### 5.1. Edge-detect introduction

Edge detect filters search for borders between different colors
and so can detect contours of objects.

They are used to make selections and for many artistic purposes.

Most of them are based on gradient calculation methods and give
thick border lines. Look at fig.1 which represents color
intensity variations. On the left is a slow color gradient which
is not a border. On the right is a quick variation which is an
edge. Now, let us calculate the gradient, the variation speed, of
this edge, i.e the first derivative (fig.2). We have to decide
that a border is detected when gradient is more than a threshold
value (the exact border is at top of the curve, but this top
varies according to borders). In most cases, threshold is under
top and border is thick.

The Laplacian edge detection uses the second derivative (fig.3).
The top of the curve is now at zero and clearly identified. That's
why Laplace filter renders a thin border, only a pixel wide. But
this derivative gives several zeros corresponding to small
ripples, resulting in false edges.

Some blurring before applying edge filters is often necessary: it
flattens small ripples in signal and so prevents false edges.