Derivative kernel

1. What are derivatives in image processing?
2. What is the derivative of a signal?
3. What are derivative filters?
4. What is the derivative of a Gaussian?

What are derivatives in image processing?

Derivative filters provide a quantitative measurement for the rate of change in pixel brightness information present in a digital image.

What is the derivative of a signal?

The first derivative of a signal is the rate of change of y with x, that is, dy/dx, which is interpreted as the slope of the tangent to the signal at each point, as illustrated by the animation on the left (script).

What are derivative filters?

DerivativeFilter is a linear filter that computes the derivatives of data based on a spline interpolation model. Regularization with a Gaussian kernel of standard deviation σ (defaults to 0) can be used to reduce susceptibility to noise.

What is the derivative of a Gaussian?

Mathematically, the derivatives of the Gaussian function can be represented using Hermite functions. For unit variance, the n-th derivative of the Gaussian is the Gaussian function itself multiplied by the n-th Hermite polynomial, up to scale.