A machine doesn’t see objects — it sees where the brightness suddenly CHANGES, and calls those cliffs edges. Slide a tiny 3×3 window across the image, measure the slope of light in x and y, and the outline of a shape falls out of raw pixels. Slide the threshold and watch the edge appear.
The Sobel operator convolves the image with two 3×3 kernels — one estimating the horizontal brightness gradient Gₓ, one the vertical Gᵧ — and the edge strength is √(Gₓ²+Gᵧ²). Pixels above a threshold are edges. A fail-loud self-check builds a clean vertical step image (black|white) and throws unless the Sobel response peaks exactly at the step column — the operator genuinely locating the discontinuity, not guessing.
Sobel is a first-derivative estimate: it fattens edges and is fooled by noise (why Canny adds blur + non-max-suppression + hysteresis). The kernel arithmetic and the step-edge localisation are exact; the disk scene is illustrative.