Question

Given a $4 \times 4$ image, find the $4 \times 4$ lowpass filtered output using the $3 \times 3$ Gaussian filter ( $\sigma=0.5$ ) with the borders periodically extended. $$ x(m, n)=\left[\begin{array}{llll} 202 & 195 & 192 & 191 \\ 216 & 211 & 200 & 209 \\ 224 & 212 & 215 & 227 \\ 224 & 205 & 227 & 230 \end{array}\right] $$

   Given a $4 \times 4$ image, find the $4 \times 4$ lowpass filtered output using the $3 \times 3$ Gaussian filter ( $\sigma=0.5$ ) with the borders periodically extended.
$$
x(m, n)=\left[\begin{array}{llll}
202 & 195 & 192 & 191 \\
216 & 211 & 200 & 209 \\
224 & 212 & 215 & 227 \\
224 & 205 & 227 & 230
\end{array}\right]
$$

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Digital Image Processing

Digital Image Processing

D. Sundararajan 1st Edition

Chapter 2, Problem 11

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Step 1

This means we replicate the values of the image to create a larger extended image. For a $4 \times 4$ image, the extended image becomes an $6 \times 6$ image as follows: $$ x_{\text{extended}}=\left[\begin{array}{llllll} 202 & 195 & 192 & 191 & 202 & 195 \\ 216 & Show more…

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Given a $4 \times 4$ image, find the $4 \times 4$ lowpass filtered output using the $3 \times 3$ Gaussian filter ( $\sigma=0.5$ ) with the borders periodically extended. $$ x(m, n)=\left[\begin{array}{llll} 202 & 195 & 192 & 191 \\ 216 & 211 & 200 & 209 \\ 224 & 212 & 215 & 227 \\ 224 & 205 & 227 & 230 \end{array}\right] $$

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