0
\end{array}\right]
$$
(iii)
$$
x(m, n)=\left[\begin{array}{llll}
0 & 0 & 0 & 0 \\
1 & 1 & 1 & 1 \\
0 & 0 & 0 & 1 \\
1 & 0 & 0 & 1
\end{array}\right]
$$
(iv)
$$
x(m, n)=\left[\begin{array}{llll}
1 & 0 & 0 & 0 \\
0 & 1 & 1 & 1 \\
0 & 0 & 1 & 1 \\
0 & 0 & 0 & 0
\end{array}\right]
$$
(v)
$$
x(m, n)=\left[\begin{array}{llll}
0 & 0 & 0 & 0 \\
1 & 1 & 1 & 1 \\
0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0
\end{array}\right]
$$
Show more…
Digital Image Processing
Digital Image Processing
D. Sundararajan 1st Edition
Chapter 7, Problem 6 ↓

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We need to detect lines in a given $4 \times 4$ binary image. A line can be horizontal, vertical, or diagonal. We will use a threshold to determine if a line is present.  Show more…

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Detect the lines in the $4 \times 4$ binary image $x(m, n)$. Choose a suitable threshold. * (i) $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 \end{array}\right] $$ (ii) $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}\right] $$ (iii) $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 \end{array}\right] $$ (iv) $$ x(m, n)=\left[\begin{array}{llll} 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right] $$ (v) $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right] $$
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