Edge detection using derivatives

1. How derivatives are used for edge detection?
2. How first order and second order derivative helps in edge detection?
3. How can we use derivatives in image processing?

How derivatives are used for edge detection?

In this method we take the 1st derivative of the intensity value across the image and find points where the derivative is maximum then the edge could be located. The gradient is a vector, whose components measure how rapid pixel value are changing with distance in the x and y direction.

How first order and second order derivative helps in edge detection?

The first-order derivatives are good to select the stongest edges by (hysteresis-)thresholding the gradient magnitude. The zero-crossings of the second-order derivatives are good for localization of the edge.

How can we use derivatives in image processing?

When a derivative filter is applied to a digital image, the resulting information about brightness change rates can be used to enhance contrast, detect edges and boundaries, and to measure feature orientation.