Exercise · ZW-2D-CONVOLUTION-ON-IMAGES-002 · ★☆☆ Basic
Which property makes 2D convolution commutative?
Choose one option.
Show answer
- B. Because the sum is reindexed by a change of variable
Explanation
Substituting the index k by m-k in the sum swaps the roles of image and kernel without changing the result. Symmetric kernels are not needed for this.
Review the concept: 2D convolution on images
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
- ZW-2D-CONVOLUTION-ON-IMAGES-001 Which operation combines an image with a kernel by sliding it and summing products?
- ZW-2D-CONVOLUTION-ON-IMAGES-003 In which domain does 2D convolution become a pointwise product?
- ZW-2D-CONVOLUTION-ON-IMAGES-004 Which type of kernel can be implemented in two 1D passes?
- ZW-2D-CONVOLUTION-ON-IMAGES-005 What effect does the 3×3 averaging kernel have on an image?
- ZW-2D-CONVOLUTION-ON-IMAGES-006 If f is a 5×5 image with a 1 at the center and zeros elsewhere, and h is a 3×3 kernel of ones, what…
- ZW-2D-CONVOLUTION-ON-IMAGES-007 A derivative kernel h in x has values -1 on the left and +1 on the right. Using the convolution def…
- ZW-2D-CONVOLUTION-ON-IMAGES-008 What is the result of convolving the single-pixel image δ[m,n] with any kernel h?
- ZW-2D-CONVOLUTION-ON-IMAGES-009 An averaging 3×3 kernel is applied twice in a row. What is the equivalent smoothing effect?
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