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 symmetrically 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 symmetrically 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 10

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Step 1

5\). The Gaussian filter is given by the formula: \[ G(x, y) = \frac{1}{2\pi\sigma^2} e^{-\frac{x^2 + y^2}{2\sigma^2}} \] For \(\sigma = 0.5\), calculate the filter values for \(x, y \in \{-1, 0, 1\}\). 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 symmetrically 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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