🏙️ Image derivative

Continuous

$f^{\prime }(x)={\lim }_{h\to 0}\frac{f(x+h)-f(x)}{h}$

Discrete

• forward difference: ${\Delta }_{x}f(x)=f(x+1)-f(x)$
• central difference: ${\delta }_{x}f(x)=f(x+1)-f(x-1)$
• backwards difference: ${\nabla }_{x}f(x)=f(x)-f(x-1)$

Use cases

• edge detection

📖 Example