How does filter separability optimize Gaussian blur and its complexity?
This tests if you know a 2D Gaussian separates into two 1D convolutions. A strong answer gives complexity as O(N^2 K^2) dropping to O(N^2 K) for an N-by-N image and K-by-K kernel. A red flag is claiming all kernels are separable or omitting dimensions.
This tests deep familiarity with linear algebra in image processing, specifically that a 2D Gaussian kernel equals the outer product of two 1D Gaussian vectors. A strong answer describes replacing one K-by-K convolution with a horizontal 1D pass followed by a vertical 1D pass, reducing per-pixel operations from O(K^2) to O(2K). It must state overall complexity as O(N^2 K^2) down to O(N^2 K) for an N-by-N image. A red flag is asserting that arbitrary kernels are separable, confusing the Gaussian's special structure with a general property.
Read the original → Wikipedia: Gaussian blur
- #computer-vision
- #image-processing
- #algorithms
- #linear-algebra
- #complexity-analysis
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