How does the Sobel operator approximate image gradients for edge detection?
This tests discrete gradient approximation via separable convolution. A strong answer covers 3x3 Gx and Gy kernels as smoothed central differences, then combines magnitude as sqrt(Gx^2 + Gy^2) or L1 norm. A red flag is treating them as arbitrary blur filters.
This tests whether you understand Sobel as a discrete separable gradient estimator, not a magic edge filter. A strong answer separates the 3x3 kernels into derivative and smoothing components: Gx uses [-1 0 1] horizontally and [1 2 1]^T vertically, while Gy reverses them. It explains that convolving these yields partial derivatives Gx and Gy at each pixel, combined into edge magnitude via sqrt(Gx^2 + Gy^2) or the faster L1 norm |Gx| + |Gy|.
Read the original → Wikipedia: Sobel operator
- #computer vision
- #image processing
- #edge detection
- #convolution
- #gradients
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