Edge Detection

Take two adjacent pixels with values 118 and 121. Neighbours, three brightness levels apart, on a scale that runs to 255. Nothing happened there. Now take two adjacent pixels with values 30 and 210. That is not a gentle slope, it is a cliff, and a cliff in brightness between neighbouring pixels is the entire definition of an edge.

An edge is not a line the camera drew. It is a place where the brightness surface has a steep slope, and steepness is measured pixel to pixel, nowhere else.

The slope itself is called a gradient — at every pixel it has a magnitude (how steep) and a direction (which way brightness is rising fastest). Compute it by comparing each pixel to its right neighbour and its neighbour below, and add up how much they disagree. A flat wall of paint gives you a gradient magnitude near zero at every pixel inside it. The join between wall and doorway gives you a spike.

A gradient magnitude is still just a number, though, and a number is not a yes-or-no answer. The key step in edge detection is one more step: pick a cutoff, and call anything above it an edge. That single decision — a threshold — is what turns a field of slopes into a clean line drawing.

Here it is on a tiny wall with a darker doorway, plus a little sensor noise. Each pixel is compared with its right neighbour and the one below.

import numpy as np # A wall (value 120) with a darker doorway (value 40), plus a little sensor noise.rng = np.random.default_rng(0)image = np.full((6, 9), 120.0)image[1:, 3:6] = 40image += rng.normal(0, 3, image.shape) # Compare each pixel with its right neighbour and with the one below.right = np.abs(np.diff(image, axis=1))[:-1, :]below = np.abs(np.diff(image, axis=0))[:, :-1]slope = right + belowprint(slope.round().astype(int)) threshold = 40   # try 5, then 100print((slope > threshold).astype(int))   # 1 marks an edge

Inside the wall and the doorway the slope stays under 20; along the door frame it jumps past 75. A threshold of 40 keeps just the frame. Drop it to 5 and the noise starts drawing lines of its own.

There is no correct threshold, only a threshold that suits what you are looking for. Set it low and you catch every real edge — and also every camera sensor’s noise, every strand of fabric texture, every visual disagreement between two pixels that happened to land on different sides of a shadow. Set it high and the noise goes away, but so does a faint, real edge: the soft border of a shadow, a low-contrast seam between two similar greys.

Drag the threshold below and watch it happen on a ten-by-ten photo of a house. At the low end the whole outline shows. Somewhere past the middle, the faintest steps in the roofline are the first to disappear — not because they stopped being edges, but because you told the threshold not to count them anymore.

Run this on any photo and you get a drawing made entirely of lines — and nothing else. An edge map has no idea what is on either side of a line. It cannot tell you the shape on the left is a dog. It cannot even tell you the line closes into a shape at all; a gap of a few missing pixels along one edge is enough to turn a closed outline into an open one, and the edge detector has no way to notice.