Question

Given a $4 \times 4$ image, find the $4 \times 4$ highpass filtered output using the $3 \times 3$ Laplacian filter $$ h(m, n)=\left[\begin{array}{rrr} 0 & 1 & 0 \\ 1 & -4 & 1 \\ 0 & 1 & 0 \end{array}\right] $$ with the borders zero-padded. $$ x(m, n)=\left[\begin{array}{llll} 45 & 52 & 56 & 52 \\ 49 & 60 & 55 & 55 \\ 47 & 55 & 53 & 46 \\ 45 & 48 & 51 & 40 \end{array}\right] $$

   Given a $4 \times 4$ image, find the $4 \times 4$ highpass filtered output using the $3 \times 3$ Laplacian filter
$$
h(m, n)=\left[\begin{array}{rrr}
0 & 1 & 0 \\
1 & -4 & 1 \\
0 & 1 & 0
\end{array}\right]
$$
with the borders zero-padded.
$$
x(m, n)=\left[\begin{array}{llll}
45 & 52 & 56 & 52 \\
49 & 60 & 55 & 55 \\
47 & 55 & 53 & 46 \\
45 & 48 & 51 & 40
\end{array}\right]
$$

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Digital Image Processing

Digital Image Processing

D. Sundararajan 1st Edition

Chapter 2, Problem 13

Instant Answer

Step 1

We add a border of zeros around the input image to handle the borders. The zero-padded input image becomes: $$ x(m, n)=\left[\begin{array}{llll} 0 & 0 & 0 & 0 \\ 0 & 45 & 52 & 56 & 52 \\ 0 & 49 & 60 & 55 & 55 \\ 0 & 47 & 55 & 53 & 46 \\ 0 & 45 & 48 & 51 & 40 \\ Show more…

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Given a $4 \times 4$ image, find the $4 \times 4$ highpass filtered output using the $3 \times 3$ Laplacian filter $$ h(m, n)=\left[\begin{array}{rrr} 0 & 1 & 0 \\ 1 & -4 & 1 \\ 0 & 1 & 0 \end{array}\right] $$ with the borders zero-padded. $$ x(m, n)=\left[\begin{array}{llll} 45 & 52 & 56 & 52 \\ 49 & 60 & 55 & 55 \\ 47 & 55 & 53 & 46 \\ 45 & 48 & 51 & 40 \end{array}\right] $$

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