Exercise · ZW-2D-CONVOLUTION-ON-IMAGES-009 · ★★☆ Intermediate
An averaging \(3\times3\) kernel is applied twice in a row. What is the equivalent smoothing effect?
Choose one option.
A Edge detection B A shift of the image C Stronger smoothing, equivalent to convolving the kernel with itself D No effect, since they cancel Show answer C. Stronger smoothing, equivalent to convolving the kernel with itself← Back to the question
Explanation Applying a filter twice is equivalent to convolving it with itself, which increases smoothing. Cancelling does not happen with low-pass filters.
2D convolution is the operation that combines an image \(f(x,y)\) with a kernel \(h(x,y)\) by sliding the kernel and summing products at each position.
\[(f*h)[m,n]=\sum_{k}\sum_{l} f[k,l]\,h[m-k,n-l]\]
More practice problems: 2d convolution on images