No. 1026 February 2026.
Image processing from first principles
Edges as gradients: finite differences on real images
An edge is where brightness changes fast, so it is a large gradient. I take it from first principles: forward differences for the two partial derivatives, the magnitude, and a threshold at a tenth of the largest value. No library does the maths.
Ix = I(i, j+1) − I(i, j),Iy = I(i+1, j) − I(i, j)
|∇I| = √(Ix² + Iy²), edge where |∇I| ≥ 0.1 max|∇I|
A bamboo specimen under the microscope in the grain-boundary lab, and the same photo through my detector with its own threshold. The specimen’s edge comes through; so does its texture.
what I don’t understand yet
Why the texture comes out as edges. Differences amplify noise, and this version never smooths. A Gaussian blur before differencing, the first step of Canny’s method, is the next version.