Given a 4 ×4 image, find the 4 ×4 median filtered output using the 3 ×3 window with the borders

Step 1: Zero-padding the image We need to zero-pad the image to apply the median filter. The zer

Question

Given a $4 \times 4$ image, find the $4 \times 4$ median filtered output using the $3 \times 3$ window with the borders zero-padded. (i) $$ x(m, n)=\left[\begin{array}{llll} 201 & 195 & 191 & 169 \\ 210 & 201 & 181 & 157 \\ 213 & 207 & 190 & 166 \\ 204 & 204 & 197 & 159 \end{array}\right] $$ (ii) $$ x(m, n)=\left[\begin{array}{llll} 138 & 163 & 162 & 177 \\ 148 & 157 & 167 & 175 \\ 153 & 165 & 160 & 178 \\ 157 & 162 & 164 & 188 \end{array}\right]

   Given a $4 \times 4$ image, find the $4 \times 4$ median filtered output using the $3 \times 3$ window with the borders zero-padded.
(i)
$$
x(m, n)=\left[\begin{array}{llll}
201 & 195 & 191 & 169 \\
210 & 201 & 181 & 157 \\
213 & 207 & 190 & 166 \\
204 & 204 & 197 & 159
\end{array}\right]
$$
(ii)
$$
x(m, n)=\left[\begin{array}{llll}
138 & 163 & 162 & 177 \\
148 & 157 & 167 & 175 \\
153 & 165 & 160 & 178 \\
157 & 162 & 164 & 188
\end{array}\right]

Digital Image Processing

D. Sundararajan 1st Edition

Chapter 2, Problem 19

Instant Answer

Step 1

The zero-padded image will be a $6 \times 6$ matrix. For the first image: $$ x(m, n)=\left[\begin{array}{llllll} 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 201 & 195 & 191 & 169 & 0 \\ 0 & 210 & 201 & 181 & 157 & 0 \\ 0 & 213 & 207 & 190 & 166 & 0 \\ 0 & 204 & 204 & 197 & 159 Show more…

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Given a $4 \times 4$ image, find the $4 \times 4$ median filtered output using the $3 \times 3$ window with the borders zero-padded. (i) $$ x(m, n)=\left[\begin{array}{llll} 201 & 195 & 191 & 169 \\ 210 & 201 & 181 & 157 \\ 213 & 207 & 190 & 166 \\ 204 & 204 & 197 & 159 \end{array}\right] $$ (ii) $$ x(m, n)=\left[\begin{array}{llll} 138 & 163 & 162 & 177 \\ 148 & 157 & 167 & 175 \\ 153 & 165 & 160 & 178 \\ 157 & 162 & 164 & 188 \end{array}\right]

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