# Active Contours

In the below link: Active Contour

http://en.wikipedia.org/wiki/Active_contour_model

Internal Energy of the snake is $$E_{internal}=\frac{(\alpha\,\!(s)\left | \mathbf{v}_s(s) \right \vert^2 + \beta\,\!(s)\left | \mathbf{v}_{ss}(s) \right \vert ^2)}{2}$$

Why it is divided by 2 ?

It's not a big deal indeed. Sometimes the $\frac {1}{2}$ term is omitted, thus the membrane term $\alpha$ and thin plate term $\beta$ are halved to achieve the same effect. The core is the trade-off between contracting behavior and sharp bends avoidance, which are reflected with the first and second derivative terms.