Question

A one-dimensional normalized kernel $\frac{1}4 [1 \, \,2 \,\,1]$ is convolved with an image to produce an intermediate result. The intermediate image of this operation is again convolved with the same kernel to produce a final result. The equivalent kernel to achieve the same final result in one step from the original image is given as

• A. $\frac1{16} [1\,\, 4 \,\,6 \,\,4\,\, 1]$
• B. $\frac1{16} [1\,\,2\,\,1\,\,2\,\,1]$
• C. $\frac1{8} [1\,\,2\,\,4\,\,2\,\,1]$
• D. $\frac1{8} [1\,\,2\,\,4\,\,2\,\,1]$

Answer 1

Answer: (A)

$\frac1{16} [1\,\, 4 \,\,6 \,\,4\,\, 1]$

Answer 2

The correct answer is (A) : $\frac1{16} [1\,\, 4 \,\,6 \,\,4\,\, 1]$